# Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)

126 articles

**Proceedings Article**

## On a Graded Inclusion of Bipolar Fuzzy Relations

Ludovic Liétard, Olivier Pivert, Daniel Rocacher

This paper deals with database fuzzy queries in the context where the fuzzy preference conditions involved are of a bipolar nature (the first pole corresponding to a constraint, the second to a wish). More precisely, we consider queries where an inclusion-based condition comes into play (a typical example...

**Proceedings Article**

## Applications of Categorical Fixed-basis Fuzzy Topological Spaces to A-valued Spaces

Mustafa Demirci

As an application of the dual equivalence between the category of L-spatial C-objects and the category of L-sober C-M-L-spaces, it is shown in this paper that for a fixed augmented partially ordered set A, there exists a dual equivalence between the category of A-spatial augmented partially ordered sets...

**Proceedings Article**

## Ensembled Self-Adaptive Fuzzy Calibration Models for On-line Cloud Point Prediction

Carlos Cernuda, Edwin Lughofer, Peter Hintenaus, Wolfgang Märzinger, Thomas Reischer, Marcin Pawlicek, Jürgen Kasberger

In this paper we investigate the usage of non-linear chemometric models, which are calibrated based on near infrared (FTNIR) spectra, in order to increase efficiency and to improve quantification quality in melamine resin production. They rely on fuzzy systems model architecture and are able to {incrementally...

**Proceedings Article**

## Data Reconciliation under Fuzzy Constraints in Material Flow Analysis

Didier Dubois, Hélène Fargier, Dominique Guyonnet

Data reconciliation consists in modifying noisy or unreliable data in order to satisfy a mathematical model (herein a material flow network). The conventional approach relies on least squares minimization. Here we show that the setting of fuzzy sets provides a generalized approach that is more flexible...

**Proceedings Article**

## Distance calculation between Level-2 fuzzy regions

Jörg Verstraete

In many applications, spatial data is often prone to uncertainty and imprecision. To model this, fuzzy regions have been developed. Our initial model was a fuzzy set over a two dimensional domain, allowing for fuzzy regions and fuzzy points to be modelled. The model had some limitations: all points where...

**Proceedings Article**

## F-transform and Fuzzy Natural logic in Time Series Analysis

Vilem Novak, Viktor Pavliska, Irina Perfilieva, Martin Stepnicka

This paper continues development of the innovative method of time series analysis and forecasting using special soft-computing techniques: fuzzy transform and Fuzzy Natural Logic. We will demonstrate that the F-transform is a proper technique for extraction of the trend-cycle of time series. Furthermore,...

**Proceedings Article**

## Tomonoid extensions: the key for the construction of t-norms

Thomas Vetterlein

Triangular norms, or t-norms for short, play an important role for the semantics of fuzzy logics. Although an enormous number of examples and a remarkable number of construction methods for this kind of operation has been established, a uniform approach is still outstanding. This paper is devoted to...

**Proceedings Article**

## A Note on Fuzzy Soft Topological Spaces

Vildan Cetkin, Halis Aygun

The main aim of this paper is to give a characterization of FSTOP, the category of fuzzy soft topological spaces and its continuous mappings. For this reason, we construct the category of antichain soft topological spaces and its continuous mappings, denoted ASTOP, and show that FSTOP is isomorphic to...

**Proceedings Article**

## Determination of regional variants in the versification of Estonian folksongs using an interpretable fuzzy rule-based classifier

Andri Riid, Mari Sarv

In this paper, a method of hierarchical clustering and a selection of fuzzy classification algorithms are applied successively to the data set that contains measured characteristics of folk verses collected from 104 historical parishes of Estonia. The aim of the study is to detect the groups of parishes...

**Proceedings Article**

## Fuzzification of probabilistic objects

Martin Papco

A categorical approach to probability allows to put basic notions of probability into a broader mathematical perspective, to evaluate their roles, and mutual relationships. Classical probability theory and fuzzy probability theory lead to two particular categories and their relationship (in categorical...

**Proceedings Article**

## A Stochastic Model for Analyzing the Interpretability-Accuracy Trade-off in Interpretable Fuzzy Systems Using Nested Hyperball Structures

Balázs Krisztián, Koczy Laszlo T.

Our recent work proposed a new meaning preservation approach together with a parameterizable nested hyperball structured search space for interpretable fuzzy systems in order to solve a problem of inconsistency observed in conventional interpretablefuzzy knowledge bases and simultaneously to address...

**Proceedings Article**

## Triangular norms which are join-morphisms in 3-dimensional fuzzy set theory

Glad Deschrijver

The n-dimensional fuzzy sets have been introduced as a generalization of interval-valued fuzzy sets, Atanassov's intuitionistic and interval-valued intuitionistic fuzzy sets. In this paper we investigate t-norms on 3-dimensional sets which are join-morphisms. Under some additional conditions we show...

