Advances in Fuzzy Logic and Technology 2017

In this contribution, we first elaborate the theory of the fuzzy transform of higher degree (F$$^m$$-transform, $$m\ge 0$$) applied to stationary processes that was initiated by Holčapek et al. in [5, 6]. Then, we provide mathematical justification for its application to reduction of irregular fluctuations (noise) generated by specific stationary processes.

A new family of fuzzy implications, motivated by classic Sheffer stroke operator, is introduced. Sheffer stroke, which is a negation of a conjunction and is called NAND as well, is one of the two operators that can be used by itself, without any other logical operators, to constitute a logical formal system. Classical implication can be presented just by Sheffer stroke operator in two ways which leads to two new families of fuzzy implication functions. It turns out that one of them is mainly a subclass of QL-operations, while the other one, called in our paper as SS$$_{qq}$$-implications, is independent of other well-known families of fuzzy implications. Basic properties of Sheffer stroke implications are also analysed.

This paper is a study of fuzzy type theory (FTT) with partial functions. Out of several possibilities we decided to introduce a special value “$$*$$” which represents “undefined”. In the interpretation of FTT, this value lays outside of the corresponding domain. In the syntax, it is naturally represented by the description operator acting on the empty (fuzzy) set which, of course, has no element and so, choosing an element from its kernel gives no result, i.e., it is undefined. We will demonstrate that our approach leads to reasonable characterization of the undefinedness. We will also show that any consistent theory of FTT has a model.

Entrepreneurship includes various activities including starting a new business from scratch, creating and developing new business areas for existing organizations. The countries should provide a supportive entrepreneurial environment since entrepreneurship is the key element for the sustainable growth of a country. In order to improve entrepreneurial support, the level of support should be measured with different dimensions in the various periods. In this study, a dynamic intuitionistic fuzzy evaluation method is developed for determining entrepreneurial support within a country. Five countries are evaluated with the proposed method, and a sensitivity analysis is conducted to show the robustness of the model.

System requirements are vital for software development. Defining the appropriate requirements and their importance levels and taking the necessary actions to fulfill the most crucial ones are the keys to a successful software program. However, prioritization of the requirements is a complex problem that involves fuzziness and ambiguities. In this study, we propose a multi-criteria decision-making approach based on HFLTS (Hesitant Fuzzy Linguistic Term Sets) to evaluate the system requirements. The proposed method is applied to G@together project that focuses on developing an electronic job-matching platform for disadvantaged people.

Because of the irrepressible growth in information technologies and telecommunication infrastructure especially for mobile devices, people are more disposed to search proper products and find out attractive offers with lower prices. In order to reach potential customers, companies deal with offering personalized messages including special promotions and discounts. In this respect, recommender systems have begun to use as one of the essential tools for making appropriate selections considering diversified conditions and personal preferences. On the other hand, users’ preferences could not be easily determined or predicted in some cases, as seen in visiting prediction of mobile users. Thus, the use of location based service applications enable the determination of users visiting patterns, except making predictions. In this study, an interval valued hesitant fuzzy clustering approach is adapted based on location similarity and fuzzy c means clustering is applied for user segmentation. After that, matching location groups and user segments is provided the representation of user visiting tendency. By using this approach, advertisers will be able to handle their advertisements considering location similarities and user groups that helps the implementation of personalized advertising recommender systems.

The paper deals with the problem of aggregation of risk level assessments. We describe the technique of a risk level evaluation taking into account values of the risk level obtained for objects which are in some sense equivalent. For this purpose we propose to use the construction of a general aggregation operator based on the corresponding fuzzy equivalence relation. Numerical example of the investment risk level aggregation using an equivalence relation obtained on the basis of different macroeconomic factors for countries of one region is considered.

