Departing from how the speaker became involved, and by what he did work with fuzzy sets and fuzzy logic, an (obviously subjective) look at their future will be discussed. Namely, by arguing on some aspects such research could follow to not only being a theoretic ground for Zadeh’s Computing with Words,...

In this age, big data applications are increasingly becoming the main focus of attention because of the enormous increment of data generation and storage that has taken place in the last years, in science, business, . . . This situation becomes a challenge when huge amounts of data are processed to extract...

In this talk, I will discuss our research in leveraging Big Data for the Common Good. I will provide an overview of different research initiatives in my research program in network and data science, including applications to grand societal challenges. I will focus on our research initiative in patient-centered...

This talk aims to discuss the main challenges in evolutionary optimization of complex systems to bridge the gap between the academic research and the urgent demands from industry. We will show that, while solving “hard” problems, such as multi-modal and strongly correlated problems, multi-objective optimization...

Closure operators defined on various sets (set of all classical fuzzy sets, set of all semi-cuts, set of all cuts in a Q-set, etc.) are investigated and it is shown how a closure operator defined on one set can be extended to a closure operator defined on another set.

This paper deals with square roots of a matrix over a complete lattice, where the matrix composition is _ U with U being an infinitely _-distributive isotonic operator. We give a general characterization for the existence of a square root of a matrix over a complete lattice. Furthermore, we give methods...

In this paper, we consider the structure of solution sets of fuzzy relation equations over complete Boolean algebras. We show that each solution of a system of fuzzy relation equations can be represented by a linear combination of a special solution of its and some certain solutions of the homogeneous...

A preference matrix is the result of pairwise comparison and is a powerful method in multi-criteria optimization. When comparing two elements, the decision maker assigns the value from a given scale which is a linearly ordered Abelian group (Alogroup) to any pair of alternatives representing the element...

Conditionally firing rules have been proposed by B. Moser and M. Navara in order to preserve natural properties that are not preserved by the usual setting of fuzzy inference systems such as Mamdani- Assilian rules joined to the CRI inference mechanism. In this paper, we follow this direction and show,...

Fuzzy relational compositions have been extensively studied by many authors. Especially, we would like to express studies of the fuzzy relational compositions motivated by their applications to medical diagnosis by Willis Bandler and Ladislav Kohout. These types of compositions use only two quantifiers:...

Three ways to find lower approximations of a given fuzzy operator are given. A Representation Theorem for fuzzy consequence operators is obtained.

This paper presents a new concept for the decomposition of fuzzy numbers into a finite number of α-cuts. Instead of subdividing the µ axis in an equidistant way, we suggest to subdivide the x axis equidistantly leading to a more efficient decomposition of the µ axis. Considering the interpolation...

For each single-parameter Gini social evaluation function, and by using the dual decomposition of the OWA operators, we derive two contributing factors. The …rst one, the self-dual core that can be considered as a positional measure, similar to the mean. The second one, the anti-self dual remainder,...

The work considers the problem of solving a system of fuzzy relational equations with inf-implication composition and introduces the concepts of a characteristic matrix and attainable components. It is first shown that solving the system is closely related with the covering problem. Further, it is proved...

The paper gives the systematic characterization of eigenspace in max-T algebra where T is equal to ukasiewicz t-norm. Max- ukasiewicz fuzzy algebra can be used for the description of the states of Discrete-event systems. The states can represent a balance of the resource unit expended during the evolution...

Graph clustering is a very popular research field with numerous practical applications. Here we focus on finding fuzzy clusters of nodes in unweighted, undirected, and irreflexive graphs. We introduce three new algorithms for fuzzy graph clustering (Newman–Girvan NERFCM, Small World NERFCM, Signal NERFCM)....

The steady states of a fuzzy discrete dynamic system correspond to invariants (eigenvectors) of the transition matrix of the system. The structure of the eigenspace of a given fuzzy matrix is considered for various max-T algebras, where T is some triangular norm (Gödel, ukasiewicz, product, drastic)....

