Theoretical Advances and Applications of Fuzzy Logic and Soft Computing

The task of finding shortest paths in graphs has been studied intensively over the past five decades. Shortest paths are one of the simplest and most widely used concepts in networks. More recently, fuzzy graphs, along with generalizations of algorithms for finding optimal paths within them, have emerged as an adequate modeling tool for imprecise systems. Fuzzy shortest paths also have a variety of applications. In this paper, the authors present a model based on dynamic programming to find the shortest paths in intuitionistic fuzzy graphs.

Traditional data repositories are typically focused on the storage and querying of crisp-precise domains of data. As a result, current commercial data repositories have no facilities for either storing or querying imprecise-approximate data. However, when considering scientific data (i.e. medical data, sensor data etc) value uncertainty is inherited to scientific measurements. In this paper we revise the context of “value uncertainty”, and examine common models related to value uncertainty as part of the OLAP model. We present our approach for extending the OLAP model to include treatment of value uncertainty as part of a multidimensional model inhabited by flexible date and non-rigid hierarchical structures of organisation.

In this work we are analyzing our ability to discover knowledge from multi-valued attributes (often referred in literature on fuzzy databases as collections [1-3]), that have been utilized in fuzzy relational database models [4-7] as a convenient way to represent uncertainty about the data recorded in the data tables. We present here implementation details and extended tests of a heuristic algorithm, which we used in the past [8-11] to interpret non-atomic values stored in fuzzy relational databases. In our evaluation we consider different data imprecision levels, as well as diverse shapes of fuzzy similarity hierarchies.

A model for representing and evaluating flexible Location-Based Spatial Queries (LBSQ) is proposed. In a LBSQ the selection condition is generally a constraint on the distance of the objects in the database (instances) from the user location. Such queries are becoming more and more useful in location-based services such as those provided by cell-phones, Wireless LAN and GPS technologies. However their usefulness is limited by the inability of current systems to represent and manage the imprecision often characterizing the knowledge of the user’s and instances’ locations. In this contribution we propose a fuzzy model of flexible LBSQs in which either the user location, or the instances locations or the selection condition itself or even all of them are imprecise. To define a unifying approach in all cases of imprecision we generalize the notion of the Minkowski sum within fuzzy sets and apply it to combine the (imprecise) user location with the (soft) query condition. This way we derive the actual soft constraint with respect to the user’s location. The instances relevant to the query are those whose locations are included in the actual soft constraint representation to some extent.

This paper is devoted to the evaluation of quantified statements in the context of flexible querying of relational databases. Two types of quantified statements can be distinguished and the most sophisticated one (of type “

Q

B

X are

A

”) is considered in this paper. The contribution is to propose a new theoretical background for their evaluation (using an arithmetic on gradual numbers (ℕ

f

, ℤ

f

, ℚ

f

)).

The goal of this paper is to investigate fundamental properties of local andness/orness. We analyze the distribution of local andness/orness in the unit hypercube from the standpoint of usability of these indicators in decision models.

The main objective of an information retrieval system is to be effective in providing a user with relevant information in response to a query. However, especially given the information explosion which has created an enormous volume of information, efficiency issues cannot be ignored. Thus, to be able to quickly process lists of documents that have the keywords stated in a given query assigned/indexed to them by merging via the Boolean logic of the query is essential in a Boolean query system. A new algorithm, based loosely on concurrent codes, is developed and discussed.

The performance of Information Retrieval Systems (IRSs) is usually measured using two different criteria, precision and recall. In such a way, the problem of tuning an IRS may be considered as a multi-objective optimization problem. In this contribution, we focus on the automatic learning of Boolean queries in IRSs by means of multi-objective evolutionary techniques. We present a comparative study of four multi-objective evolutionary optimization techniques of general-purpose (NSGA-II, SPEA2 and two MOGLS) to learn Boolean queries.

Search keywords can be considered as decision criteria (goals), whereas the documents contained in the original result list of a search engine can be considered as decision alternatives in the sense of adequate search results. The paper shows how a decision making model based on interactions between decision goals can be used for re-ranking of the search results obtained by classical search engines. The decision making model was previously applied to real world problems in production optimization and business process management. In contrast to other approaches, the interactive structure of decision goals for each decision situation is calculated explicitly based on fuzzy types of interaction. In this paper, after a brief description of the model an application to the calculation of context depending re-rankings of search results of internet search engines is presented. It is shown that keywords of search queries can be understood as decision goals and that the decision making model can be successfully applied for context dependent re-ranking of the search results. Using the model, popularity based rankings can be re-ranked making use of context dependent information derived from the query keywords.

This paper provides an investigation of the potential application of fuzzy logic to semantic music recommendation. We show that a set of affective/emotive, structural and kinaesthetic descriptors can be used to formulate a query which allows the retrieval of intended music. A semantic music recommendation system was built, based on an elaborate study of potential users of music information retrieval systems. In this study analysis was made of the descriptors that best characterize the user’s understanding of music. Significant relationships between expressive and structural descriptions of music were found. A straightforward fuzzy logic methodology was then applied to handle the quality ratings associated with the descriptions. Rigorous real-world testing of the semantic music recommendation system revealed high user satisfaction.

In philosophy of science we find two epistemological traditions: rationalism and empiricism. Rationalists believe that the criterion of knowledge is not sensory but intellectual and deductive whereas from the empiricist point of view the source of our knowledge is sense experience. Bridging this gap between these theories of knowledge has been a problem in philosophical approaches, both past and present. This philosophical paper focuses on using fuzzy sets and systems (FSS), computing with words (CW), and the computational theory of perceptions (CTP) as methodologies to help bridge the gap between systems and phenomena in the real world and scientific theories. It presents a proposal in which fuzzy methods are used to extend the so-called structuralist view of scientific theories in order to rep resent the relation of empiricism and theoretical structures in science.

An Ontological and Epistemological foundation of Fuzzy Set and Logic Theory is reviewed in comparison to Classical Set and Logic Theory. It is shown that basic equivalences of classical theory breakdown but are re-established as weak equivalences as a containment relation in fuzzy theory. It is also stressed that the law of conservation of information is still upheld within fuzzy theory.

Soft computing modeling of business planning is considered. Our ultimate aim is to provide new proactive and innovative resolutions for designing a soft computing simulation tool for learning business planning. In our Learning Business Plan Project we have established a theory on business planning which assumes that we should replace the traditional business planning with a more creative approach and thus we should focus more on invention and development of business ideas. We have designed a model of five stages according to our theory, and we apply soft computing and cognitive maps for our model simulations. In simulation we particularly apply linguistic cognitive maps which seem more versatile than the corresponding numerical maps. Two modeling examples are also provided.

