Novel Developments in Uncertainty Representation and Processing

Opposition-based models are a current hot-topic in knowledge representation. The point of this paper is to suggest that opposition can be in fact introduced at two different levels, those of the predicates of interest being represented (as short/tall) and of the logical references (true/false) used to evaluate the verification of the former. We study this issue by means of the consideration of different paired structures at each level. We also pay attention at how different types of fuzziness may be introduced in these paired structures to model imprecision and lack of knowledge. As a consequence, we obtain a unifying framework for studying the relationships between different knowledge representation models and different kinds of uncertainty.

The paper deals with the Dempster’s rule for the basic probability assignment combining from the point of view of a medical diagnosis support. The assignment determined on different sources of information is useful to establish symptoms weights, but often results of the combination are far from intuition. A modification of the Dempster’s formula is proposed to make it possible to tune the resulting assignment according to the distance between the combined assignments. Properties of the proposed methods which are important for practical applications are shown on simulated data.

In the paper a very general system is presented including some known important structures, as continous effect algebras. As an illustration the generalization of the classical Poincaré theorem from ergodic theory is presented.

In this contribution new ways of constructing of ordininal sum of fuzzy implications are presented. Moreover, some of their properties are examined, in particular neutral property, identity property, and ordering property.

In this paper we will prove that the new structure called A-poset, defined by Frič and Skřivánek (Generalized random events, 2015) is equivalent to D-posets and effect algebras. In next section we introduce a multiplicative operation on A-postes and prove that these two structures are isomorphic. In the last part of this paper we try to build probability theory on A-posets.

This paper proposes a new method for directly discovering the uncertainty from a sample of discrete data, which is then used in the formation of an Interval Type-2 Fuzzy Inference System. A Coefficient of Variation is used to measure the uncertainty on a finite sample of discrete data. Based on the maximum possible coverage area of the Footprint of Uncertainty of Gaussian membership functions, with uncertainty on the standard deviation, which then are modified according to the found index values, obtaining all antecedents in the process. Afterwards, the Cuckoo Search algorithm is used to optimize the Interval Sugeno consequents of the Fuzzy Inference System. Some sample datasets are used to measure the output interval coverage.

This article presents a proposal for a new method of defuzzification a fuzzy controller, which is based on the concept of the golden ratio, derived from the Fibonacci series [1]. The origin of the method was the observation of numerous instances of the golden ratio in such diverse fields as biology, architecture, medicine, and painting. A particular area of its occurrence is genetics, where we find the golden ratio in the very structure of the DNA molecule [2] (deoxyribonucleic acid molecules are 21 angstroms wide and 34 angstroms long for each full length of one double helix cycle). This fact makes the ratio in the Fibonacci series in some sense a universal design principle used by man and nature alike. In keeping with the requirements, the authors of the present study first explain the essential concepts of fuzzy logic, including in particular the notions of a fuzzy controller and a method of defuzzification. Then, they postulate the use of the golden ratio in the process of defuzzification and call the idea the Golden Ratio (GR) Method. In the subsequent part of the article, the proposed GR-based instrument is compared with the classical methods of defuzzification, including COG, FOM, and LOM. In the final part, the authors carry out numerous calculations and formulate conclusions which serve to classify the proposed method. At the end they present directions of further research.

In the paper the condition for equivalence of problem-oriented databases (DB) models has been formulated. A data segment and problem-focused data manipulation language of database for multi-stage recognition of objects has been characterized. The relational and a corresponding object-oriented models of DB has been described. A few assertions regarding the equivalence of the relational and object DB models for recognition have been proved.

During years of research, there have been defined 149 intuitionistic fuzzy implications. In the paper, it is checked which of these implications satisfy Klir-Yuan’s axioms, whether as (classical) tautologies or as intuitionistic fuzzy tautologies.

Intuitionistic fuzzy sets prove very useful in modelling uncertain and imprecise information when in the evaluations, concerned with a bipolar type of evidence, the “pro” and “contra” estimations do not sum to one (truth) but there is a degree of uncertainty. Relying on the concept of IF-neighbourhoods, introduced in Marinov et al. (On intuitionistic fuzzy metric neighbourhoods, 2015), we propose in this paper a few notions of separability between intuitionistic fuzzy sets and give some applications employing the extended modal operators.

We present some basic facts about a probability theory on IF-events. It is based on the Lukasiewicz operations and on the corresponding probability theory. We present a representation theorem originally published, as reported by Riečan (Soft Methodology and Random Information Systems, pp 243–248, [21]). We also show that the probability IF algebra can be embedded to a probability MV-algebra.