We take advantage of a recent development in Social Choice in order to propose a new algorithm for the prioritization of objects characterized by fuzzy soft sets. It benefits from the performance of an endogenous scoring rule recently proposed by Herrero [1]. Our procedure constructs a “comparison matrix”...

The aim of this contribution is to discuss the characterizations of L-semilinear spaces which are generated by strong linearly independent vectors. First, we show that the basis in L-semilinear spaces which are generated by strong linearly independent vectors is also strong linearly independent. Then...

The paper proposes a novel fuzzy system structure to enhance the performance of fuzzy neural network systems. The structure of enhanced fuzzy system (EFS) is to decompose each fuzzy variable into fuzzy subsystems called component fuzzy systems to act as type 2 fuzzy, and each component fuzzy system is...

The law of contraposition with respect to a negation (usually strong) is one of the most studied properties in the theory of fuzzy implication functions. We already know some methods for modifying an implication with the aim that the new implication satisfies this property, these methods are called contrapositivisation....

Since Sen’s seminal article in 1976, it is very known that every poverty measure should be sensitive to the three components of poverty: incidence, intensity and inequality. The paper concentrates on the poverty measure proposed by Kakwani. If the Kakwani index is normalized, an ordered weighted averaging...

Empirical studies show that individual investors do not always behave rationally and do not use standard investment portfolio selection tasks. In this paper we focus on investor choices and the basic elements affecting them. The paper presents optimization model based on a measure of investor satisfaction....

To face the big data challenge, sampling can be used as a preprocessing step for clustering. In this paper, an hybrid algorithm is proposed. It is density-based while managing distance concepts. The algorithm behavior is investigated using synthetic and realworld data sets. The first experiments proved...

Uncertainty treatment in self-optimising systems touches two design-issues. Firstly, a valid estimation of uncertainties within the system is impossible beforehand as the uncertainties as well as the systems behaviour changes during run-time due to self-optimisation. Secondly, the design of a selfoptimising...

Rule-level feature selection, also termed as rule compression, is an important technique for improving interpretability of fuzzy rule-based classifiers. In this paper we present three different rule compression algorithms and analyze their performance and characteristics on the classifiers identified...

Soft Computing is being widely used in Information Security applications. Particularly, Neuro-Fuzzy approach provides a classification with humanunderstandable rules, yet the accuracy may not be sufficiently high. In this paper we seek for an optimal fuzzy patch configuration that uses elliptic fuzzy...

The paper presents a generalization of the Strength Pareto Evolutionary Algorithm 2 (SPEA2) and its application in selected well-known two- and threeobjective optimization benchmark problems. The proposed solution is referred to as our SPEA3. The generalization consists in the exchange of the environmental...

This paper presents our clustering technique based on generalized SOMs with evolving splittingmerging tree-like structures and its application to complex clustering problems including some benchmark data sets and, first of all, WWW-document clustering. Our approach that works in a fully unsupervised...

Possibilistic networks are important tools for modelling and reasoning, especially in the presence of imprecise and/or uncertain information. These graphical models have been successfully used in several real applications. Since their construction by experts is complex and time consuming, several researchers...

The analysis of the perceptual properties of texture plays a fundamental role in tasks like semantic description of images or content-based image retrieval using linguistic queries. In this paper, we propose to model these properties by means of fuzzy sets defined on the domain of some representative...

Aggregation theory often deals with measures of central tendency of quantitative data. As sometimes a different kind of information fusion is needed, an axiomatization of spread measures was introduced recently. In this contribution we explore the properties of WDpWAM and WDpOWA operators, which are...

In this paper the concept of fuzzy descriptor as a level-two fuzzy set to represent some visual features is proposed. In particular, a fuzzy descriptor based on the dominance of color and texture features is defined and applied to image retrieval. For this purpose, the color and texture are modelled...

In this paper a weaker kind of transitive property for interval-valued fuzzy relations (IVFRs) is introduced. It is called ’only comparable’ T-transitivity because it relaxes the need that all intervals must be comparable, by just the need of having T-transitive cycles only for comparable intervals....