Six Sigma approaches aim at providing almost defect-free products and/or services to customers. Six Sigma is a powerful and comprehensive management tool for meeting customer needs. Well-designed projects are capable to provide significant financial benefits, bring competitive advantage and increased customer satisfaction.Well-designed projects having clear and concise descriptions and objectives are capable to provide significant financial benefits, increased customer satisfaction and bring competitive advantage. Selecting Six Sigma improvement projects has been one of the most challenging and frequently discussed issues in the literature. Selecting the most useful project/s is a key success factor in Six Sigma approach. Selecting Six Sigma projects is a multi criteria decision making problem involving many tangible and intangible criteria under uncertainty. In this paper, uncertainty will be handled by neutrosophic sets. “A neutrosophic set deals with the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra” [1]. In neutrosophic sets, truth-membership, indeterminacy-membership and falsity-membership are all together included. Neutrosophic sets are accepted as a super set of the other types of sets such as classical sets, ordinary fuzzy sets, hesitant fuzzy sets, intuitionistic fuzzy sets, and soft sets.In this paper, we employ interval neutrosophic TOPSIS method to evaluate Six Sigma projects. By reviewing the literature, seven criteria e.g. total cost, required time and customer satisfaction are taken into account. To the best knowledge of the authors, this is the first study to evaluate Six Sigma projects using interval neutrosophic TOPSIS approach with group decision making.

Measurement of performance is an important management process which deals with assessment and evaluation of a particular process or its’ outcomes. Performance measurement is used in different managerial levels for different purposes. While top management, use it to evaluate the results and construct new goals, at the personal level, performance measurement is good for recognising the current weaknesses and motivating for the future accomplishments. For a particular process, team or individual, first critical performance indicators (KPI) are determined, then targets for each KPI is set at the beginning of the period. At end of the assessment period, performance assessment is done for each KPI and the overall performance is calculated. When subjective and qualitative KPIs are used the overall performance measurement has the possibility to be affected by the evaluator. In this study, a performance measurement model for Call Centers are proposed. In the proposed approach hierarchical intuitionistic fuzzy axiomatic de-sign is used to calculate overall performance.

Because of emerging technologies, a vast amount of data can be stored and processed very easily. These advances also affect companies and many new projects are being proposed. Business analytics is the umbrella term for these projects and it denotes to the skills, technologies, activities aiming at assessment and exploration of past performance to gain an understanding for better decision making. Data and analytical models are the two main pillars of business analytics. Business analytics project can be grouped into three main groups: (i) descriptive analytics, efforts to understand what has happened in the company, (ii) predictive analytics, efforts to figure out the result of an future event, and (iii) prescriptive analytics use mathematical and computational sciences to suggest decision options to take advantage of the results of descriptive and predictive analytics. In this study a prioritization method for possible business analytics projects using Type-2 fuzzy AHP is proposed. Proposed model is composed of six criteria namely, strategic value, competitiveness, customer relations, improved decision-making, improved operations, and data quality.

In this work we propose an image compression algorithm based on the fuzzy transform. The algorithm tries to find the best fuzzy partition of the functions domain in order to obtain the best compressed image (in terms of quality). To solve the optimization problem we based ourselves in the Gravitational Search Algorithm, in which each agent represents a possible fuzzy partition of a fixed size.

Decision matrices represent a common tool for solving decision-making problems under risk. Elements of the matrix express the outcomes if a decision-maker chooses the particular alternative and the particular state of the world occurs. We deal with the problem of extension of a decision matrix to the case of fuzzy states of the world and fuzzy outcomes of alternatives. We consider the approach based on the idea that a fuzzy decision matrix determines a collection of fuzzy rule-based systems. The aim of the paper is to study extension of this approach to the case where the states of the world are fuzzy sets on the finite universal set and the probabilities of elementary events are determined by a tuple of fuzzy probabilities. We derive the formulas for computations of the fuzzy expected values and fuzzy variances of the outcomes of alternatives, based on which the alternatives can be compared.

In this paper it is investigated when some kinds of aggregation functions satisfy the Modus Ponens with respect to other aggregation function, or equivalently, when they are $$\mathcal {A}$$-conditionals. Moreover, some operation connected with $$\mathcal {A}$$-conditionals is examined and used to algorithm of approximate reasoning.