**Proceedings Article**

## Holistic Preference Learning with the Choquet Integral

Bénédicte Goujon, Christophe Labreuche

The current approaches to construct a multi-criteria model based on a Choquet integral are split into two separate steps: construct first the utility functions and then the aggregation function. Unfortunately, the decision maker may feel some difficulties in addressing these tricky steps. In this paper,...

**Proceedings Article**

## A Genetic Tuned Fuzzy Classifier Based on Prototypes

Enrique Leyva, Antonio González, Raúl Pérez

It is known that main drawbacks of KNN classifier are related to the need for keeping all the training prototypes. Although there are several approaches capable to significantly reduce the size of the case base, they damage the classification accuracy. We propose a novel fuzzy approach capable to significantly...

**Proceedings Article**

## Introducing Floating Singletons with an example application in clinic spirometry

Luis Arguelles Mendez

Fuzzy-logic models where singletons are placed in the consequents of rules of the type if x is Ai and y is Bj then zi = si are used nowadays in many soft computing applications. In this work we introduce the concept of floating singletons where their precise location on the real axis is only known at...

**Proceedings Article**

## Reflections on a Fuzzy Logic of Scientific Discovery and Fuzzy Structures of Scientific Revolutions

Rudolf Seising

Popper’s Logic of Scientific Discovery and Kuhn’s Structures of Scientific Revolutions are enormous important concepts on theories and their dynamic in 20th century history and philosophy of science. However, the works of the two have been criticized in the last half century and new views on theory nets...

**Proceedings Article**

## Exploring Paraconsistency in Degree-Preserving Fuzzy Logics

Rodolfo Ertola, Francesc Esteva, Tommaso Flaminio, Lluis Godo, Carles Noguera

Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. In the last decade, mathematical fuzzy logic has been developed as a discipline studying formal many-valued systems underlying fuzzy logic in narrow sense. In this...

**Proceedings Article**

## Irreducible elements in multi-adjoint concept lattices

Jesús Medina-Moreno, Maria Eugenia Cornejo, Eloisa Ramírez

The irreducible elements in a lattice are very important. For example, when the lattice is finite, which is the usual in the computational case, they form a base from which the complete lattice is obtained. These elements are also important in Formal Concept Analysis, since they are the basic information...

**Proceedings Article**

## The incidence relation of an L-Fuzzy Context as structuring element in Fuzzy Mathematical Morphology

Cristina Alcalde, Ana Burusco, Ramon Fuentes-Gonzalez

The goal of this work is to prove a link between the Fuzzy Mathematical Morphology and the L-fuzzy Concept Analysis when we are using structuring relations which represent the effect that we want to produce over an initial fuzzy image or signal. In this case, we prove that the problem of obtaining the...

**Proceedings Article**

## Reasons for a careful design of fuzzy sets

Enric Trillas, Claudio Moraga

This paper is, basically, a reflection on modeling, starting by asking what happens when the meaning of a predicate P is interpreted by the membership function of a fuzzy set that, labeled P, is designed with the information available to the designer on the use of the predicate in the corresponding universe...

**Proceedings Article**

## Towards recommender systems based on a fuzzy preference aggregation

Samia Boulkrinat, Allel Hadjali, Aicha Mokhtari

An approach to deal with user preference relations, instead of absolute ratings, in recommender systems is discussed. User’s preferences are then ratings expressed qualitatively by using linguistic terms. This is a suitable technique when preferences are imprecise and vague. On the other hand, to avoid...

**Proceedings Article**

## A fuzzy tri-level decision making algorithm and its application in supply chain

Zhen Zhang, Guangquan Zhang, Jie Lu, Chonghui Guo

In this paper, we develop a fuzzy tri-level decision making (FTLDM) model to deal with decentralized decision making problems with three levels of decision makers. Based on the -cut of fuzzy set, we transform an FTLDM problem into a multi-objective multi-follower tri-level decision making problem. Based...

**Proceedings Article**

## On power stable quasi-copulas

Anna Kolesárová, Radko Mesiar

In our contribution we discuss the power stability of 1-Lipschitz binary aggregation functions. The main result is the characterization of power stable quasi-copulas by means of their dependence functions. The notions are illustrated by examples.

**Proceedings Article**

## Type-2 aggregation operators

Zdenko Takác

The paper deals with an extension of aggregation operators from the set of real numbers (or interval [0, 1]) to the set of fuzzy truth values (fuzzy sets in [0, 1]). We define so-called type-2 aggregation operator and show that an extension of ordinary aggregation operator by convolution is a type-2...

**Proceedings Article**

## About t-norms on type-2 fuzzy sets

Pablo Hernández, Susana Cubillo, Carmen Torres

Walker et al. ([19], [20]) defined two families of binary operations on M (set of functions of [0,1] in [0,1]), and they determined that, under certain conditions, those operations are t-norms (triangular norm) or t-conorms on L (all the normal and convex functions of M). We define binary operations...