Modus Ponens is a key property for fuzzy implication functions that are going to be used in fuzzy inference processes. In this paper it is investigated when fuzzy implication functions derived from uninorms via residuation, usually called RUimplications, satisfy the modus ponens with respect to a continuous...

Identifying suspicious financial transactions and linking relevant records is an important data related problem. An appropriate identification may improve fraud detec-tion and international security. The main problems in this linking process are the missing data, errors in the entries or out of date...

Association rules is a useful tool to extract new information from raw data expressed in a comprehensive way for decision makers. However, in some applications raw data might not be available for several reasons. First, stream data are only temporarily available for their processing or if it is stored,...

Hesitant fuzzy sets are an extension of ordinary fuzzy sets. They are composed of dual hesitant fuzzy sets, interval valued hesitant fuzzy sets, generalized hesitant fuzzy sets, hesitant fuzzy linguistic term sets, and triangular fuzzy hesitant fuzzy sets. Multiexperts evaluations are integrated by aggregation...

In this paper we introduce a class of linear orders for discrete gradual real numbers. Based on the linear orders we propose an OWA operator on the set of discrete gradual numbers and discuss some its properties. This is a first step of our intentions to introduce a class of linear orders, and consequently...

When summarizing the location of a random fuzzy number, some more robust approaches than the well-known Aumann-type mean have been proposed in the literature. Among them, the φ-wabl/ldev/rdev median extends the concept of median from the real-valued case. The characterization for fuzzy numbers and...

This paper develops a PI-like interval type-2 (IT2) fuzzy maximum power point tracking (MPPT) control method for a class of wind power generation and battery charging systems with DC/DC buck converters. After the brief model descriptions of the wind power turbine, generator and DC/DC buck converter,...

We present an axiomatic approach to conditional measures of fuzzy events which is inspired by the Dupré–Tipler argument for Bayesianism. Unlike there or in the older and related Cox argument, although we are able to derive additive probabilities other non-additive solutions exist. Our motivation is to...

One of the core problems in soft computing is dealing with uncertainty in data. In this paper, we revisit the formal foundation of a class of probabilistic databases with the purpose to (1) obtain data model independence, (2) separate metadata on uncertainty and probabilities from the raw data, (3) better...

This paper shows the use of Fingrams –Fuzzy Inference-grams– aimed at unveiling graphically some hidden details in the usual behavior of the precise fuzzy modeling algorithm FURIA –Fuzzy Unordered Rule Induction Algorithm–. FURIA is recognized as one of the most outstanding fuzzy rule-based classification...

In Game theory, there are situations in which it is very difficult to characterize the private information of each player. In this case, the payoffs can be given by approximate values, represented by fuzzy numbers. Whenever there is uncertainty in the modeling of those fuzzy numbers, interval fuzzy numbers...

Likelihood functions, as well as the more recent concept of evidential likelihood, are essential statistical tools to perform estimation. Beyond the maximal likelihood value, the shape of the likelihood can also give interesting information about the data used to get the estimation. Indeed, it is generally...

The fast and accurate forecasting thod can help mak-ers to make appropriate strategy. Zadeh was given the efinition of a fuzzy set in 1965. Song and Chissom proposed the definition and the forecasting framework of fuzzy time series in 1993. Sullivan and Woodall first proposed the forecasting method to...

In this article, we present an algorithm for defuzzifying multiple fuzzy sets simultaneously, where the defuzzified values are bound by a constraint. The algorithm aims at maximizing the lowest membership grade of the defuzzified values in each fuzzy set, while satisfying the constraint. In the examples,...

We propose a poverty measure based on a non trivial balance between the aggregated value of the income gaps of the poor and the headcount ratio of the poor in the population. The new poverty measure extends a previous proposal also based on the exponential mean but with an exclusive focus on the poor...