Interval-valued fuzzy relations can be interpreted as a tool that may help to model in a better way imperfect information, especially under imperfectly defined facts and imprecise knowledge. Preference structures are of great interest nowadays because of their applications. From a weak preference relation derive the following relations: strict preference, indifference and incomparability, which by aggregations and negations are created and examined in this paper. Moreover, we propose the algorithm of decision making by using new preference structure.

At present the use of fuzzy systems applied to problem solving is very common, since the use of linguistic variables is less complex when solving a problem. This article presents a study of the use of type-1 and interval type-2 fuzzy system applied to the solution of problems of optimization using metaheuristic algorithms. There are many types of algorithms that mimic social, biological, etc. behaviors. In this case the work focuses on the metaheuristic algorithms in specific the fuzzy harmony search algorithm (FHS), the metaheuristic algorithms use a technique to obtain a suitable exploration in a definite space to finish with an exploitation around the best position found, with this it is possible to obtain a good solution of the problem. In particular, it was applied to 11 mathematical reference functions using different numbers of dimensions.

The field of aggregation theory addresses the mathematical formalization of aggregation processes. Historically, the developed mathematical framework has been largely confined to the aggregation of real numbers, while the aggregation of other types of structures, such as rankings, has been independently considered in different fields of application. However, one could lately perceive an increasing interest in the study and formalization of aggregation processes on new types of data. Mostly, this aggregation outside the framework of real numbers is based on the use of a penalty function measuring the disagreement with a consensus element. Unfortunately, there does not exist a comprehensive theoretical framework yet. In this paper, we propose a natural extension of the definition of a penalty function to a more general setting based on the compatibility with a given betweenness relation. In particular, we revisit one of the most common methods for the aggregation of rankings – the method of Kemeny – which will be positioned in the penalty-based aggregation framework.

Present versions of fuzzy arithmetic (FA) are not ideal. For some computational problems they deliver credible results. However for many other problems the results are less credible or sometimes clearly incredible. Reason of this state of matter is the fact that present FA-versions partially or fully (depending on a method) do not possess mathematical properties that are necessary for achieving correct calculation results as: distributivity law, cancellation law, neutral elements of addition and multiplication, property of restoration, possibility of decomposition of calculation in parts, ability of credible equations’ solving, property of delivering universal algebraic solutions, possibility of formula transformation, and other. Lack of above properties is, in the authors’ opinion, caused by incorrect assumption of all existing FA-versions that result of arithmetic operations on unidimensional fuzzy intervals is also a unidimensional fuzzy interval. In the paper authors show that the correct result is a multidimensional fuzzy set and present a fuzzy arithmetic based on this proposition, which possess all necessary mathematical properties and delivers credible results.

Currently the great advances in Web technologies are changing the process of access to information and the Web is one of the most important source of information. Furthermore, the Web influences the development of others media, for example, newspapers, journals, books, libraries, etc. In this paper we analyze its impact in the development of the university digital libraries. As well as on the Web, the information growth is a big problem for academic digital libraries, and similar tools can be applied in university digital libraries to provide users with access to the information. Given the importance of this aspect, in this paper we analyze and review different proposals that improve the processes of dissemination of information in these university digital libraries, promoting access to information of interest. These proposals manage to adapt access to information according to the needs and preferences of each user. As we can see in the literature, one of the techniques with the best results, is the application of recommender systems. Recommender systems are tools whose objective is to evaluate and filter the large amount of information available on the Web to assist users in their process of access to information. Thus, in this paper we analyze some proposals based on recommender system to help students, teachers and researchers to find research resources that can improve the services provided by the university digital libraries.