**Proceedings Article**

## Use of the GAI model in multi-criteria decision making: inconsistency handling, interpretation

Christophe Labreuche, Michel Grabisch

This paper is devoted to the use of the GAI (Generalized Additive) model in a Multi-Criteria Decision Making context. We first discuss on some new conditions (concerning the sign and monotonicity) to add on the terms appearing in a GAI model. Secondly, we propose some algorithms to propose the learning...

**Proceedings Article**

## Sample-based XPath Ranking for Web Information Extraction

Oliver Jundt, Maurice Van Keulen

Web information extraction typically relies on a wrapper, i.e., program code or a configuration that specifies how to extract information for certain fields for a specific website. Manually creating and maintaining wrappers for all target websites is a cumbersome and error-prone task. It may even be...

**Proceedings Article**

## Shape Retrieval by Partially Supervised Fuzzy Clustering

Giovanna Castellano, Anna Maria Fanelli, Maria Alessandra Torsello

In this work we propose the use of partially supervised fuzzy clustering to create a two-level indexing structure useful for enabling efficient shape retrieval. Similar shapes are grouped by a fuzzy clustering algorithm that embeds a partial supervision mechanism exploiting domain knowledge expressed...

**Proceedings Article**

## A fuzzy methodology to alleviate information overload in eLearning

Fabio Aurelio D'Asaro, Valerio Perticone, Marco Elio Tabacchi

Some aspects of eLearning experience can be enhanced in a very natural way by using the basic tools offered by fuzzy logic. As a matter of example, consider the uncontrolled growth of information produced in a collaborative-oriented context, in which each participant (e.g. students, teachers) is able...

**Proceedings Article**

## Theory of Computation, Fuzziness and a physics of the immaterial

Marco_Elio Tabacchi, Settimo Termini

In this paper we advance three clear-cut proposals as a contribution to the discussion on the role of Theory of Computation and Fuzziness as a bridge between Hard and Soft Sciences. We suggest that an important difference between the two great families of science lies in their subject or research having...

**Proceedings Article**

## Using a Linguistic Scorecard for Peer-Assessment Through an On-Line System

Pasi Luukka, Mikael Collan

Peer-assessment is a way to include evaluation as a part of the learning process and simultaneously to cut teacher load in grading of assignments. eLearning systems can be used to automate peer-assessment to a large extent. Peer-assessment benefits from multiple-peer-assessment as it is likely to even-out...

**Proceedings Article**

## Evaluation and interval approximation of fuzzy quantities

Luca Anzilli, Gisella Facchinetti, Giovanni Mastroleo

In this paper we present a general framework to face the problem of evaluate fuzzy quantities. A fuzzy quantity is a fuzzy set that may be non normal and/or non convex. This new formulation contains as particular cases the ones proposed by Fortemps and Roubens (1996), Yager and Filev (1981,1999) and...

**Proceedings Article**

## Fuzzy implications satisfying convexity relations

Mirko Navara

It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

**Proceedings Article**

## Constructing non-functionally expressible fuzzy implications

Sebastià Massanet, Gaspar Mayor, Joan Torrens

This article discusses a new method for the construction of non-functionally expressible fuzzy implications. In a recent work, we have considered non-functionally expressible fuzzy implications from an implication function acting on the inputs followed by an aggregation process. Now, we first perform...

**Proceedings Article**

## First-order EQ-logic

Martin Dyba, Vilém Novák

This paper represents the third step in the development of EQ-logics. Namely, after developing propositional and higher-order EQ-logics, we focus also on predicate one. First, we give a brief overview of the propositional EQ-logic and then develop syntax and semantics of predicate EQ-logic. Finally,...

**Proceedings Article**

## Coimplications in the set of discrete fuzzy numbers

Juan Vicente Riera, Joan Torrens

Given a coimplication function $J$ defined on the finite chain $L_n={0,...,n}$, a method for extending $J$ to the set of discrete fuzzy numbers whose support is an interval contained in $L_n$ (denoted by ${cal A}_1^{L_n}$) is given. The resulting extension is in fact a fuzzy coimplication on ${cal A}_1^{L_n}$...

**Proceedings Article**

## A fixed-shape fuzzy median of a fuzzy sample

Adrian Ban, Lucian Coroianu, Przemyslaw Grzegorzewski

Since fuzzy numbers are not linearly ordered a median of a fuzzy sample cannot be determined directly as it happens with crisp observations. Even the very notion of a median of a fuzzy sample is not well established. Therefore we propose some definitions of the fixed-shape fuzzy median of a fuzzy sample...

**Proceedings Article**

## Priestley duality for N4-lattices

Ramon Jansana, Umberto Rivieccio

We present a new Priestley-style topological duality for N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras...