The aim of this article is to introduce a novel way to illustrate human-like reasoning by using a pictorial language and fuzzy sets. We follow the newest developments on soft computing, but approach the perceptions from a different point of view. We introduce a pictorial language to define human-like multi-domain reasoning. We start to further develop an existing simple pictorial language Bliss and increase its expressive power by fuzzy sets and by presenting several sentences in a graph. These extra sentences are used to show the right use (meaning) of a concept in the reasoning. Several examples of the approach are provided.

Semantic image retrieval basically can be viewed as a pattern recognition problem. For human, pattern recognition is inherent in herself/himself by the inference rules through a long time experience. However, for computer, on the one hand, the simulated human identification of objects is impressive at its experience (training) like a baby learns to identify objects; on the other hand, the precise identification is unreasonable because the similar features are usually shared by different objects, e.g., “an white animal like cat and dog”, “a structural transportation like car and truck”. In traditional approaches, disambiguate the images by eliminating irrelevant semantics does not fit in with human behavior. Accordingly, the ambiguous concepts of each image estimated throughout the collaboration of similarity function and membership function is sensible. To this end, in this paper, we propose a novel fuzzy matching technique named

Fuzzy Content-Based Image Retrieval (FCBIR)

that primarily contains three characteristics: 1) conceptualize image automatically, 2) identify image roughly, and 3) retrieve image efficiently. Out of human perspective, experiments reveal that our proposed approach can bring out good results effectively and efficiently in terms of image retrieval.

The theory of “computing with words” offers mathematical tools to formally represent and reason with perceptive information, which are delivered in natural language text by imprecisely defined terms, concepts classes and chains of thinking and reasoning. It thus provides relevant methods for understand-based text summarization systems. In this paper we propose a framework for text summarization and examine the possibilities as well as challenges in using the concepts and methods of CW in text summarization.

In this paper, we go beyond the traditional web search engines that are based on keyword search and the Semantic Web which provides a common framework that allows data to be shared and reused across application,. For this reason, our view is that “Before one can use the power of web search the relevant information has to be mined through the concept-based search mechanism and logical reasoning with capability to Q&A representation rather than simple keyword search”. In this paper, we will focus on development of a framework for reasoning and deduction in the web. A new web search model will be presented. One of the main core ideas that we will use to extend our technique is to change terms-documents-concepts (TDC) matrix into a rule-based and graph-based representation. This will allow us to evolve the traditional search engine (keyword-based search) into a concept-based search and then into Q&A model. Given TDC, we will transform each document into a rule-based model including it’s equivalent graph model. Once the TDC matrix has been transformed into maximally compact concept based on graph representation and rules based on possibilistic relational universal fuzzy–type II (pertaining to composition), one can use Z(n)-compact algorithm and transform the TDC into a decision-tree and hierarchical graph that will represents a Q&A model. Finally, the concept of semantic equivalence and semantic entailment based on possibilistic relational universal fuzzy will be used as a basis for question-answering (Q&A) and inference from fuzzy premises. This will provide a foundation for approximate reasoning, language for representation of imprecise knowledge, a meaning representation language for natural languages, precisiation of fuzzy propositions expressed in a natural language, and as a tool for Precisiated Natural Language (PNL) and precisation of meaning. The maximally compact documents based on Z(n)-compact algorithm and possibilistic relational universal fuzzy–type II will be used to cluster the documents based on concept-based query-based search criteria.

A new model for document clustering is proposed in order to manage with conceptual aspects. To measure the presence degree of a concept in a document (or even in a document collection), a concept frequency formula is introduced. This formula is based on new fuzzy formulas to calculate the synonymy and polysemy degrees between terms. To solve the several shortcomings of classical clustering algorithm a soft approach to hybrid model is proposed. The clustering procedure is implemented by two connected and tailored algorithms with the aim to build a fuzzy-hierarchical structure. A fuzzy hierarchical clustering algorithm is used to determine an initial clustering and the process is completed using an improved soft clustering algorithm. Experiments show that using this model, clustering tends to perform better than the classical approach.

In this paper, we introduce a new type of computation called “

Morphic Computing

”.

Morphic Computing

is based on

Field Theory

and more specifically

Morphic Field

s.

Morphic Fields

were first introduced by Rupert Sheldrake [1981] from his hypothesis of formative causation that made use of the older notion of

Morphogenetic Fields

. In this paper, we introduce the basis for this new computing paradigm.

Morphic Computing

is based on

Field Theory

and more specifically

Morphic Field

s. In this paper, we introduce extensions of Morphic Computing to non classical fields and logic.

Morphic Computing

change or compute non physical conceptual fields. One example is in representing the semantics of words. In this paper, application to the field of computation by words as an example of the

Morphic Computing, Morphic Fields - concepts and Web search, and agents and fuzzy in Morphic Computing will be discussed.

In the paper we propose a very simple method for the analysis of dependencies between consecutive observations of a short time series when individual observations are imprecise (fuzzy). For this purpose we propose to apply a fuzzy version of the Kendall’s

τ

statistic. The proposed methodology can be used for the analysis of a short series of opinion polls when answers of individual respondents are presented in an imprecise (fuzzy) form.

In this paper, several aspects of perception based time series data mining based on the methodology of computing with words and perceptions are discusses. First, we consider possible approaches to precisiate perception based patterns in time series data bases and types of fuzzy constraints used in such precisiation. Next, several types of associations in time series data bases and the possible approaches to convert these associations in generalized constraint rules are discussed. Finally, we summarize the methods of translation of expert knowledge and retranslation of solutions.

Methods of Perception-based Data Mining (Data Miners DM) for fuzzy relational data servers are considered in the article. The considering problems of DM are limited by problems of clustering and mining of dependences in the form of fuzzy rules because these problems are especially important in practice. The hybrid algorithm of fuzzy clustering and the way of use of a fuzzy inference system as a DM for fuzzy relational data is offered in the article.

The article deals with simulation of the distributed technological complexes. Visual simulation structure of manufacture is offered. On base of visual model the simulation model is formed automatically. The simulation model is described by means of the mathematical apparatus of Multitask Presence Logic (MAL). The basic concepts of MAL and some of examples of their application for construction of manufacture model are given. The knowledge base structure is designed on the basis of frame models for problems of decision-making support. The application of frame models allows to change structure base of knowledge directly during of simulation. The knowledge base is designed for use of linguistic variables and, accordingly, a linguistic data input/output.