The paper presents the analysis and application of hierarchical fuzzy system to the problem of evaluation/measurement of the rehabilitation effects in post-stroke patients. Healthy people constitute reference group. Prevalence and impact of the stroke-related disorders on Health-Related Quality of Life (HRQoL) as a recognized and important outcome after stroke is huge. Quick, valid and reliable assessment of HRQoL in people after stroke constitutes a worldwide significant problem for scientists and clinicians - there are many tools, but no one fulfills all requirements or has prevailing advantages. Evaluation model presented here is improved version of earlier attempts and applies the potential of fuzzy systems for linguistic modeling of rules. It provides a great advantage as there are experienced clinicians working on the improvement of the rehabilitation methods but there is no intuitive formal model to measure their effects. The innovative element here is the use of Ordered Fuzzy Number model. It is a good tool for modeling the trends in information used to create the fuzzy rules of small fuzzy systems which together form a hierarchical fuzzy evaluation model.

We describe the use of fuzzy sets within MonitorSI-Text. It is a real and operative data-to-text system that generates textual information about the operational state of Information Technology services, monitored by the commercial software platform Obsidian. Until now, Obsidian provided several dashboards that allowed to monitor in real time the state of the service infrastructure of the clients. MonitorSI-Text extends the capabilities of Obsidian with the automatic generation of textual reports, live descriptions and notifications that complement the visualization dashboards with enhanced textual information. Moreover, our system performs an analysis of time series data based on a fuzzy filtering approach as part of its content determination process. MonitorSI-Text has been tested, commercialized and deployed as part of the Obsidian Business Service Intelligence platform, which is currently in use by several customer companies, such as Camper and PwC.

In this paper a novel approach to design data driven based fault diagnosis systems using fuzzy clustering techniques is presented. In the proposal, the data was first pre-processed using the Noise Clustering algorithm. This permits to eliminate outliers and reduce the confusion as a first part of the classification process. Secondly, the Kernel Fuzzy C-means algorithm was used to achieve greater separability among the classes, and reduce the classification errors. Finally, it can be implemented a step for optimizing the parameters of the NC and KFCM algorithms. The proposed approach was validated using the iris benchmark data sets. The obtained results indicate the feasibility of the proposal.

In the present paper, the apparatus of generalized nets is used to describe the metaheuristic technique Bat algorithm. Generalized nets are considered an effective and appropriate tool for description of the logics of different optimization techniques. As a result, the developed generalized net model executes the Bat algorithm procedures, conducting basic steps and performing optimal search. The paper elaborates on the already proposed Universal generalized net model for description of the population-based metaheuristic algorithms, which was used so far to model the Cuckoo search, Firefly algorithm and Artificial bee colony optimization, and is used here for modelling of Bat algorithm. It is shown that the Bat algorithm can be described in terms of Universal generalized net model by only varying the characteristic functions of the tokens. Thus, verification of the Universal generalized net model is performed.

In this paper, an integrated insurer’s portfolio, which consists of a few layers of insurance and financial instruments, is numerically analysed. A future behaviour of such a portfolio is related to stochastic processes (like a random interest rate yield and uncertain catastrophic losses), therefore the Monte Carlo (MC) approach is applied. A special attention is paid to a problem of a share of catastrophe bonds in such a portfolio and to an analysis of an influence of an additional layer—an external (e.g. governmental) help. Some important measures of an insurer’s risk (like a probability of his bankruptcy) are then numerically analysed. In considered examples, apart from strictly crisp sets of parameters, also fuzzy numbers are used to model an imprecise information concerning the possible external help.

Association rules and fuzzy association rules are vastly studied topics. Various measures for quantifying a quality of a (fuzzy) association rule were proposed in the past. In this article, we survey existing and propose some new quality measures for the whole rule bases of fuzzy association rules.

In this paper a new method for Modular Granular Neural Network (MGNN) optimization with a granular approach is presented. A Particle Swarm Optimization technique is proposed to perform the granulation of information with a fuzzy dynamic parameters adaptation to prevent stagnation. The proposed fuzzy inference system seeks to adjust some PSO parameters such as w, C₁ and C₂ to ensure that the parameters have adequate values depending on the current behavior of the particles. The objective of the proposed PSO is design optimal MGNN architectures. The modular granular neural networks are applied to human recognition based on iris biometrics, where a benchmark database is used and the objective function in this work is the minimization of the error of recognition.