In this paper properties of Atanassov intuitionistic fuzzy relations are examined, i.e.: semi-reflexivity, semi-irreflexivity, semi-symmetry, semi-connectedness, semi-asymmetry, semi-transitivity. The special attention is paid to the semi-transitivity property. Its characterization is given and connections with other transitivity properties are presented, i.e. transitivity itself and weak transitivity. Moreover, transformations of Atanassov intuitionistic fuzzy relations in the context of preservation of the given semi-properties of these relations are presented. The transformations that are considered: lattice operations, the converse, the complement, the composition of relations are the basic ones.

In this paper, the concept of intuitionistic complete lattices is introduced. Some characterizations of such intuitionistic complete lattices are given. The Tarski-Davis fixed point theorem for intuitionistic fuzzy complete lattices is proved, which establish an other criterion for completeness of intuitionistic fuzzy complete lattices in terms of fixed points of intuitionistic monotone maps.

In this leg of research, we explore the question of traversing and ranking elements of an intuitionistic fuzzy set in the intuitionistic fuzzy interpretation triangle. This is necessary in the light of the new developments of the InterCriteria Analysis (ICA), a decision support approach based on intuitionistic fuzzy sets and index matrices. In the ICA, from the data about the evaluations or measurements of a set of objects against a set of criteria, we perform pairwise comparisons of any two objects against each pair of criteria, and perform computations that yield in result intuitionistic fuzzy pairs of numbers in the [0; 1]-interval that give the levels of correlation between any two of the evaluation criteria. In previous works, the correlations between the criteria (hence the term ‘intercriteria’) were analysed separately, by first setting priority on either the membership, or the non-membership component, and plotting them linearly; while currently the efforts are oriented to handling both IF components simultaneously by plotting them in the plane of the intuitionistic fuzzy interpretation triangle.

This paper deals with the problem of constructing intuitionistic fuzzy tolerance from a family of intuitionistic fuzzy sets. A method to calculate the intuitionistic fuzzy tolerance degrees between intuitionistic fuzzy sets on the basis of the Euclidean distance is proposed. An illustrative example used to compare the proposed similarity measure with other similarity measures and an application of the proposed similarity measure to clustering problem is considered. Preliminary conclusions are formulated.

In this paper we propose a method to defuzzify an intuitionistic fuzzy quantity that, depending on two parameters, recover previous methods and leaves freedom to the user.

This paper introduces a novel intuitionistic fuzzy set-based heuristic algorithm of possibilistic clustering. For the purpose, some remarks on the fuzzy approach to clustering are discussed and a brief review of intuitionistic fuzzy set-based clustering procedures is given, basic concepts of the intuitionistic fuzzy set theory and the intuitionistic fuzzy generalization of the heuristic approach to possibilistic clustering are considered, a general plan of the proposed clustering procedure is described in detail, two illustrative examples confirm good performance of the proposed algorithm, and some preliminary conclusions are formulated.

Single expert opinion expressed in form of an intuitionistic membership function (IMF) has uncertainty of the second order because it consists of the membership—$$\mu (x)$$μ(x) and of the non-membership function $$\nu (x)$$ν(x). Two different, considerably inconsistent expert opinions have an increased uncertainty order. Often we do not know, which of the opinion is more or less credible. Hence, IMF representing both aggregated opinions cannot be a standard IMF. It should have an increased order of uncertainty. Possibility of appropriate modeling aggregated opinions offers theory of fuzzy sets type-2 developed mainly by J. Mendel. In this paper authors show how application of this theory in connection with horizontal version of IMFs allows for constructing of an aggregated IMF of two inconsistent intuitionistic expert opinions.

Following (Ribagin et al. 2015, In: 19th International Workshop on IFSs, [8]), in this paper it is proposed a technique to evaluate the functional capacity of the elbow joint during a complex movement using intuitionistic fuzzy and interval valued intuitionistic fuzzy sets. The membership and non-membership values are not always possible up to our satisfaction, but in deterministic (hesitation) part has more important role here, the fact that in decision making, particularly in case of orthopedic physical assessment, there is a fair chance of the existence of a non-zero hesitation part at each moment of evaluation. Based on our previous study here we will introduce intuitionistic fuzzy estimations of flexion-extension and pronation-supination movements of the elbow joint.