Similarity and distance are matters of degree for which we can find crisp and fuzzy concepts in the history of mathematics. In this paper we present Lotfi Zadeh’s and Karl Menger’s crisp concepts before the time of fuzzy sets. Finally we show an application in medical philosophy by Kazem Sadegh-Zadeh that extends into new theoretical research in the field of modern genetics.

The concepts of the Choquet and Sugeno integrals, based on a fuzzy measure, can be adopted as useful tools in estimation of the total effectiveness of a drug when appreciating its positive influence on a collection of symptoms typical of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting the words at first to fuzzy sets and then numbers we can regard the effectiveness structures as measures in the Choquet and Sugeno problem formulations. After comparing the quantities of total effectiveness among medicines, expressed as the values of the Choquet or Sugeno integrals, we accomplish the selection of the most efficacious drug.

Medical informatics has changed tremendously over the past few decades, and changes in the approach to uncertainty are probably the most important advances in this field. The envisioned role of computer programs in health care is perhaps the most important. Uncertainty is the central, critical fact about medical reasoning. Particularly in an intensive care environment, where decisions must often be made quickly, or that physicians will follow it rather than openly or surreptitiously limiting care on their own.

This paper surveys the utilization of fuzzy logic on the basis of two medical applications. The first, an intelligent on-line monitoring program for the intensive care data of patients with Acute Respiratory Distress Syndrome (ARDS), so called FuzzyARDS which is using the concept of fuzzy automata, and the second is a fuzzy knowledge-based control system, FuzzyKBWean, which was established as a real-time application based on the use of a Patient Data Management System (PDMS) in an intensive care unit (ICU). These complex systems confirm that fuzzy logic is quite suitable for medical application in a per definition uncertainty environment as an ICU, because of its tolerance to some imprecision.

This paper presents a monitoring methodology to identify complex systems faults. This methodology combines the production of meaningful error signals (residuals) obtained by comparison between the model outputs and the system outputs, with a posterior fuzzy classification. In a first off-line phase (learning) the classification method characterises each fault. In the recognition phase, the classification method identifies the faults. The chose classification method permits to characterize faults non included in the learning data. This monitoring process avoids the problem of defining thresholds for faults isolation. The residuals analysis and not the system variables themselves, permit us to separate fault recognition from system operation point influence. The paper describes the proposed methodology using a benchmark of a two interconnected tanks system.

The optimization methodology proposed in this work is inspired to [1] and is named Possibilistic Worst-Case Distance (PWCD). This scheme has been tested on an application related to the MOS device sizing of a two stage Operational Transconductance Amplifier circuit (OTA) [2]. In order to model the uncertainties arising from circuit parameter simulations the fuzzy set theory, introduced by Zadeh [3], has been used. A linearization of the circuit performances as function of circuit parameters has been fitted as suitable approximation in a finite range, this choice was suggested to reduce the computational cost related to simulations of the real design. By means of linearization the circuit performances were fuzzyfied and a possibility measure of performance failure was minimized. The proposed case study will show that the possibilistic approach to the worst case analysis, even though less accurate for indirect yield estimation with respect to the probabilistic one, can identify an optimal design in yield terms. Furthermore the possibilistic methodology allows to develop calculation without any statistical hypothesis or sensitive analysis.

The paper presents an algorithm to solve two-person nonzero-sum fuzzy games using decomposition of a bilinear programming model into a series of linear programming models. Despite considerable research and advances in the area, most computational algorithms developed require solution of nonlinear optimization models. The approach discussed here provides a mechanism to translate the original fuzzy model into a family of its (-cut equivalents and a decomposition scheme to split them in linear models. A simple example is given to illustrate the algorithm.

In this paper, a new possibilistic decision approach for one-shot decision problem is proposed where two focus points, called active focus point and passive focus point are introduced for balancing satisfaction and plausibility to show which state of nature should be considered for making decision with possibilistic information. Based on the proposed one-shot decision approach, real estate investment problem is analyzed, that is, whether the landowner should construct a house at the present time for sale in the future considering the uncertainty of house price. Uncertainty of house price is characterized by the possibility distribution to reflect the potential of how much the house price being in the future, which is a kind of likelihood to show the similarity between the situation of housing market in the future and in the past time. The proposed model provides insights into individual investment behavior of urban land development in the real world and shows that possibilistic decision analysis based on active and passive focus points is reasonable for such one-shot decision problems, which extensively exist in business and economic society.

In this paper, we propose the solution method about the multiobjective portfolio selection problem, particularly the scenario model to include the ambiguous factors and chance constraints. Generally, mathematical programming problems with probabilities and possibilities are called to stochastic programming problem and fuzzy programming problem, and it is difficult to find its global optimal solution. In this paper, we manage to develop the efficient solution method to find its global optimal solution of such a problem introducing the some subproblems.

For calculating a solution of a linear program where coefficients of the objective function(s) may be fuzzy, we have to explain how the optimization of a fuzzy objective can be interpreted. In the literature of fuzzy linear programming, a lot of procedures for substituting fuzzy objectives by crisp ones are proposed. In this paper, a critical survey of these different methods is given.

Lattice implication algebra is a logical algebraic system which is constructed by combining lattice with implication algebra. In this paper, we focus on the extension of LI-ideal of lattice implication algebras, i.e., weak LI-ideals (briefly, WLI-ideals) and maximal weak LI-ideals. The properties of weak LI-ideals are studied and several characterizations of weak LI-ideals are given. Finally, we study the relationships among WLI-ideals, LI-ideals and Lattice ideals.

Two equivalent conditions for LI-ideals are given. The lattice implication quotient algebras induced by obstinate filters and LI-ideals are studied, that is, the lattice implication quotient algebras

L

/

F

induced by obstinate filters is {[0]

F

, [1]

F

}. It is also concluded that there is a bijection between

L

(

L

,

A

) = {

J

:

A

 ⊆ 

J

 ⊆ 

L

,

J

is a LI − ideal if

L

} and the LI-ideals of

L

/

F

(the lattice implication quotient algebras induced by LI-ideal

A

).

In the present paper, the weak completeness of

a

-resolution principle for a lattice-valued logic (L

n

×L

2

)P(X) with truth value in a logical algebra ( lattice implication algebra L

n

×L

2

, is established. Accordingly, the weak completeness of (Exactly, True)-resolution principle for a linguistic truth-valued propositional logic ℓ based on the linguistic truth-valued lattice implication algebra L-LIA is derived.