**Proceedings Article**

## Optimum Allocation of Centers in Transportation Networks by Means of Fuzzy Graph Bases

Leonid Bershtein, Alexandr Bozhenyuk, Igor Rozenberg

In this paper the questions of defining the optimum allocation of centers in fuzzy transportation networks are observed by the minimax criterion. It is supposed that the information received from the geographical information system is presented as a fuzzy graph. In this case the task of defining optimum...

**Proceedings Article**

## Forecasting Exchange Rates with Fuzzy Granular Evolving Modeling for Trading Strategies

Leandro Maciel, Fernando Gomide, Rosangela Ballini

This paper addresses a fuzzy set based evolving modeling (FBeM) approach and the task of forecasting exchange rates in order to perform trading strategies. FBeM is a granular computing technique that uses fuzzy information granules to model nonstationary functions providing functional and linguistic...

**Proceedings Article**

## A fuzzy extension of explanatory relations based on mathematical morphology

Jamal Atif, Isabelle Bloch, Felix Distel, Hudelot Celine

In this paper, we build upon previous work defining explanatory relations based on mathematical morphology operators on logical formulas in propositional logics. We propose to extend such relations to the case where the set of models of a formula is fuzzy, as a first step towards morphological fuzzy...

**Proceedings Article**

## The analysis of the generalized square of opposition

Petra Murinová, Vilém Novák

In this paper, we continue development of a formal theory of intermediate quantifiers (linguistic expressions such as ``most'', ``many'', ``few'', ``almost all'', etc.). In previous work, we demonstrated that 105 generalized syllogisms are valid in our theory. We turn our attention to another problem...

**Proceedings Article**

## Fuzzy preference modelling and some consequences for fuzzy implications and quasi-copulas

Dana Hlin ná, Martin Kalina, Pavol Krá

In this paper we study connection between quasi-copulas and generator triples of a fuzzy preference structures. We study also conditions under which fuzzy implications can be used to construct generator triples. As we show, an important property of fuzzy implications that enables us to construct a generator...

**Proceedings Article**

## Distance to bipolar information from morphological dilation

Isabelle Bloch, Jamal Atif

In this paper we propose definitions of distances to bipolar information. This notion is important to find a solution that matches bipolar queries, to exhibit recommendations satisfying preferences of an agent while respecting her constraints, to find an agreement between several agents. All these situations...

**Proceedings Article**

## Constructing implication functions from fuzzy negations

Aguiló Isabel, Suñer Jaume, Torrens Joan

A class of implication functions is constructed from fuzzy negations. The interest of this new class lies in its simplicity and in the fact that when $N$ is Id-symmetrical, the corresponding implication agrees with the residuum of a commutative semicopula.

**Proceedings Article**

## Flexible Querying of Volunteered Geographic Information for Risk Management

Paolo Arcaini, Gloria Bordogna, Simone Sterlacchini

The paper presents an approach to manage Volunteered Geographic Information (VGI) to point out anomalous conditions of the environment. This can help administrators in charge of the governance and maintenance activities of the territory to plan mitigation and safeguard interventions. To this end, a system...

**Proceedings Article**

## An analytical approach to evaluating monotonic functions of fuzzy numbers

Arthur Seibel, Josef Schlattmann

This paper presents a practical analytical approach to evaluating continuous, monotonic functions of independent fuzzy numbers. The approach is based on a parametric -cut representation of fuzzy numbers and allows for the inclusion of parameter uncertainties into mathematical models.

**Proceedings Article**

## Convex combination of grouping functions for image thresholding. Selection of weighting vectors

Aranzazu Jurio, Miguel Pagola, Daniel Paternain, Nicolas Madrid, Humberto Bustince

In this work we present a thresholding algorithm for greyscale images. Our proposal is based on the use of grouping functions to find the best threshold. These functions are able to measure the membership of a grey intensity to the background or to the object of the image, so the best threshold is the...

**Proceedings Article**

## On Different Types of Heterogeneous Formal Contexts

Ubomír Antoni, Stanislav Krajči, Ondrej Krídlo

We provide a generalization of another fuzzy formal contexts of Formal Concept Analysis that works with different types of the values in a context. An appropriate counterpart to the so-called basic theorem of concept lattice is formulated. We suggest the process of transformation of heterogeneous formal...

**Proceedings Article**

## Efficient energy dispatching in smart microgrids using an integration of fuzzy AHP and TOPSIS assisted by linear programming

Beatrice Lazzerini, Francesco Pistolesi

Energy dispatching in smart (micro)grids must take into account more conflicting objectives (or criteria), such as power reliability and quality, proper handling of the electricity demand, and cost decrease. The choice of the best alternative in energy dispatching decisions can be dealt with as a multi-criteria...