Customer orientation is a business strategy in the lean business model that requires management and employees to focus on the changing demands and requirements of the customers.Improved business performance can be enhanced by .customer orientation. In this chapter, a systematic approach based on hesitant fuzzy AHP is proposed to deal with incomplete information due to the ambiguity to solve complex customer oriented multi criteria decision making problem of performance assessments of service departments.

We present an image edge detection algorithm that is based on the concept of ordered directionally monotone functions, which permit our proposal to consider the direction of the edges at each pixel and perform accordingly. The results of this method are presented to the EUSFLAT 2017 Competition on Edge Detection.

In the paper the method of fuzzy clustering task for multivariate short time series with unevenly distributed observations is proposed. Proposed method allows to process the time series both in batch mode and sequential on-line mode. In the first case we can use the matrix modification of fuzzy C-means method, and in second case we can use the matrix modification of neuro-fuzzy network by T. Kohonen, which is learned using the rule “Winner takes more”. Proposed fuzzy clustering algorithms are enough simple in computational implementation and can be used for solving of wide class of Big Data and Data Stream Mining problems. The effectiveness of proposed approach is confirmed by many experiments based on real data sets.

We discuss how to train and tune comparators aimed at multi-similarity-based classification of compound objects. The proposed approach is supported by a collection of techniques and algorithms for construction and use of comparator networks. The described methodology has been implemented as a software library and may be used for a variety of future applications.

By replacing the axiom $$m(x,x,t) = 1$$ for all $$x\in X, t>0$$ in the definition of a fuzzy pseudometric in the sense of George-Veeramani with a weaker axiom $$m(x,x,t) = \varphi (t)$$ for all $$x\in X, t>0$$ where $$\varphi : {\mathbb R}^+ \rightarrow (0,1]$$ is a non-decreasing function, we come to the concept of a fuzzy $$\varphi $$-pseudometric space. Basic properties of fuzzy $$\varphi $$-pseudometric spaces and their mappings are studied. We show also an application of fuzzy $$\varphi $$-pseudometrics in the words combinatorics.

In the paper is proposed a method for evaluation of the quality assurance in universities and scientific organizations. The evaluation of the quality is based on criteria, which measure different aspects of university activities and consists of different sub-criteria. For the assessment the theory of intuitionistic fuzzy sets is used. The obtained intuitionistic fuzzy estimations reflect the degree of each criterion’ satisfaction, and non-satisfaction. We also consider a degree of uncertainty that represents such cases wherein is no information about sub-criteria of the current criterion. The generalized model gives possibility for algorithmization of the methodology of forming the quality evaluations is constructed. It provides the possibility for the algorithmization of the process of forming the evaluation of the quality assurance in universities.

Utility functions content parameters related to risk aversion coefficients which represent natural extensions of utility function properties. They measure how much utility we gain (or lose) as we add (or subtract) from our wealth. We set up these parameters for a person based on her/his answers to a questionnaire constructed to identify individual risk behavior. Calibration of such a questionnaire, and subsequently of utility functions, is based on an expected utility maximization of different alternatives of investment strategies. In the paper, we present questionnaire calibration methodology which we illustrate using absolute and relative risk aversion coefficients of two selected utility functions which have common, as well as different properties.

The present paper proposes a diagnosis support inference in which input evidence are fuzzy sets. Diagnostic rules are formulated as fuzzy focal elements in the Dempster-Shafer theory. An inclusion measure is used to evaluate matching knowledge with evidence and to calculate belief of the diagnosis. Data simulated for two diagnostic situations show that the method allow for using linguistic values as a diagnostic information.