We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at the treatment of fuzzy IF-THEN rules as linguistically expressed genuine logical implications. Besides the original PbLD, we propose a new balancing variant of PbLD, introduce both variants with fuzzy inputs...

Interval-Valued Fuzzy Sets handle uncertainty and vagueness effectively. These features are particularly useful for clustering. In this paper it is showed the utility of Interval-Valued Fuzzy Sets for clustering with no accurate information. An easy method for clustering is proposed by generating transitive...

In some cases, the relationship between an object set X and an attribute set Y is set up by means of a fuzzy context sequence. A particular case of this situation appears when we want to study the evolution in time of a fuzzy context. In this work, we deepen in the study of these situations. First we...

In a group decision making setting, we consider the potential impact an expert can have on the overall ranking by providing a biased assessment of the alternatives that differs substantially from the majority opinion. In the framework of similarity based veraging functions, we show that some alternative...

Opinion formation is well used to investigate a consensus or several clusters among the opinions of a group of interaction agents. This study proposes several bounded confidence models to discuss the uncertain opinion formation. In the proposed models, the agents’ various tolerances (zero-tolerance,...

The K-Nearest Neighbors (k-NN) classifier has become a well-known, successful method for pattern classification tasks. In recent years, many enhancements to the original algorithm have been proposed. Fuzzy sets theory has been the basis of several proposed models towards the enhancement of the nearest...

In this paper the method for the minimum cost flow determining in fuzzy dynamic network with nonzero lower flow bounds is proposed. Considered method takes into account fuzzy nature of networks’ parameters and deals with fuzzy arc flow bounds, fuzzy transmission costs. Fuzzy arc flow bounds, costs and...

Histograms are a tool for graphical representation of frequency data and thus helpful in creating a fast understanding of, e.g., contents of frequency data. Comparing histograms is topic of increasing importance due to an increase in the availability of data sets containing frequency information. Automatic...

In this paper we introduce the concepts of a multimode multi-relational fuzzy network and a regular fuzzy equivalence on such a network, and provide procedures for computing the greatest regular fuzzy and crisp equivalences contained in a given tuple of fuzzy equivalences.

In this paper we introduce two types of simulations and five types of bisimulations for fuzzy social networks, and we study one of them – regular bisimulations. We prove that if there exists at least one regular bisimulation between two fuzzy networks, then there exists the greatest bisimulation of this...

The goal of this study is to introduce a novel exact string searching (i.e., matching) method based on the fuzzy transform, or F-transform (FTSS). The theoretical background of the F-transform, specifically the Fs-transform, s 0, for functions of one variable is reviewed, and a string searching algorithm...

In this paper we describe recent advances in our R code similarity detection algorithm. We propose a modification of the Program Dependence Graph (PDG) procedure used in the GPLAG system that better fits the nature of functional programming languages like R. The major strength of our approach lies in...

The previous correlation measures for hesitant fuzzy sets proposed in the literature only capture the strength of the correlations. We present a new approach based on the classical Pearson correlation coefficient for crisp values. In this way we can express not only the strength of the relationship between...

Medoid clustering frequently gives better results than those of the K-means clustering in the sense that a unique object is the representative element of a cluster. Moreover the method of medoids can be applied to nonmetric cases such as weighted graphs that arise in analyzing SNS(Social Networking Service)...

Axiomatic generalizations of OWA operators are introduces and discussed. First, OMA operators based on comonotone modularity are recalled. Then, several kinds of comonotone pseudo-additivity based OWA generalizations are characterized and exemplified. Some of already known OWA generalizations are thus...

Evolutionary Fuzzy Systems (EFSs) are fuzzy systems augmented by a learning process based on evolutionary computation such as evolutionary algorithms (EAs). These systems contribute with several advantages in the development of algorithms, and specifically in the development of subgroup discovery (SD)...

The recurrent exponential fuzzy associative memory (RE-FAM) can be viewed as a recurrent neural network that employs a fuzzy similarity measure in its hidden layer. This paper introduces the generalized recurrent exponential fuzzy associative memory (GRE-FAM). In contrast to the RE-FAM, the GREFAM is...