In this paper, we develop a decision-based questionnaire system. Toward this end, we use evolutionary computation techniques. Initially, we work on a first order aggregation model and performed its learning using genetic algorithms, in which these preferences will be represented by a weighting vector associated with the variables involved in the aggregation process. In this model tree nodes represent aggregators, terminals or leaves correspond to variables, and weight values are added to the children branches for each aggregator. The parameters characterizing this multi-aggregation model are aggregators, weights and their combination in form of a tree structure. In this case, the learning process has to find the optimal combination of these parameters based on training data. In this learning process, the evolution principle remains the same as in a conventional GP but the DNA encoding needs to be defined according to the considered problem

As data is getting more complex and complicated, it is increasingly difficult to construct an effective complex decision model. Two very obvious examples where such a need emerges are in the economic and the medical fields. This paper presents the fuzzy signature and cognitive modeling approach which could improve such decision models. Fuzzy signatures are introduced to handle complex structured data and problems with interdependent features. A fuzzy signature can also be used in cases where data is missing. The proposed fuzzy signature structure will be used in problems that fall into this category. This paper also investigates a novel cognitive model to extend the usage of fuzzy signatures. This Fuzzy Cognitive Signature Modelling will enhance the usability of fuzzy theory in modelling complex systems as well as facilitating complex decision making process based on ill structured information or data.

This paper describes results concerning the capability of supervised machine learning techniques to predict production potential for a single formation, prior to drilling, over a 16,000 square mile area of SE New Mexico. In this paper a neural network is used to predict production potential for a single formation of SE New Mexico region. The process involved gathering data for use as potential inputs, collecting production data at known wells, selecting optimal inputs, developing and testing various network architectures, making predictions, analyzing and applying the results. This predicted production was further refined by excluding production at locations where the Woodford shale was not present. Results were evaluated by inspecting a map of predicted production and performing statistical testing, including a correlation of predicted and actual production, which produced a correlation coefficient of 0.79. The results were then used by the Devonian FEE Tool, an expert system designed to reduce exploration risk.

Reservoir characterization plays a crucial role in modern reservoir management. It helps to make sound reservoir decisions and improves the asset value of the oil and gas companies. It maximizes integration of multi-disciplinary data and knowledge and improves the reliability of the reservoir predictions. The ultimate product is a reservoir model with realistic tolerance for imprecision and uncertainty. Soft computing aims to exploit such a tolerance for solving practical problems. In reservoir characterization, these intelligent techniques can be used for uncertainty analysis, risk assessment, data fusion and data mining which are applicable to feature extraction from seismic attributes, well logging, reservoir mapping and engineering. The main goal is to integrate soft data such as geological data with hard data such as 3D seismic and production data to build a reservoir and stratigraphic model. While some individual methodologies (esp. neurocomputing) have gained much popularity during the past few years, the true benefit of soft computing lies on the integration of its constituent methodologies rather than use in isolation.

This work presents a methodology for characterization of human reliability based on fuzzy sets concepts, aiming at reducing the possibility of human errors in oil refineries. It is suited for operation, maintenance and inspection activities in oil production and distribution units and is based on the API-770 guide for reduction of human errors, which identifies 64 performance factors. In order to assess the possibility of a human fault, the model analyses the elements that interact with each operator. It is possible, by this methodology, to obtain a human reliability index, to find out the problems that may constitute causes of human errors and to devise strategies for the control of potentially adverse impacts of interactions that add uncertainty and complexity to processes.

This work presents a new decision support system for intelligent wells control considering technical uncertainties. The intelligent control of valves operation tends to become a competitive advantage for reservoirs development. Such control refers to the opening and shutting of the valves that distinguish the intelligent wells. The strategy consists in identifying a valve configuration that maximizes the net present value. The developed system uses Genetic Algorithms, reservoir simulation, Monte Carlo simulation, techniques of sampling variance reduction and uncertainties representation by probability distribution and geologic sceneries. The theoretical concepts applied and the implementation of a system capable of supporting, managing and developing the intelligent fields, constitute an advance to petroleum exploration area. The obtained results demonstrate that the approach given to the problem and the used methodologies deal with the control valves in an efficient and practical way.

This paper is a result of the application of soft computing technologies to solve the pick up and delivery problem (PDP). In this paper, we consider a practical PDP that is frequently encountered in the real-world logistics operations, such as Helicopter Offshore Crew Transportation of Oil & Gas Company. We consider a typical scenario of relatively large number of participants, about 70 persons and 5 helicopters. Logistics planning turns to be a combinatorial problem, and that makes it very difficult to find reasonable solutions within a short computational time. We present an algorithm based on two optimization techniques, genetic algorithms and heuristic optimization. Our solution is tested on an example with a known optimal solution, and on actual data provided by PEMEX, Mexican Oil Company. Currently, the algorithm is implemented as part of the system for simulation and optimization of offshore logistics called SMART-Logistics and it is at a field-testing phase.

A decision to invest in the development of an oil reserve requires an in-depth analysis of several uncertainty factors. Such uncertainties may involve either technical uncertainties related to the size and economic quality of the reserve, or market uncertainties. When a great number of alternatives or options of investment are involved, the task of selecting the best alternative or a decision rule is very important and complex due to the considerable number of possibilities and parameters that must be taken into account. This paper proposes a new model, based on Real Option Theory, Genetic Algorithms and on Monte Carlo simulation to find an optimal decision rule for alternatives of investment regarding the development of an oil field under market uncertainty that may help decision-making in the following situation: immediate development of a field or wait until market conditions are more favorable. This optimal decision rule is formed by three mutually exclusive alternatives, which describe three exercise regions through time, up to the expiration of the concession of the field. The Monte Carlo simulation is employed within the genetic algorithm to simulate the possible paths of oil prices up to the expiration date. The Geometric Brownian Motion is assumed as stochastic process for represents the oil price. A technique of variance reduction was also used to improve the computational efficiency of the Monte Carlo simulation.