As reaching the maximum consensus degree in the group decision making problems is very important, many consensus reaching processes have been proposed in the literature. An important step within a consensus reaching process is the feedback mechanism, in which the experts involved in the decision problem under consideration are advised to modify their opinions in order to increase the level of consensus achieved. Therefore, many different feedback mechanisms have been proposed in the existing literature. The aim of this study is to present three of them and analyze their strengths and weaknesses. To do so, an illustrative example is provided.

In a group decision making problem the selection process is decisive to find a solution. In these problems there is a widespread agreement to use fuzzy preference relations to express different preferences about possible alternatives. Previous papers have proposed different selection methods in this context. An usual way is the use of a ranking method to obtain a classification of the alternatives. One of the methods used is based on two choice degrees: quantifier guided dominance degree and quantifier guided non-dominance degree. This paper presents a limited comparative study about the application of the two previously cited quantifier guided choice degrees. By using statistical tools, it is concluded that both choice degrees can offer significantly different rankings of alternatives. In addition, it has been observed that the variability of the alternatives in the ranking obtained by dominance choice degree is generally greater, which may facilitate a better discrimination between different alternatives.

Every recommender system approach suffers the cold start problem to a greater or lesser extent. To soften this impact, the more common solution is to find the way of populating users profiles either using hybrid approach or finding external data sources. In this paper, we present a fuzzy linguistic approach that using bibliometrics aids to soft or remove the necessity of interaction of users providing them with personalized profiles built beforehand, thus reducing the cold start problem. To prove the effectiveness of the system, we conduct a test involving some researchers, aiming to build their profiles automatically. The results obtained proved to be satisfactory for the researchers.

Besides control charts are used in many fields, they are important because the process gives information about the product’s situation. Thanks to control charts, necessary precautions are taken by noticing abnormal and normal situations of process and/or product. It is considered that at this point the most important and critical thing is that there will be loss of information about the expert opinions. It can be said that this situation is more common especially for the qualitative data. To prevent losses of data like this and so on and to transform linguistic expressions into crisp data, it is needed to take advantage of fuzzy logic that is commonly used recently. Although some studies about creating control charts by fuzzy sets have been done recently, all of them are done only by using type 1 fuzzy sets. However, it is known that much of the data used in daily life cannot be expressed by type 1 fuzzy number. Some data may be more suitable for type 2 fuzzy numbers. In this study, type 2 fuzzy control charts are obtained by using the methods of defuzzification and likelihood. The results are compared with the classical control charts This study aims to use type 2 fuzzy sets in control charts as a new approach.

Linked Open Data (LOD) is a graph-based repository of data that uses data representation format called Resource Description Framework (RDF). The basic piece of RDF data is a triple subject-property-object. LOD seen as a network of interconnected pieces of data creates an environment suitable for developing methods enabling learning processes that rely on data integration. Application of frequentionistic-based approaches to integrate data leads to identification of pieces of information that are consistent and frequently used. An essential element of such methods is the ability to identify similar pieces of data. In reality, multiple sources of information use different vocabularies to represent relations (properties) existing between data. That introduces a challenge for data integration methods.In this paper, we propose a simple approach to determine degrees of equivalences between relations (properties) defined by different LOD vocabularies. We process numbers of occurrences of matching pairs of RDF triples in order to determine intervals representing lower and upper levels of property equivalences. As the result, we obtain a graph of equivalent properties where interval-based strength of edges represent degrees of similarity between properties. A case study illustrating the details of the approach and a validation experiment are included.

The Successive Likelihood Index Method establishes the degree of liability, and therefore the corresponding compensation, of the various errors that have caused an accident. From an expert judgment, the successive likelihood index of each error is calculated by a weighted arithmetic mean of their opinions. In this work we have considered other averaging functions for aggregating this information and we have studied their behavior. In particular, we have studied in detail the case of power means applied to the accident of the oil tanker Aegean Sea.

In the paper is extended two dimensional intercriteria analysis over intuitionistic fuzzy data to three dimensional and will be discussed possibility for application of this analysis as an illustration of the application of the intercriteria analysis.