We present a technique for size reduction of a base of fuzzy association rules which is created using an automated approach and which is intended for inference. Our approach is based on controlling the coverage of training data by the rule base and removing only such rules that do not increase that coverage....

Soft computing techniques may provide various forms of human-consistent summaries about large time series databases, e.g., linguistic summaries, frequent patterns, fuzzy IF-THEN rules. Within this research, we focus on linguistic summaries constructed as linguistically quantified propositions, that may...

This paper presents a new technology for automatically generating linguistic reports and immediate feedback from actions performed by players during play sessions. These reports allow us to provide players with a more complete and personalized feedback about their behaviors, abilities, attitudes, skills...

In the field of informetrics, agents are often represented by numeric sequences of non necessarily conforming lengths. There are numerous aggregation techniques of such sequences, e.g., the g-index, the h-index, that may be used to compare the output of pairs of agents. In this paper we address a question...

Probabilistic and fuzzy choice theory are used to describe decision situations in which a certain degree of imprecision is involved. In this work we propose a correspondence between probabilistic and fuzzy choice functions, based on implication operators. Given a probabilistic choice function a fuzzy...

We present a quality-based fuzzy linguistic recommender system for researchers. We propose the use of some bibliometrics measures as the way to quantify the quality of both items and users. The system takes into account the measured quality as the main factor for the re-ranking of the top-N recommendations...

The more skills a student acquires, the more successful this student is with the corresponding tasks. Empirical data shows that the success in a task grows as a logistic function of skills; this dependence is known as the Rasch model. In this paper, we provide two uncertainty-based justifications for...

Haptic feedback is currently emerging as a feasible solution to cope with the security-related issues of automobile touch-screen displays, and at the same time to improve users satisfaction and quality of use. Therefore, we have developed a fuzzy symbolic model of haptic perception for automobile interfaces...

Rule base generation from numerical data has been a dynamic research topic within the fuzzy community in the last decades, and several well-established methods have been proposed. While some authors presented simple, empirical approaches, but which generally show high error rates, others turned to complex...

In this paper we will inquiry about the role of precise and imprecise syllogisms for diagnosing reasoning im-pairments in people suffering some mental disorders. Additionally, we propose some new questions that can help to better understand the already studied deficits and, perhaps, to progress in the...

The K-means algorithm is one of the most often used clustering techniques. However, when it comes to discovering clusters in informetric data sets that consist of non-increasingly ordered vectors of not necessarily conforming lengths, such a method cannot be applied directly. Hence, in this paper, we...

The notion of social roles is a centerpiece of most sociological theoretical considerations. Regular equivalences arise as a result of an attempt to capture the sociological notion of a relational or structural role. Regular equivalences were introduced by White and Reitz in [28] as the least restrictive...

Nowadays, decision making using fuzzy logic is a ma-jor research area for scientists, researchers and project managers. Construction of membership functions and fuzzy rules from numerical data is very important in various applications of the fuzzy set theory. Therefore, in this paper a model is proposed...

This paper presents an extension of Fuzzy Deformable Prototypes (FDPs) based on the use of interval type-2 fuzzy sets. The aim is to improve FDPs’ capabilities for managing uncertainty and imprecision. This extension is applied to predict the academic performance of the students who make use of Web-based...

In the setting of fuzzy choice functions (Georgescu [6]), we explore the relationships among known and new consistency axioms. Then we define the notion of sequential application of fuzzy choice functions, and investigate its normative implications. The Fuzzy Arrow Axiom is preserved by this sequential...

Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0, 1]. So, we can apply techniques of interval-valued fuzzy sets to fuzzy automata. In particular, we prove that Atanassov’s...

We state a problem concerning how to make an effective and proper decision in the presence of data incompleteness. As an example we consider a medical diagnostic system where the problem of missing data is commonly encountered. We propose and evaluate an approach that makes it possible to reduce the...