Depositional and post-depositional (diagenetic) processes control the distribution of porosity and permeability within petroleum reservoir rocks. The understanding of these controls is essential for the construction of models for the systematic characterization and prediction of the quality (porosity, permeability) of petroleum reservoirs during their exploration and production. The description and documentation of key petrographic features is an important tool for the evaluation of reservoir quality that try to minimize the uncertainty associated to visual recognition of the features. This paper describes the role of visual controls on the petrographic analysis of reservoir rocks, and presents a knowledge-based tool that supports a workflow for the collection and documentation of visual information. This tool allows the spatial referencing of significant features in thin sections of reservoir rocks and the association of these features to a complete ontology of description. The whole process allows the preservation of original information that would support reservoir evaluation and guarantees further analysis even when the original rock sample is not available.

The inference of temporal information from past event occurrences is relevant in several applications for geological domains. In such applications, the order in which events have happened is imprinted in the domain as visual-spatial relations among its elements. The interpretation of the relative ordering in which events have occurred is essential for understanding the geological evolution in different scales of observation and for various kinds of objects, as in Petrology and Geological Modelling. From the analysis of the cognitive abilities of experts in these domains we propose an ontology for event ordering reasoning within domains whose elements have been modified by past events. We show that the

Event Ontology

can work as a pattern for domain conceptualization to be applied in distinct domains. It can be used to specify the sequence order of diagenetic paragenesis. It can also be operative for automatic reconstruction of geological surface assemblages.

Disruption on a supply chain provokes lost that can be minimized through an alternative solution. This solution involves a strategy to manage the impact of the disruption and thus to recuperate the supply chain. Difficulty of this management is the diversity of factors such that becomes complex to provide or choice a solution among the possible ones. Depending on the objective(s) to optimize are the strategy to follow and the solution to choice. In this work the Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization NSGA-II is used as the strategy to generate and optimize (minimize) solutions (lost) in front of a disruption. The included objectives are cost, risk and the place of facilities supporting the supply chain recuperation. These objectives are combined to generate possible solutions and to choice one such that it provides a proposal to minimize the disruption impact on a delimited period of time. Advantage of NSGA-II utilization is the provision of a practical formal and computational tool to analyze different scenarios without simplifies the complexity of a standard real supply chain. The illustrative exercise presents recovery scenarios for a crude oil refinery supply chain.

In many applications fields, we can obtain benefits from analyzing large distributed data sets by using the high performance computational power. The Grid provides an unrivalled technology for large scale distributed computing as it enables collaboration over the global and the use of distributed computing resources, while also facilitating access to geographically distributed data sets. In this paper, we present a framework for high performance DDM applications in Computational Grid environments called DMGrid, which is based on Grid mechanisms and implemented on top of the Globus 4.0 toolkit.

Bucket sort algorithm is an effective approach to sort very large files, whereas the probability of bucket overflow hinders its efficiency. The paper puts forward a more effective bucket sort algorithm, THShort2, which subtly handles the overflowed buckets. For a different degree of bucket overflow, we propose a corresponding processing scheme. The correctness and efficiency of THShort2 is proofed theoretically. The experiment results show that the performance of THSort2 is about triple times of NTSort, and 50% faster than THSort.

Fractal image coding is a novel technique for still image compression. Compared with the distance between the range block and the matching domain block, setting of the initial threshold value is one of the most difficult problems in Fisher Quadtree-based fractal image coding. In this paper, a novel fractal image coding based on Quadtree partition of the adaptive threshold value is proposed. Considering the input image feature fully, we put forward the computation derivation process of the adaptive threshold value progressively and declare that the adaptive threshold value has the direct proportion with the variance of the current range block. Experimental results show that compared with Fisher Quadtree-based fractal coding for the same image, the proposed coding scheme obtains better performance including the improved quality of the decoded image, shorter compression time and higher compression ratio.

The paper explores some crucial technologies of Distributed Database in University MIS, such as the distribution and replication of data, and studies its feasibility on the basis of campus networks.

For graphs of various local complex degrees, this paper will investigate their fitting approach and conduct experiments by using the mixture processing method which is a combination of the Box dimension’s pretreatment with self-affine fractal interpolation function (AFIF).

Spam is in spate, which accounts for over 60 percent of all emails in the world recently. Researchers are trying to develop ways to fight it but few are effective. The paper put forward a new filtering scheme based on grid technology and statistical method, which regards the user computers and email servers as nodes of the grid. They contribute and consume statistics information on the grid platform. If the number of copies of an email is obviously err from normal value, to flag it as a spam then can be a reasonable operation. As more and more nodes join the platform, the filtering precision can be further improved, just as the simulation study shows.

With the rapid growth of web services on the Internet, users are experiencing access delays more often than ever. Recent studies showed that web prefetching could alleviate the WWW latency to a larger extent than the traditional caching. Web prefetching is one of the most popular strategies in web mining research domain, which are proposed for reducing the perceived access delay, improving the service quality of web site and mining the user requirement information in advance. In this paper, we introduce the features of the web site model named web ontology, and build a web prefetching agent-WebAGENT based on the web ontology and the hidden Markov model. With the agent, we analyze the user access path and how to mine the latent information requirement concepts, then we could make semantic-based prefetching decisions. Experimental results show that the web prefetching scheme of the WebAGENT has better predictive mining effect and prefetching precision.

Probability and possibility are both convenient scales of uncertainty, because they are defined by a distribution function. They also have complementary properties in the sense that probability is a quantitative and objective ratio scale, while possibility is a qualitative and subjective ordinal scale. The paper discusses probabilistic and possibilistic causal models with a time-series effect from the viewpoint of Evidence theory, and shows that they can be defined by a single equation with different conditions of focal elements using the basic probability assignments. The equation could be recognized as a causal model with a general representation of uncertainty in the form of Evidence theory. The paper finalizes the discussion with the properties of the generalized uncertain causal model.

Systems of linear equations with elements being affine linear functions of fuzzy parameters are relevant to many practical problems. A method for solving such systems is proposed. It consists of two steps. First a finite number of parametric interval linear systems is solved using the direct method. Then membership functions of fuzzy solution elements are interpolated. Parameters are modeled by arbitrary fuzzy numbers with convex membership function and compact support. Conditions for existence of the fuzzy solution are given. The performance of the proposed method is presented using an illustrative example of truss structure.

The proposition about generalization of the existence of the residuum for left continuous uninorm

U

on a commutative, residuated

l

-monoid, with a neutral element is proved. The question raised previously was whether there are general operation groups which satisfy the residuum-based approximate reasoning, but at the same time are easily comprehensible and acceptable to application-oriented experts. The basic backgrounds of this research are the distance-based operators.

We introduce an alternative method to approach the addition of discrete fuzzy numbers when the application of the Zadeh’s extension principle does not obtain a convex membership function.