**Proceedings Article**

## Qualitative integrals and desintegrals as lower and upper possibilistic expectations

Didier Dubois, Henri Prade, Agnès Rico

Any capacity (i.e., an increasing set function) has been proved to be a lower possibility measure and an upper necessity measure. Similarly, it is shown that any anti-capacity (i.e., a decreasing set function) can be viewed both as an upper guaranteed possibility measure and as a lower weak necessity...

**Proceedings Article**

## On various forms of bipolarity in flexible querying

Didier Dubois, Henri Prade

The paper discusses the modeling of ''if possible" in requirements of the form ''A and if possible B". We distinguish between two types of understanding: either i) A and B are requirements of the same nature and are viewed as constraints with different levels of priority, or ii) they are of different...

**Proceedings Article**

## Partial first-order logic relying on optimistic, pessimistic and average partial membership functions

Tamás Mihálydeák

One of the common features of decision-theoretic rough set models is that they rely on total background (available) knowledge in the sense that the knowledge covers the discourse universe. In the proposed framework the author gives up this requirement and allows that available knowledge about the discourse...

**Proceedings Article**

## Building multi-adjoint concept lattices

Juan Carlos Díaz, J. Bosco García, Jesús Medina-Moreno, Rafael Rodríguez

In Formal Concept Analysis it is very important to study fast algorithms to compute concept lattices. This paper introduces an algorithm on the multi-adjoint concept lattice framework, in order to compute the whole concept lattice. This fuzzy framework is very general and provides more flexibility in...

**Proceedings Article**

## Prototype Construction for Clustering of Point Processes based on Imprecise Synchrony

Christian Borgelt, Christian Braune

We consider the task to cluster realizations of point processes, that is, lists of points in time. Our guiding principle is that two such lists are the more similar, the more (approximately) synchronous points they contain. This task occurs in the analysis of parallel spike trains in neurobiology, where...

**Proceedings Article**

## About Relation between the Measure of Conflict and Decreasing of Ignorance in Theory of Evidence

Alexander Lepskiy

The conflict measure and index of decreasing of igno-rance in frame of Dempster-Shafer theory are intro-duced. Those functionals are analyzed on the bodies of evidences of special type. It is shown that the great correlation between the bodies of evidence is a sufficient condition of decreasing of ignorance...

**Proceedings Article**

## A new integrated group decision making framework with linguistic interval fuzzy preference relations

Gulcin Buyukozkan, Sezin Güleryüz

The high complexity of socioeconomic environments often makes it difficult for a single decision maker (DM) to consider all the important aspects of some de-cision problems. Therefore, a group decision making (GDM) process is often preferred by the organizations. Moreover, during the decision process,...

**Proceedings Article**

## On the Role of Soft Computing in Modelling the Spread of Infectious Diseases

Nick Pizzi

Infectious disease modelling is an interdisciplinary research activity that has become more prevalent over the last decade as a valuable and practical tool for public health experts. Soft computing, with its suite of techniques and strategies, which effectively handles imprecise, approximate, and vague...

**Proceedings Article**

## Preservation of t-norm and t-conorm based properties of fuzzy relations during aggregation process

Urszula Dudziak

In the paper aggregations of fuzzy relations using functions of n variables are considered. After recalling properties of fuzzy relations, aggregation functions which preserve: reflexivity, irreflexivity, T-asymmetry, T-antisymmetry, symmetry, S-connectedness, T-transitivity, negative S-transitivity,...

**Proceedings Article**

## Fuzzy Rule-Based Approach for Detecting Adverse Drug Reaction Signal Pairs

Ayman Mansour

Detecting Adverse Drug Reactions (ADR) signal pairs is technically a complex problem. This is the case if we realistically assume that there does not exist a set of rules that are readily acceptable to all human experts (e.g., physicians, epidemiologists and pharmacists). The parameters used in identifying...

**Proceedings Article**

## Picking the one that does not fit - A matter of logical proportions

Henri Prade, Gilles Richard

Quiz or tests about reasoning capabilities often pertain to the perception of similarity and dissimilarity between situations. Thus, one may be asked to complete a series of entities $A$, $B$, $C$ by an appropriate $X$, or to pick the one that does not fit in a list. It has been shown that the first...

**Proceedings Article**

## New results on redundancies of fuzzy/linguistic IF-THEN rules

Lenka Stepnickova, Martin Stepnicka, Antonin Dvorak

In this paper we present new results on detection and removal of redundancies of IF-THEN rules in so-called linguistic descriptions (systems of such rules). We introduce an algorithm for removal of redundancies and describe a practical application.

**Proceedings Article**

## Fuzzy rule-based ensemble with use linguistic associations mining for time series prediction

Lenka Št pni ková, Martin Stepnicka, David Sikora

There are many various methods to forecast time series. However, there is no single forecasting method that generally outperforms any other. Consequently, there always exists a danger of choosing a method that is inappropriate for a given time series. To overcome such a problem, distinct ensemble techniques...