We develop an approach to the concept of bornology in the framework of many-valued mathematical structures. It is based on the introduced concept of an M-bornology on an L-valued set (X, E), or an LM-bornology for short; here L is an iccl-monoid, M is a completely distributive lattice and $$E: X\times X \rightarrow L$$ is an L-valued equality on the set X. We develop the basics of the theory of LM-bornological spaces and initiate the study of the category of LM-bornological spaces and appropriately defined bounded “mappings” of such spaces.

The implicative fuzzy associative memories (IFAM) is a tool used to store patterns in a database and to recall desired pattern upon a presentation. The original IFAM model has been later updated to simplify the weight matrix construction. As a result of this improvement, model internally contains only significant values. This article describes how sparse matrix used to capture model’s weight matrix can be used to reduce memory-space consumption.

In this paper we propose new type of intuitionistic fuzzy modal-like operators generated by the application of the power mean. We study some of their properties and establish some relations between them.

In this paper we revisit the topic of orderings between intuitionistic fuzzy pairs and then provide a more general point of view in their introduction. This would allows us to use less strict orderings in producing similarity scores for objects whose evaluations are in the form of intuitionistic fuzzy pair.

In this paper, we propose and analyze a fuzzy SIR model with an asymptotic transmission rate. Specifically, the fuzziness is due to the consideration of the disease transmission rate, additional death due to disease and rate of recovery from infection as fuzzy sets. Further, a comparative study of the equilibrium points of the disease for the classical and fuzzy models are performed. We study the fuzzy basic reproduction number for groups of infected individuals with different virus loads and compare with a basic reproduction number for the classical model. Finally, a program based on the basic reproduction value $$\mathcal {R}^{f}_{0}$$ of disease control is suggested and the numerical simulations are carried out to illustrate the analytical results.

Processing of spatial data can benefit from the use of fuzzy inference systems, and such systems have been proposed to deal with the map overlay problem for gridded data. The development of fuzzy inference system for solving spatial problems poses specific challenges due to the type of data and specific properties of the spatial context. In this contribution, we take into account that a spatial dataset can exhibit a big variety in different areas and determine the most possible ranges for the variables in the rulebase system in a more appropriate and dynamic way. In addition, we show how the construction and application of a rulebase can be modified in order to handle this changed definition of the most possible ranges.

In a previous paper by Bou et al., the minimal modal logic over a finite residuated lattice with a necessity operator $$\square $$ was characterized under different semantics. In the general context of a residuated lattice, the residual negation $$\lnot $$ is not necessarily involutive, and hence a corresponding possibility operator cannot be introduced by duality. In the first part of this paper we address the problem of extending such a minimal modal logic with a suitable possibility operator $$\Diamond $$. In the second part of the paper, we introduce suitable axiomatic extensions of the resulting bimodal logic and define a logic to reason about fuzzy preferences, generalising to the many-valued case a basic preference modal logic considered by van Benthem et al.

The aim of supervised classification algorithms is to assign objects/items to known classes. Before carrying out the final assignment, many classification algorithms obtain a soft score (probability, fuzzy, possibility, cost...) between each item and each class. In order to improve this final decision, we build a bipolar probabilistic model that considers some extra information about the dissimilarity structure between the classes. We present here some improvements for several supervised classification algorithms such as random forest, decision trees and neural networks for binary classification problems.

Edge detection plays an essential role in many computer vision tasks, but there is limited literature on the fusion of multiscale edge strength measurements. In this paper, we extend an edge detector using both isotropic and anisotropic Gaussian kernels in multiscale space to obtain the multiscale anisotropic edge strength measurements (AESMs). Subsequently, we propose a fusion scheme of multiscale AESMs based on geometric mean. This scheme inherits the merits of the isotropic/anisotropic Gaussian kernel based method and suppress the scale-space diffusion at the same time. Experimental results on example images in the EUSFLAT Edge Detection Competition dataset illustrate that the proposed method outperforms the widely used Canny method and the state-of-the-art isotropic/anisotropic Gaussian kernel method.