In this paper, two new notions called core-concept and core-concept lattice are proposed and applied to collaborative recommendation system. The core-concept lattice is constructed based on the core-concept, which is extracted from rating matrix between users and items in collaborative recommendation systems. Compared with traditional FCA, it is obviously that the extraction of core-concept very easy and fast. We present the improved nearest neighbors algorithm, it use core-concept lattice as an index to the recommendation’s ratings matrix. The improved nearest neighbors algorithm could remarkably accelerate finding the nearest neighbors. Therefore, it could evidently improve efficiency of recommendation.

In this paper, we present a sufficient and necessary condition to decide whether a weakly implicative logic has the proof by cases property (PCP for short). This result gives a general method for constructing a weakly implicative fuzzy logic from any given weakly implicative logic.

Fuzzy quantifiers have important applications in a great variety of fields such as database querying, data mining and knowledge discovering, inductive learning and so on. Recently, M.S.Ying introduces a novel fuzzy framework for linguistic quantifiers which are modeled by Sugeno integrals. Essentially, the conjunction and disjunction in Ying’s framework are interpreted as the “min” and “max” operations, which restricts the application of this theory in some sense. In this paper, we extended Ying’s framework by interpreting the conjunction and disjunction as t-norm and t-conorm respectively. And some elegant logical results for our framework have been obtained.

Classical decision-theoretic planning methods assume that the probabilistic model of the domain is always accurate. We present two algorithms rLAO* and qLAO* in this paper. rLAO* and qLAO* can solve uncertainty Markov decision problems and qualitative Markov decision problems respectively. We prove that given an admissible heuristic function, both rLAO* and qLAO* can find an optimal solution. Experimental results also show that rLAO* and qLAO* inherit the merits of excellent performance of LAO* for solving uncertainty problems.

Defining the standard Boolean operations on fuzzy Booleans with the compositional rule of inference (CRI) or Zadeh’s extension principle gives counter-intuitive results. We introduce and motivate a slight adaptation of the CRI, which only effects the results for non-normal fuzzy sets. It is shown that the adapted CRI gives the expected results for the standard Boolean operations on fuzzy Booleans. As a second application, we show that the adapted CRI enables a don’t-care value in approximate reasoning. From the close connection between the CRI and Zadeh’s extension principle, we derive an adaptation of the extension principle, which, like the modified CRI, also gives the expected Boolean operations on fuzzy Booleans.

In this paper, we focus on the linguistic-valued logic system with truth-values in the lattice-ordered linguistic truth-valued algebra, then investigate its satisfiability problem and its corresponding Quasi-Horn-clause logic framework, while their soundness and completeness theorems are provided. The present framework reflects the symbolic approach acts by direct reasoning on linguistic truth values, i.e., reasoning with words, and provides a theoretical support for natural-language based reasoning and decision making system.

J-K flip-flops are elementary digital units providing sequential features/memory functions. Their definitive equation is used both in the minimal disjunctive and conjunctive forms. Fuzzy connectives do not satisfy all Boolean axioms, thus the fuzzy equivalents of these equations result in two non-equivalent definitions, “reset and set type” fuzzy flip-flops (F

3

) by Hirota

& al.

when introducing the concept of F

3

. There are many alternatives for “fuzzifying” digital flip-flops, using standard, algebraic or other connectives. The paper gives an overview of some of the most famous F

3

-s by presenting their definitions and presenting graphs of the inner state for a typical state value situation. Then a pair of non-associative operators is introduced, and the properties of the respective F

3

are discussed. The investigation of possible fuzzy flip-flops is continued by examining Türkşen’s IVFS, its midpoint values, and by introducing “minimized IVFS” (MIVFS), along with the MIVFS midpoints.

Although search engines represent the main means to access on-line data, the increasing demand in terms of performance, precision and relevance in the information retrieval is too far from to being acceptable. The gap existing between the wanted information and the gathered information is often bound to hindrances of semantic rather than syntactic nature. The continuing growth of the Internet usage and contents makes difficult the information access, making the task of information retrieval highly critical.

The paper introduces a system for supporting the Web search activity: on the basis of the interpretation of input query, a suitable list of links to relevant web pages is presented to the user. In fact, the system builds additional queries whose content is similar to the initial one and returns a refined list, resulting from the “multiple” query submissions.

Bio-signal/behavior pattern acquisition and its use are essential in human-friendly human-robot interaction to recognize human intention. However, it is usually difficult to model and handle such interaction due to variability of the user’s behavior and uncertainty of the environment in human-in-the-loop system. In this paper, we shall show the benefits of a PFR (probabilistic fuzzy rule)-based learning system to handle inconsistent data pattern in view of combining fuzzy logic, fuzzy clustering, and probabilistic reasoning in a single system as an effective engineering solution to resolve inconsistency of the complicated human behavioral characteristics. Moreover, we introduce a PFR-based inductive life-long learning structure for continual adaptation throughout incessant learning and control. The learning system gradually extracts more meaningful/reliable rule-based knowledge in incorporation of learning processes in short-term memory, interim transition memory and long-term memory. To show the effectiveness of the proposed system, we introduce a successful example as a case study in view of probabilistic fuzzy rule-based knowledge discovery to handle TV watching behavior data pattern learning.

In this paper, the robust stability analysis of a fuzzy vehicle lateral system with perturbed parameters is presented. Firstly, the fuzzy controller can be linearized by utilizing the describing function method with experiments. After the describing function is obtained, the stability analysis of the vehicle lateral control system with the variations of velocity and friction is then carried out by the use of parameter plane method. Afterward some limit cycle loci caused by the fuzzy controller can be easily pointed out in the parameter plane. Computer simulation shows the efficiency of this approach.

Location services are used in mobile ad hoc and hybrid networks either to locate the geographic position of a given node in the network or for locating a data item. One of the main usages of position location services is in location based routing algorithms. In particular, geographic routing protocols can route messages more efficiently to their destinations based on the destination node’s geographic position, which is provided by a location service. In this paper, we propose an adaptive location service on the basis of fuzzy logic called FHLS (

Fuzzy Hierarchical Location Service

) for mobile ad hoc networks. The FHLS uses the adaptive location update scheme using the fuzzy logic on the basis of the mobility and the call preference of mobile nodes. The performance of the FHLS is to be evaluated by using a simulation, and compared with that of existing HLS scheme.