**Proceedings Article**

## New Framework of HSL System Based Color Clustering Algorithm

Vasile Patrascu

In this paper one presents a fuzzy c-means algorithm enhancement for the particular case of color clustering. It was used the perceptual color system for color representation. The main step is represented by definition of a new distance in the color space. In this construction, there were used two multipliers...

**Proceedings Article**

## Design of Strong Fuzzy Partitions from Cuts

Corrado Mencar, Marco Lucarelli, Ciro Castiello, Fanelli Anna Maria

The adoption of triangular fuzzy sets to define Strong Fuzzy Partitions (SFPs) is a common practice in the research community: due to their inherent simplicity, triangular fuzzy sets can be easily derived from data by applying suitable clustering algorithms. However, the choice of triangular fuzzy sets...

**Proceedings Article**

## The Webbed Emergence of Fuzzy Sets and Computer Science Education from Electrical Engineering

Rudolf Seising, Marco Elio Tabacchi

Historically, Computer science emerged from electrical engineering in the 1960s. From the content of some un- published documents and also some rather less-well- known papers by Lotfi A. Zadeh it is argued that the emergences of Computer science and Fuzzy Set Theory have been interlinked. Zadeh’s task...

**Proceedings Article**

## Probabilistic Fuzzy Reasoning in a Coherent Setting

Giulianella Coletti, Davide Petturiti, Barbara Vantaggi

We use the interpretation of fuzzy sets in terms of coherent conditional probabilities for handling probabilistic fuzzy IF-THEN rules. We show by some examples how this interpretation can help when fuzzy and statistical information need to be combined and the available probabilistic information on the...

**Proceedings Article**

## Fuzzy Dissimilarity-Based Classification for Disaster Initial Assessment

J. Tinguaro Rodríguez, Begoña Vitoriano, Javier Montero

conditional probabilities for handling probabilistic fuzzy IF-THEN rules. We show by some examples how this interpretation can help when fuzzy and statistical information need to be combined and the available probabilistic information on the fuzzy events is possibly imprecise or incomplete.

**Proceedings Article**

## Discrete uninorms with smooth underlying operators

Daniel Ruiz-Aguilera, Joan Torrens

The class of discrete uninorms U such that their underlying t-norm T and t-conorm S are smooth is studied. The different cases combining when T is the minimum or the Lukasiewicz t-norm and S is the maximum or the Lukasiewicz t-conorm, are characterized and the number of discrete uninorms with these underlying...

**Proceedings Article**

## Interpretable fuzzy system allowing to be framed in a profile photo through linguistic expressions

Patricia Conde Clemente, Jose M. Alonso, Gracian Trivino

This work was grounded in the idea that the user should not be a simple data summaries recipient, and explores the possibilities of building interpretable fuzzy control systems with human-in-the-loop. For this purpose, fuzzy computational perceptions are embedded in a highly interpretable linguistic...

**Proceedings Article**

## Interpretability analysis of fuzzy association rules supported by fingrams

David P. Pancho, Jose M. Alonso, Jesús Alcalá-Fdez, Luis Magdalena

This work extends fuzzy inference-grams (fingrams) to fuzzy association rules (FAR), yielding FARFingrams. Their analysis pays attention to interpretability issues. An important open problem in association rule mining is the huge number of frequent itemsets and interesting rules to discover and communicate...

**Proceedings Article**

## Compatible operations in some subvarieties of the variety of weak Heyting algebras

Hernán San Martín

Weak Heyting algebras are a natural generalization of Heyting algebras (see [2], [5]). In this work we study some subvarieties of the varieties of weak Heyting algebras in order to extend some known results about compatible functions in Heyting algebras.

**Proceedings Article**

## Bornological structures in the context of L-fuzzy sets

Alexander Sostak, Ingrida Uljane

In order to apply the concept of boundedness, so crucial in the theory of metric spaces, to the case of a general topological space Hu Sze-Tsen introduced the notions of a bornological space and of boundedness for a mapping of bornological spaces. In this work we discuss two alternative approaches how...

**Proceedings Article**

## A choice of bilevel linear programming solving parameters: factoraggregation approach

Pavels Orlovs, Olga Montvida, Svetlana Asmuss

Our paper deals with the problem of choosing correct parameters for the bilevel linear programming solving algorithm proposed by M. Sakawa and I.~Nishizaki. We suggest an approach based on factoraggregation, which is a specially designed general aggregation operator. The idea of factoraggregation arises...

**Proceedings Article**

## Influence of various types of basic functions on image reconstruction using F-transform

Pavel Vlašánek, Irina Perfilieva

Technique of image reconstruction using Ftransform uses basic functions for computation. Radius and partition of these functions affects quality of the reconstruction. In this article we are focusing on influence of the basic function shape on the quality of reconstruction and providing results of nondecreasing,...