Interval AHP was proposed to express the decision maker’s vague evaluations on criteria by interval weights from a given pairwise comparison matrix. It has been extended to group decision problems. Three complementary approaches have been proposed: the perfect incorporation approach for counting out...

Type – II fuzzy number is introduced in decision mak-ing analysis as a concept that is capable to effectively deal with uncertainty in the information about a deci-sion. As type – II fuzzy number is represented by possi-bility distribution, it is hard to determine which type – II fuzzy number is greater...

This paper establishes a theory of decision making under uncertainty with fuzzy utilities. The extension of expected utility and stochastic dominance to the comparison of sets of random variables plays a crucial role. Their properties as fuzzy rankings are studied, and their definitions are further generalized...

In a previous work we proposed to enhance the performance of FARC-HD fuzzy classifier in multi-class classification problems using decomposition strategies. This synergy was further improved by introducing n-dimensional overlap functions in the learning algorithm and the inference of FARC-HD instead...

We propose using fuzzy time series (FTS) to forecast the future performance of returns on portfolios. We model the portfolio selection problem by means of possibilistic moments, and approximate the uncertainty of the return on a given portfolio by trapezoidal fuzzy numbers. Some modifications into the...

In this paper, the integration of mutual information (MI) and fuzzy model is proposed to predict stock indexes with complex and non-linear characteristics. Technical indicators are considered as initial input candidates and significant inputs are determined by MI-based input selection method. To identify...

Once introduced a definition of symmetric difference function on the unit real interval [0,1], we consider a method to construct such functions based on a triplet formed by a t-norm, a t-conorm and a strong negation. Our main goal is to characterize those triplets that define symmetric difference functions...

Competitive intelligence analysis based on user gener-ated contents (UGCs) shows advantages on possessing the benefit of the wisdom of crowds, evading cognitive biases and timely updating. This paper investigates and constructs a bipartite graph model by extracting joint co-occurrence of competitors...

This work aims to develop a practical study of the uni-norms as rule antecedent aggregation operator family in Linguistic Fuzzy Modeling. Although they are well known from a theoretical point of view, they have only recently been introduced in a few specific and recent applications. Uninorms are parameterized...

In this paper we review four fuzzy extensions of the socalled tight pair of covering based rough set approximation operators. Furthermore, we propose two new extensions of the tight pair: for the first model, we apply the technique of representation by levels to define the approximation operators, while...

This paper presents a software aimed at making easier the design of customized products in accordance with consumers’ expectations. It is based on a user-centered design methodology which combines techniques provided by Kansei Engineering, Sensory Analysis, and Soft Computing. Consumers’ expectations...

In the context of data mining, missing data can be handled in several ways. The most common is the artificial construction of missing data, but we can predict it, or transform the whole database in a fuzzy way. In this article we propose a different approach: we extend our rough classification to incomplete...

Path-finding algorithms (PFA) are successfully used to find the optimal path between two locations. Good results are obtained if they are used in scenarios where the entire environment can be described mathematically. Production environments of automated guided vehicles (AGVs) are not one of those. PFA...

We consider the task of finding frequent parallel episodes in parallel point processes, allowing for imprecise synchrony of the events constituting occurrences (temporal imprecision) as well as incomplete occurrences (selective participation). We tackle this problem with frequent pattern mining based...

We explore the possible benefit that provides a linguistic approach to Big Data. The proposal illustrates how implement Linguistic Aggregation Functions using the MapReduce paradigm. The best known paradigm applied to Big Data. The proposal allows several benefits to Big Data e.g., it allows to interpret...

Fuzzy sets are a popular tool to model vague properties. It is, however, well-known that this model usually involves a good degree of arbitrariness. In this contribution we consider the possibility of standardising the construction of fuzzy sets at least withregard to the borderline cases. To this end,...

Several definitions of difference between fuzzy numbers are well established in literature: standard, Hukuhara, generalized Hukuhara, generalized, CIA and other differences based on joint possibility distributions. We present and compare them. An example of epidemiological model of a disease with direct...