The work describes an automatically on-line Self-Tunable Fuzzy Inference System (STFIS) of a mini-flying called XSF drone. A Fuzzy controller based on an on-line optimization of a zero order Takagi-Sugeno fuzzy inference system (FIS) by a back propagation-like algorithm is successfully applied. It is used to minimize a cost function that is made up of a quadratic error term and a weight decay term that prevents an excessive growth of parameters. Simulation results and a comparison with a Static Feedback Linearization controller (SFL) are presented and discussed. A path-like flying road, described as straight-lines with rounded corners permits to prove the effectiveness of the proposed control law.

Temperature control system (TCS) of texturing machine (TM) has many control channels, requires high control precision, and it is prone to be influenced by peripheral environmental factors. Since traditional temperature control method hardly realize ideal control effect, a kind of TCS realization method based on self-turning PID technology for constant temperature box (CTB) of TM was put forward based on the wide analysis of characteristics and methods of TCS. According to structure characteristic and working environment of TM-CTB, its discrete mathematics model was established by thermodynamics principle. The self-turning PID minimum phase control system for TM temperature controller was designed using pole points placement method, and its application instance was established by embedded system technology. System parameters were identified by recursion least square method, and forgetting factor was introduced to improve the model tracing ability of TCS. Experiments results showed that the method can satisfy the multi-channel requirement of texturing machine TCS, and its temperature control error can be limited under one percent.

This paper presents a Fuzzy-Lyapunov approach to design trajectory tracking controllers. This methodology uses a Lyapunov function candidate to obtain the rules of the Mamdani-type fuzzy controllers which are implemented to track a desired trajectory. Two fuzzy controllers are implemented to control the position and velocity of a servo trainer and real time results are presented to evaluate the performance of designed controllers against the performance of classical controller.

The paper describes the application of an artificial neural network in natural language text reasoning. The task of knowledge discovery in text from a database, represented with a database file consisting of sentences with similar meanings but different lexico-grammatical patterns, was solved with the application of neural networks which recognize the meaning of the text using designed training files. We propose a new method for natural language text reasoning that utilizes three-layer neural networks. The paper deals with recognition algorithms of text meaning from a selected source using an artificial neural network. In this paper we present that new method for natural language text reasoning and also describe our research and tests performed on the neural network.

A new method for modeling and knowledge extraction at each neuron of a neural network using type-I fuzzy sets is presented. This approach of neuron modeling provides a new technique to adjust the fuzzy neural network (FNN) structure for feasible number of hidden neurons and efficient reduction in computation complexity. Through repeated simulations of a crisp neural network, we propose the idea that for each neuron in the network, we can obtain reduced model with high efficiency using wavelet based multiresolution analysis (MRA) to form wavelet based fuzzy weight sets (WBFWS). Triangular and Gaussian membership functions (MFs) are imposed on wavelet based crisp weight sets to form Wavelet Based Quasi Fuzzy Weight Sets (WBQFWS) and Wavelet Based Gaussian Fuzzy Weight Sets (WBGFWS). Such type of WBFWS provides good initial solution for training in type-I FNNs. Thus the possibility space for each synoptic connection is reduced significantly, resulting in fast and confident learning of FNNs. It is shown that propsed modeling approach hold low computational complexity as compared to existing type-I fuzzy neural network models.

Fault detection in gear train system is important in order to transmitting power effectively. The artificial intelligent such as neural network is widely used in fault diagnosis and substituted for traditional methods. In rotary machinery, the symptoms of vibration signals in frequency domain have been used as inputs to the neural network and diagnosis results are obtained by network computation. However, in gear or rolling bearing system, it is difficult to extract the symptoms from vibration signals in frequency domain which have shock vibration signals. The diagnosis results are not satisfied by using artificial neural network, if the training samples are not enough. The Bayesian networks (BN) is an effective method for uncertain knowledge and less information in faults diagnosis. In order to classify the instantaneous shock of vibration signals in gear train system, the statistical parameters of vibration signals in time-domain are used in this study. These statistical parameters include kurtosis, crest, skewness factors etc. There, based on the statistical parameters of vibration signals in time-domain, the fault diagnosis is implemented by using BN and compared with two methods back-propagation neural network (BPNN) and probabilistic neural network (PNN) in gear train system.

An improvement of a fuzzy Artificial Neural Network model based on correlation coefficients is presented. As aggregation operator to compute the net input to target neuron a uninorm is used, instead of the sum of all the influences that the neuron receives usually used in typical artificial neurons. Such combination allows increasing the model performance in problem solving. While the natural framework and the interpretability presented in the former model are preserved by using fuzzy sets, experimental results show the improvement can be accomplished by using the proposed model. Significant differences of performance with the previous model in favor of the new one, and comparable results with a traditional classifier were statistically demonstrated. It is also remarkable that the model proposed shows a better behavior in presence of irrelevant attributes than the rest of tested classifiers.

A Recurrent Trainable Neural Network (RTNN) with a two layer canonical architecture learned by a dynamic Backpropagation learning algorithm is incorporated in a Hierarchical Fuzzy-Neural Multi-Model (HFNMM) identifier, combining the fuzzy model flexibility with the learning abilities of the RTNNs. The local and global features of the proposed HFNMM identifier are implemented by a Hierarchical Sliding Mode Controller (HSMC). The proposed HSMC scheme is applied for 1-DOF mechanical plant with friction control, where the obtained comparative results show that the HSMC with a HFNMM identifier outperforms the SMC with a single RTNN identifier.

Ensemble Neural Networks are a learning paradigm where many neural networks are used together to solve a particular problem. In this paper, the relationship between the ensemble and its component neural networks is analyzed with the goal of creating of a set of nets for an ensemble with the use of a sampling-technique. This technique is such that each net in the ensemble is trained on a different sub-sample of the training data.

Texture is a visual feature frequently used in image analysis that has associated certain vagueness. However, the majority of the approaches found in the literature do not either consider such vagueness or they do not take into account human perception to model the related uncertainty. In this paper we model the concept of ”coarseness”, one of the most important textural features, by means of fuzzy sets and considering the way humans perceive this kind of texture. Specifically, we relate representative measures of coarseness with its presence degree. To obtain these ”presence degrees”, we collect assessments from polls filled by human subjects, performing an aggregation of such assessments. Thus, the membership function corresponding to the fuzzy set ”coarseness” is modelled by using as reference set the representative measures and the aggregated data.