**Proceedings Article**

## On functions that solve Mulholland inequality and on compositions of such functions

Milan Petrík

Two results related to Mulholland inequality are presented. First, there are functions that are not geo-convex but solve Mulholland inequality; thus Mulholland's condition is not necessary. Second, the set of functions that solve Mulholland inequality is not closed with respect to compositions. As a...

**Proceedings Article**

## Context, information’s meaning, and perception

Clara Barroso

Computer representation of human knowledge must be approached using the human ability to assign different meanings to information according to our perceptions, which at the same time are constructed and constitute the interpretative context in which possible meanings acquire varying degrees of validity....

**Proceedings Article**

## Weak Preservation of Multi-Valued Fusion

Antoon Bronselaer, Guy De Tre

Fusion functions are important data integration tools that map a multiset of objects (i.e., the sources) onto a single object (i.e., the solution). Traditionally, it is assumed that the objects of interest are single-valued. In this paper, it will be assumed that each object has a multi-valued data structure,...

**Proceedings Article**

## Image compression methodology based on fuzzy transform using block similarity

Petr Hurtik, Irina Perfilieva

The aim of the work is to continue in improvement of the image compression based on the F-transform. The image is decomposed into blocks and characterized by the F-transform components. The latter constitutes a simple lossy compression. For better quality of reconstructed images, we compress certain...

**Proceedings Article**

## Optimization and Reoptimization in Fuzzy Linear Programming problems

Behrouz Kheirfam, José-Luis Verdegay

Fuzzy Linear Programming models are quite frequent in practice. The dynamic nature of the real problems often requires reoptimize from the optimal solutions found, what may mean a significant consumption of time and funds. In this paper, in order to efficiently solve this problem, first the optimality...

**Proceedings Article**

## Solutions of the Distributivity Equation $mathcal{I}(mathcal{T}(x,y),z) = mathcal{S}(mathcal{I}(x,z),mathcal{I}(y,z))$ for Some t-Representable T-Norms and T-Conorms

Michal Baczynski

Recently, in [4], [5], [6], and [8] we have discussed the distributivity equation of implications $mathcal{I}(x,mathcal{T}_1(y,z)) = mathcal{T}_2(mathcal{I}(x,y),mathcal{I}(x,z))$ over t-representable t-norms, generated from (classical) continuous Archimedean mbox{t-norms}, in interval-valued fuzzy sets...

**Proceedings Article**

## Hellinger distance for fuzzy measures

Vicenc Torra, Yasuo Narukawa, Michio Sugeno, Michael Carlson

Hellinger distance is a distance between two additive measures defined in terms of the Radon-Nikodym derivative of these two measures. This measure proposed in 1909 has been used in a large variety of contexts. In this paper we define an analogous measure for fuzzy measures. We discuss them for distorted...

**Proceedings Article**

## F^1-transform of Functions of Two Variables

Petra Hodakova, Irina Perfilieva

In this contribution, the F^1-transform of functions of two variables is introduced. It combines properties of the F-transform of functions of two variables and the F^1-transform of functions of one variable. The aim of this study is to prove approximation properties of the F^1-transform components and...

**Proceedings Article**

## A Multi-Expert Fuzzy TOPSIS-based Model for the Evaluation of e-Learning Paths

Mario Fedrizzi, Andrea Molinari

In e-learning settings, the evaluation of different alternatives regarding learning paths’ proposal is nowadays crucial, due to the great attention devoted to the construction of learning objects (LO) available through Learning Management Systems (LMS). In this paper, we present a model devoted to support...

**Proceedings Article**

## Expectile Smoothing using F.transform

Maria Letizia Guerra, Luciano Stefanini

In this paper, we will illustrate the F-transform based on generalized fuzzy partitions as a tool for expectile smoothing. This allows to represent a time series in terms of a fuzzy-valued function whose level-cuts are modeled by F-transform and estimated by expectile regression. The proposed methodology...

**Proceedings Article**

## Biconic semi-copulas with a given section

Tarad Jwaid, Bernard De Baets, Hans De Meyer, Radko Mesiar

Inspired by the notion of biconic semi-copulas, we introduce biconic semi-copulas with a given section. Such semi-copulas are constructed by linear interpolation on segments connecting the graph of a continuous and decreasing function to the points (0,0) and (1,1). Special classes of biconic semi-copulas...

**Proceedings Article**

## Aggregation of implication functions

Tomasa Calvo, Javier Martín, Gaspar Mayor

This paper deals with the problem of the aggregation of implication functions. After characterizing those binary operations which merge two implication functions into an implication function, we study some aspects of the aggregated implication functions in terms of the two given ones. In particular,...

**Proceedings Article**

## A new algorithm for color image comparison based on similarity measures

Daniel Paternain, Mikel Galar, Aranzazu Jurio, Edurne Barrenechea

In this work we address the problem of the quality assessments in the process of color images segmentation. We consider each component of a color image as a fuzzy set and therefore, we propose to use similarity measures (between fuzzy sets) to compare image segmentations. We test three segmentation algorithms,...