Multi-criteria decision analysis (MCDA) in the fuzzy environment needs not only in implementation of functions of fuzzy variables but also inevitably leads to ranking fuzzy quantities. The use of simplification and defuzzification methods at different stages of fuzzy MCDA (FMCDA) results in a loss of information and does not meet the concept of fuzzy decision analysis that “the decision taken in the fuzzy environment must be inherently fuzzy”. In this contribution, a new approach to FMCDA is suggested, in which fuzzy criterion values and fuzzy weight coefficients are considered as fuzzy numbers (FNs) of a general type. Ranking alternatives is based on a novel methodological approach, fuzzy rank acceptability analysis (FRAA), for ranking FNs, whose use within FMCDA forms the fuzzy multicriteria acceptability analysis (FMAA) and implements a consistent approach to fuzzy decision analysis providing both ranking alternatives and the degree of confidence for each alternative to have the corresponding rank. Properties of FRAA ranking and integration of FRAA with a fuzzy extension of MAVT (FMAVT) as an example are considered and discussed along with the overestimation problem, which can arise when implementing FMCDA. The outcomes of FMAVT application for analysis of a multicriteria problem within the case study on land-use planning are considered and compared with the results by (classical) MAVT method.

We investigate a minimum risk portfolio model under conditions of a hybrid uncertainty of a possibilistic-probabilistic type with weak and strong triangular norms (t-norms) describing the interaction of fuzzy factors of the model. For the case of the weakest t-norm, a formula for variance is derived, which makes it possible to estimate the risk of the portfolio. An equivalent crisp analog of the model is constructed and demonstrated on a numerical example.

This paper proposes the combination of discrete wavelet transform (DWT) and fuzzy logic to classify the fault type in underground distribution cable. The DWT is employed to decompose high frequency component from fault signal with the mother wavelet daubechies4 (db4). The maximum coefficients detail of DWT from phase A, B, C and zero sequence for post-fault current waveforms are considered as an input pattern of decision algorithm. Triangle-shaped S-shaped and Z-shaped membership function with maximum, medium, minimum, and zero are used to create a function for the input variable. Output variable of fuzzy are designated as values range 1 to 10 which corresponding with type of fault. The obtained average accuracy results shown that the proposed decision algorithm is able to classify the fault type with satisfactory accuracy.

This paper aims to investigate switching capacitor bank of the 115 kV Nong Chok substation under the Electricity Generating Authority of Thailand (EGAT). The substation comprises of 3 steps capacitor banks with reactive power of 48 Mvar in each step. In case study, the substation is downscaled to be an experimental unit with 415 V and 5 Mvar in each step in laboratory. Inrush currents, the behavior of transient signals, that occurs when capacitors are switched into the system are studied and analyzed. To reduce the effect of switching capacitors, current limiting reactors connected in series with the capacitors are proposed. In addition, a zero-crossing circuit is designed to control switching angle of the capacitors, since it has a significant effect on the inrush currents. The results of experiment are compared with two case studies: switching capacitors without integrated 7% of reactors and switching capacitors with integrated 7%. It can be summarized that the switching capacitor without integrated reactors has inrush currents change based on the switched angles of the capacitors. However, the switching capacitor with integrated reactors gives inrush current values are almost approximate in each angles of switching and they are lower the case of the switching capacitor without integrated reactors. Nevertheless, reactor integration into the system leads to high current values at the steady states.

This paper presents an approach to applying stochastic orderings to evaluate classification algorithms for low quality data. It discusses some known stochastic orderings along with practical notes about their application to classifier evaluation. Finally, a new approach based on fuzzy cost function is presented. The new method allows comparing any two classifiers, but does not require a precise definition of the cost function. All proposed methods were evaluated on real life medical data. The obtained results are very similar to those previously reported but comparatively much weaker assumptions about costs values are adopted.