The authors propose an algorithm for assessment of the estimates of “correspondence” and “opposition” obtained by InterCriteria Analysis (ICA) in the form of intuitionistic fuzzy vector pairs. For this aim the modified Pearson coefficient of Karl Pearson, called $$\varphi $$φ coefficient (“mean square contingency coefficient”). The algorithm is applied on real data from neurosurgery. The statistical significance of the relations between the considered criteria is verified by data found in literature. The authors believe this approach for data exploration may prove useful in many areas.

In this paper, modeling of logic gates is presented for the first time. Four models of Generalized Nets (GN)—AND gate, a binary to decimal decoder, delay type flip-flop, n-bit binary counter and logical circuits are presented in the following paper. Here we also suggest using the recently proposed approach of InterCriteria Analysis, based on index matrices and intuitionistic fuzzy sets, which aim to detect possible correlations between pairs of criteria. We can perform the measurements, if we have a set of several logical circuits that can be used to obtain identical output data. The aforementioned logical circuits must be composed of different logical elements. By using several measurement points and different schematics, we can suggest the best solution for the considered type of task.

In this paper we present a method for the purpose to detect a certain person in an image. We use the tools of neural networks and face recognition algorithm to achieve our goal. The type of neural network is unsupervised adaptive resonance theory 2 (ART2). It is trained by the set of person images and divided into two clusters—the first cluster represents the human who has to be found and the second one represents the other people. The algorithm which is used for face detection is Viola-Jones and the combination with neural networks helps to identify the person. The generalized net model is used to describe the recognition process.

In this paper, the optimization of LVQ neural networks with modular approach is presented for classification of arrhythmias, using particle swarm optimization. This work focuses only in the optimization of the number of modules and the number of cluster centers. Other parameters, such as the learning rate or number of epochs are static values and are not optimized. Here, the MIT-BIH arrhythmia database with 15 classes was used. Results show that using 5 modules architecture could be a good approach for classification of arrhythmias.

This paper applies the imperialist competitive algorithm (ICA) to benchmark mathematical functions with the original method to analyze and perform a study of the variation of the results obtained with the ICA algorithm as we vary the parameters manually for 4 mathematical functions. The results demonstrate the efficiency of the algorithm to optimization problems and give us the pattern for future work in dynamically adapting these parameters.

The description of a product or an ad’s text can be rewritten in many ways if other text fragments similar in meaning substitute different words or phrases. A good selection of words or phrases, composing an ad, is very important for the creation of an advertisement text, as the meaning of the text depends on this and it affects in a positive or a negative way the interest of the possible consumers towards the advertised product. In this paper we present a method for the optimization of advertisement texts through the use of interactive evolutionary computing techniques. The EvoSpace platform is used to perform the evolution of a text, resulting in an optimized text, which should have a better impact on its readers in terms of persuasion.

In this investigation InterCriteria Analysis (ICA) is applied to examine the influences of one of the genetic algorithms parameters—the generation gap (ggap). The investigation is carried out during the model parameter identification of E. coli MC4110 cultivation process. The apparatuses of index matrices and intuitionistic fuzzy sets, which are the core of ICA, are used to establish the relations between ggap and GAs outcomes (computational time and decision accuracy), on one hand, and cultivation process model parameters on the other hand. The obtained results after ICA application are analyzed in terms of convergence time and model accuracy and some conclusions about derived interactions are reported.

This paper presents practical applications of the cellular automata theory for building fire simulation using the CAEva method. Thanks to the tests carried out using appropriately configured program, realistic results of simulated evacuation of people from the building have been achieved. The paper includes the references to actual fire disasters and provides numbers of their resulting casualties. Using such a kind of predication in civil engineering should increase the fire safety of buildings. Simulations described in this paper seem to be very useful, particularly in case of building renovation or temporary unavailability of escape routes. Using them, it is possible to visualize potential hazards and to avoid increased risk in case of fire. Inappropriate operation of buildings, including insouciant planning of renovations are among frequent reasons of tragic accidents cited by fire brigade information services. Similar problems are encountered by inspectors who assess spontaneous fire accidents or arsons during mas events, where wrong safety procedures or inappropriate attempts to cut costs resulted in tragedy. Thanks to the proposed solutions it shall be easier to envisage consequences of problematic decisions causing temporary or permanent unavailability of escape routes. This is exactly the problem analyzed by this paper. It does not take into account, by the rule, the influence of $$\mathrm{CO}_{2}$$CO2 and other gases on evacuation difficulty. The described method has been analyzed using descriptions of real life fires, the participants of which were neither asleep nor asphyxiated with carbon monoxide, while the escape was hindered by fire, room layout as well as stress and number of the event participants. The results achieved for such conditions are approximate to the actual (reallife) outcomes, which proved the method to be correct.