**Proceedings Article**

## Generalizing Precisiated Natural Language: A Formal Logic as a Precisiation Language

Takehiko Nakama, Enrique Muñoz, Enrique Ruspini

We generalize precisiated natrual language by establishing a formal logic as a generalized precisiation language. In this formal logic, each proposition has a syntactic structure observed in natural language. Various syntactic structures are incorporated in the formal logic so that it precisiates not...

**Proceedings Article**

## h k aggregation functions, measures and integrals

Fabio Rindone, Salvatore Greco

In many decision making problems evaluations with respect to several points of view (criteria) are ex-pressed by means of h interval (or fuzzy numbers). For example a pessimistic and an optimistic eval-uation generate an interval containing the exact evaluation. These situations reflect lack of infor-mation...

**Proceedings Article**

## An extension of Yager's implications

Sebastià Massanet, Joan Torrens

In this paper, an extension of Yager's implications is proposed by means of generalizing the internal factor x, in the case of f-generated implications, or 1/x, in the case of g-generated implications, to more general unary functions. The importance of this extension stems from the fact that both subclasses...

**Proceedings Article**

## On Applying Random Oracles to Fuzzy Rule-Based Classifier Ensembles for High Complexity Datasets

Krzysztof Trawinski, Oscar Cordon, Arnaud Quirin

Fuzzy rule-based systems suffer from the so-called curse of dimensionality when applied to high com- plexity datasets, which consist of a large number of variables and/or examples. Fuzzy rule-based clas- sifier ensembles have shown to be a good approach to deal with this kind of problems. In this contri-...

**Proceedings Article**

## Possibility transformation of the sum of two symmetric unimodal independent/comonotone random variables

Gilles Mauris

The paper extends author’s previous works on a proba-bility/possibility transformation based on a maximum specificity principle to the case of the sum of two iden-tical unimodal symmetric random variables. This trans-formation requires the knowledge of the dependency relationship between the two added...

**Proceedings Article**

## On the use of restricted dissimilarity and dissimilarity-like functions for defining penalty functions

Gleb Beliakov, Humberto Bustince, Javier Fernandez, Radko Mesiar, Ana Pradera

In this work we study the relation between restricted dissimilarity functions-and, more generally, dissimilarity-like functions- and penalty functions and the possibility of building the latter using the former. Several results on convexity and quasi-convexity are also considered.

**Proceedings Article**

## A Comparison of Approaches to Model Uncertainty in Time Intervals

Christophe Billiet, Jose Enrique Pons, Olga Pons, Guy De Tre

Information systems model parts of reality by representing properties of real-world objects or concepts. As real objects or concepts often have temporal aspects, temporal notions such as time intervals are often represented. However, these may contain imperfections like uncertainties, complicating their...

**Proceedings Article**

## An approach to graph-based analysis of textual documents

Antoon Bronselaer, Gabriella Pasi

In this paper a new graph-based model is proposed for the representation of textual documents. Graph-structures are obtained from textual documents by making use of the well-known Part-Of-Speech (POS) tagging technique. More specifically, a simple rule-based (re)classifier is used to map each tag onto...

**Proceedings Article**

## At-least At-most Modifications in a Space with Fuzzy Preoreder

Irina Perfilieva

In this paper, we utilize the theory of solvability of systems of fuzzy relation equations in a space with fuzzy preorder and propose a justification of solvability of the systems that are modified with ``at least'' (``at most'') quantifiers. We show that the respectively modified fuzzy sets are upper...

**Proceedings Article**

## A Consensus Model in Group Decision Making Based on Interpolative Boolean Algebra

Ana Poledica, Pavle Milosevic, Ivana Dragovic, Dragan Radojevic, Bratislav Petrovic

The aim of this paper is to propose a soft consensus model based on interpolative Boolean algebra for group decision making problems. Consensus degrees are calculated on three levels (on pairs of alternatives, alternatives, relation) by means of pseudo-logical aggregation. The relation of equivalence...

**Proceedings Article**

## Efficient GCD functions in SQL

Joachim Nielandt, Antoon Bronselaer, Guy De Tre

Querying a database in an intuitive way is becoming more important. Users expect their tools to present an easy-to-use interface that can interpret complex search criteria. These criteria can be optional, mandatory, unwanted or grouped together, according to what the developer of a tool wishes to offer...

**Proceedings Article**

## Hidden functional dependencies found by the technique of F-transform

Jiri Kupka, Iva Tomanova

In this contribution we provide an application of the technique of F-transform. We demonstrate that by using a simple density-based preprocessing, the applicability of F-transform in data analysis can be significantly improved. Despite of the fact that our procedure is demonstrated by a well-known DBSCAN...