First, a new pattern classification model with

T

-fuzzy data is built on the basis of definition in

T

-fuzzy data and of its operation properties. Besides,

T

-fuzzy data are determined to measure

T

-fuzzy numbers by using a distance formula, so that a model is also decided. Meanwhile four methods to the model are presented, which are applied to pattern classification and recognition of environmental quality. The result gained from a sample coincides with practice, providing a valid method for a pursuit of indeterminacy problems in human imitation identification, because the sample contains more information, where a little training results from the sample is integrated with estimation from expert’s experience, and information resources are made full use of in analysis of confirmation. Finally, we give some method with which

T

-fuzzy data is obtained.

It is difficult to define a comfortable space for people. It is partly because comfortness relates to many attributes specify a space, partly because all people have different preferences, and also because even the same person changes his/her preference according the state of their health, body conditions, working states and so on. Various parameters and attributes should be controlled to realize such a comfortable space according the data-base of past usages. Information obtained from human bodies such as temperature, blood pressure,

α

brainwave, heart beats and etc. can be employed to adjust the space to the best condition. In order to realize a comfortable space, first we recognize human states and behabiors, and second we provide an apporpriate environment for a focal person according to his/her state.

The objective of this paper is to achieve a comfortable space in terms of affectie behaviors or actions. We deal with such techneaques as KANSEI engineering. In other words, it is required to realize our comfortable environment suitable to feelings. Kansei Engineering is one to offer better products to the customers by employing human sensitivity.

As a kind of logical algebra, lattice implication algebra has been applied in lattice-valued logic. Study in algebraic structure of sub-algebra of lattice implication algebra can help to construct and apply lattice implication algebra to real applications. In this paper, we studied the structural properties of sub-algebra of a finite lattice implication algebra and proposed a method for extracting a sub-algebra from it.

After generating simple evaluating syntagms which are constructed by linguistic hedges and atomic evaluating syntagms, a voting mechanism is adopted for truth values of evaluating syntagms propositions on universe

D

. Then, a formal context of voting mechanism about evaluating syntagms is proposed. Based on the formal context, formal concepts of evaluating syntagms are obtained, and these formal concepts are used to semantics of simple evaluating syntagms and compound evaluating syntagms which are generated by simple evaluating syntagms and the connectives ∧ , ∨ , →, ¬.

Let

Ω

be a complete residuated lattice. By

SetF

(

Ω

) we denote a category of sets with similarity relations (

A

,

δ

) with values in

Ω

. We investigate an interpretation of a first order predicate fuzzy logic in a model based on objects of this category

SetF

(

Ω

). A notion of a fuzzy set in this category is introduced and interpretation of formulas as fuzzy sets are defined. Characteristic morphisms are defined for such fuzzy sets and relationship between interpretation by fuzzy sets and interpretation defined by characteristic morphisms are investigated.

The problem of solvability of a system of fuzzy relation equations with sup− *-composition is considered in a finite semilinear space over a residuated lattice. In this setting the problem of solvability given above is similar to the problem of solvability of a system of linear equations in the form

A

x

 = 

b

. We put emphasis on a right-hand side vector

b

and consider the problem of solvability as a problem of characterization of all vectors

b

for which the original system of (fuzzy relation) equations is solvable. We prove that a system of equations with sup− *-composition is solvable if and only if

b

is a fixed point of the shrivel operator (introduced in this paper). Moreover, a set of all fixed points is a semi-linear subspace of an original space. Some other results are presented as well.

Proof systems based on rules with the property that all formulas contained in the assumptions are contained as subformulas in the conclusion as well, are particularly suitable for automated proof search. Systems of this kind were found for several well-known fuzzy logics. However, for BL (Basic Logic), the logic of continuous t-norms and their residua, the situation is less satisfactory. We consider two proof systems for BL which fulfill the desired property in quite contrasting ways.

We study the structures which satisfy a generalization of the Cantor–Bernstein theorem. This work is inspired by related results concerning quantum structures (orthomodular lattices). It has been proved that

σ

-complete MV-algebras satisfy a version of the Cantor–Bernstein theorem which assumes that the bounds of isomorphic intervals are boolean. This result has been extended to more general structures, e.g., effect algebras and pseudo-BCK-algebras.

There is another direction of research which has been paid less attention. We ask which algebras satisfy the Cantor–Bernstein theorem in the same form as for

σ

-complete boolean algebras (due to Sikorski and Tarski) without any additional assumption. In the case of orthomodular lattices, it has been proved that this class is rather large. E.g., every orthomodular lattice can be embedded as a subalgebra or expressed as an epimorphic image of a member of this class. On the other hand, also the complement of this class is large in the same sense. We study the analogous question for MV-algebras and we find out interesting examples of MV-algebras which possess or do not possess this property. This contributes to the mathematical foundations by showing the scope of validity of the Cantor–Bernstein theorem in its original form.

Canonical completeness results for Ł

$(\mathcal{C})$

, the expansion of Łukasiewicz logic Ł with a countable set of truth-constants

$\mathcal{C}$

, have been recently proved in [5] for the case when the algebra of truth constants

$\mathcal{C}$

is a subalgebra of the rational interval [0, 1] ∩ ℚ. The case when

$C \not \subseteq [0, 1] \cap \mathbb{Q}$

was left as an open problem. In this paper we solve positively this open problem by showing that Ł

$(\mathcal{C})$

is strongly canonical complete for finite theories for

any

countable subalgebra

$\mathcal{C}$

of the standard Łukasiewicz chain [0,1]

Ł

.

EQ-algebra is an algebra with three binary operations (meet, product, fuzzy equality) and a top element that has been introduced in [13] as an algebra of truth values for the fuzzy type theory (a higher-order fuzzy logic). Recall that till now, truth values in fuzzy type theory have been supposed to form either of IMTL, BL, MV or Ł

Π

-algebra that are special residuated lattices. However, since fuzzy equality is a derived operation in residuated lattice, it is not so natural for fuzzy type theory as the EQ-algebra. In this paper, we continue the research of EQ-algebras. Namely, we have modified some axioms, show further properties of them and outline the filter theory.

Research in educational adaptive hypermedia systems has been concerned with the generation of personalized courses, in this work we focus on a task of these kind of systems: the semi-automatic sequencing of didactic resources. Sequencing defines the order in which topics (and didactic resources) in a course will be presented to learners, considering for this, their previous knowledge and particular objectives. This task is based on subjective information, for example the learner knowledge, preferences, learning style, and even assessment results are perceived differently depending the context. In this paper we define an architecture for sequencing of didactic materials using fuzzy attributes and rules.