This article is a part of the series dedicated to AI Methods Inspired by Nature and their implementation in the mechatronic systems. The CutMAG algorithm uses hybrid approach to optimisation, i.e. a combination of classic genetic algorithms (GA) with morphologic optimisation (M) thus creating innovative approach to optimisation of cutting disk design (Cut) for the multi-edge grinder. The input data include population of individuals. Each individual is represented by a set of cutting disks. Whereas the fitness function was assumed as a combination of several postulates of the mechanical design foundations. The method includes mechanical, design and energy aspects. Each individual constitutes a complete solution of the disk set whereas the population represents the entire class of solutions. The fitness function of an individual is calculated as the average fitness of each disk supplemented by information describing the relationship between both adjacent disks. The method for calculation of function values was selected so as to ensure its maximisation in the process of evolution. Although promising results of the genetic algorithms operation were achieved, one can consider further improvement of the method efficiency. The authors used morphological operations in order to better adopt the method to the task.

One of the most dangerous diseases for humans is the Arterial Hypertension, which this kind of disease that often leads to fatal outcomes, such as heart attack, stroke and renal failure. The hypertension seriously threats the health of the people worldwide. One of the dangerous aspects of the hypertension is that you may not know that you have it. In fact, nearly one-third of people who have high blood pressure don’t know it. The only way to know if the blood pressure is high is through the regular checkups. The evaluation of a patient with Hypertension should (1) confirm the diagnosis of hypertension, (2) detect causes of secondary hypertension y (3) assess cardio vascular risk and organ damage. Therefore, is very important a correct measurement of the blood pressure (BP). Traditionally, office BP measurement has been performed using a sphygmomanometer and stethoscope. Recently, automated office and home BP measurements has been proposed as an alternative to traditional measurement. It has several advantages over manual BP, especially in routine clinical practice. Therefore, we have developed a Fuzzy System for the diagnosis of the Hypertension. Firstly, the input parameters include Systolic Blood Pressure and Diastolic Blood Pressure. Secondly, we have as an output parameter: Blood Pressure Levels (BPL). The input linguistic value includes Low, Low Normal, Normal, High Normal, High, Very High, Too High and Isolated Systolic Hypertension. Finally, we have 14 fuzzy rules to determine the diagnosis output.

In this paper we are presenting the recently proposed approach Intercriteria Analysis (ICrA) for assessment of the pollution index of the Struma River in Bulgaria. The approach is based on the apparatus of the index matrices and the intuitionistic fuzzy sets. At the first we have investigated all indexes at the all measurement point with ICrA and we have searched the dependences between points. Results show the measurement points are dependent criteria and we have ignored some over others. At the second we have applied the ICrA to establish the pollution relations and the model structure based on different criteria involved in the Struma River. The investigations show that there are three positive consonances and dissonances between criteria. Using of a Modification of the Time Series Analysis (MTSA) method we have developed an adequate mathematical model of the pollution dynamic as function of time.

In this paper we present an application of the InterCriteria Decision Making (ICDM) approach to real data extracted from the Polish University Ranking System [13] in the years 2012–2014. The aim is to analyze the correlations between the indicators used by the Ranking System.

This paper presents the new approach of creating the database of acoustic units in concatenative TTS synthesis. Nowadays databases like this are created manually, which is very time-consuming and takes at least several months of work. Creation such base in automatic way shortens this time to hours. One of the next problem in the concatenative synthesis is the problem of reproduction any text using a voice and a way of speaking of particular man. Presented algorithms allow to create the allophone units database of particular man after receiving a sample of his voice and as a result synthesizer speaking with exactly this voice.

In this investigation recently developed InterCriteria Analysis (ICA) is applied aiming at examination of the influence of a genetic algorithm (GA) parameter in the procedure of a parameter identification of a fermentation process model. Proven as the most sensitive GA parameter, generation gap is in the focus of this investigation. The apparatuses of index matrices and intuitionistic fuzzy sets, laid in the ICA core, are implemented to establish the relations between investigated here generation gap, from one side, and model parameters of fed-batch fermentation process of Saccharomyces cerevisiae, from the other side. The obtained results after ICA application are analysed towards convergence time and model accuracy and some conclusions about observed interactions are derived.