Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)

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156 articles

Induced Unbalanced Linguistic Ordered Weighted Average

Lucas Marin, José M. Merigó, Aida Valls, Antonio Moreno, David Isern
Aggregation operators for linguistic variables usually assume a uniform and symmetrical distribution of the linguistic terms that define the variable. This paper defines the Induced Unbalanced Linguistic Ordered Weighted Average (IULOWA). This aggregator takes into account the fuzzy membership functions...

On generalizations of weighted means and OWA operators

Bonifacio Llamazares
In this paper we analyze two classes of functions proposed in the literature to simultaneously generalize weighted means and OWA operators: WOWA operators and HWA operators. Since, in some cases, the results provided by these operators may be questionable, we introduce functions that also generalize...

The Type-1 OWA Operator and the Centroid of Type-2 Fuzzy Sets

Francisco Chiclana, Shang-Ming Zhou
This paper aims to establish the relationship between two apparent disparate problems: (i) the aggregation of uncertain information modelled by type-1 fuzzy sets via OWA mechanism, and (ii) the computation of the centroid of type-2 fuzzy sets. In order to cut down the computational complexity of the...

On another view of aggregation of fuzzy relations

Olga Grigorenko, Julija Lebedinska
The paper is devoted to a concept of aggregation of binary fuzzy relations. Consider two n-ary vectors, when we know the degrees to which corresponding components are in relation we can measure the degree to which vectors are in relation. Tasks with such background justify the necessity of aggregation...

On extension of fuzzy measures to aggregation functions

Anna Kolesárová, Andrea Stupnanová, Juliana Beganová
In the paper we study a method extending fuzzy measures on the set N = {1, . . ., n} to n-ary aggregation functions on the interval [0, 1]. The method is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. This approach generalizes the wellknown...

The Gini index and the consistent measurement of inequality among the poor

Oihana Aristondo, José Luis García-Lapresta, Casilda Lasso De La Vega, Ricardo Alberto Marques Pereira
In several economic fields, such as those related to health, education or poverty, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed....

Functionally Expressible Multidistances

Javier Martín, Gaspar Mayor, Oscar Valero
In this paper we deal with the problem of aggregating pairwise distance values in order to obtain a multi-argument distance function. After introducing the concept of functionally expressible multidistance, several essential types of multidimensional aggregation functions are considered to construct...

General aggregation operators acting on the L-fuzzy real line

Pavels Orlovs
The paper is devoted to a general aggregation operator acting on L-fuzzy real numbers. It is defined as a t-norm based extension of an ordinary aggregation operator. The aim of our research is to analyze properties of the general aggregation operator depending on properties of the ordinary aggregation...

Axiomatic characterizations of (quasi-) L-statistics and S-statistics and the Producer Assessment Problem

Marek Gagolewski, Przemyslaw Grzegorzewski
Two classes of aggregation functions: L-statistics and S-statistics and their generalizations called quasi-L-statistics and quasi-S-statistics are considered. Some interesting characterizations of these families of operators are given. The aforementioned functions are useful for various applications....

Uninorms and nullnorms on the set of discrete fuzzy numbers

Juan Vicente Riera, Joan Torrens
In this paper a method to extend discrete uninorms and nullnorms on the finite chain L = {0, . . . , n}, to uninorms and nullnorms defined on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L is presented. Some basic properties of discrete uninorms...

Biconic aggregation functions with a given diagonal or opposite diagonal section

Tarad Jwaid, Bernard De Baets, Hans De Meyer
A new method to construct aggregation functions is introduced. These aggregation functions are called biconic aggregation functions with a given diagonal (resp. opposite diagonal) section and their construction method is based on linear interpolation on segments connecting the diagonal (resp. opposite...

Aggregation operators of general aimed information

Doretta Vivona, Maria Divari
The aim of this paper is to introduce, by axiomatic way, the measure of the general (i.e. without probability) aimed information for crisp sets. We traslate the problem in a system of functional equation and we present a class of solutions; in the case of independence we characterize the solution. Finally,...

Restricted dissimilarity functions and penalty functions

Humberto Bustince, Javier Fernandez, Radko Mesiar, Anna Pradera, Gleb Beliakov
In this work we introduce the definition of restricted dissimilarity functions and we link it with some other notions, such as metrics. In particular, we also show how restricted dissimilarity functions can be used to build penalty functions.

Aggregation Functionals on Complete Lattices

Marta Cardin
The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. Two different types of aggregation functionals are introduced and investigated. We consider a target-based approach that has been studied in Decision Theory and we focus on...

Construction of a Choquet integral and the value functions without any commensurateness assumption in multi-criteria decision making

Christophe Labreuche
We consider a multi-criteria evaluation function U defined over a Cartesian product of attributes. We assume that U is written as the combination of an aggregation function and one value function over each attribute. The aggregation function is assumed to be a Choquet integral w.r.t. an unknown capacity....

On Convergence of Fuzzy Integrals over Complete Residuated Lattices

Antonín Dvorak, Michal Holcapek
Recently we proposed a new type of fuzzy integrals defined over complete residuated lattices. These integrals are intended for the modeling of type 1, 1 fuzzy quantifiers. An interesting theoretical question is, how to introduce various notions of convergence of this type of fuzzy integrals. In this...

Evaluating Consulting Firms Using a Centroid Ranking Approach based Fuzzy MCDM Method

Ta-Chung Chu
The purpose of this paper is to evaluate and select consulting firms by suggesting a centroid ranking approach based fuzzy multiple criteria decision making (MCDM) method, where ratings of alternatives versus qualitative criteria and the different importance weights among criteria are assessed in linguistic...

Dealing with inconsistencies in the representation of ordinal information by a 2-additive Choquet integral

Brice Mayag, Michel Grabisch, Christophe Labreuche
We propose an algorithm to solve inconsistencies when the preferences of a decision-maker, given by a strict and an indifference relations on a set of binary actions, are not representable by a 2-additive Choquet integral. According to the characterization of this type of information, these inconsistencies...

L-fuzzy valued measure and integral

Vecislavs Ruza, Svetlana Asmuss
We continue to develop a construction of an L-fuzzy valued measure by extending a measure defined on a algebra of crisp sets to an L-fuzzy valued measure defined on a TM-tribe in the case when operations with L-sets and L-fuzzy numbers are defined by using the minimum triangular norm TM. We introduce...

Parameter identification in Choquet Integral by the Kullback-Leibler divergence on continuous densities with application to classification fusion

Emmanuel Ramasso, Sylvie Jullien
Classifier fusion is a means to increase accuracy and decision-making of classification systems by designing a set of basis classifiers and then combining their outputs. The combination is made up by non linear functional dependent on fuzzy measures called Choquet integral. It constitues a vast family...

Riesz MV-algebras and their logic

Antonio Di Nola, Ioana Leustean
We develop the general theory of RMV-algebras, which are essentially unit intervals in Riesz spaces with strong unit. Since the variety of RMV-algebras is generated by [0, 1], we get an equational characterization of the real product on [0,1] interpreted as scalar multiplication.

Fuzzy logics with truth hedges revisited

Francesc Esteva, Lluís Godo, Carles Noguera
In this paper we build upon previous works of Hájek and Vychodil on the axiomatization of truthstressing and depressing hedges as expansions of BL logic by new unary connectives. They show that their logics are chain-complete, but standard completeness is only proved for the expansions over Gödel logic....

On the variety of equality algebras

Sándor Jenei, László Kóródi
Equality algebras has recently been introduced. A subclass of equality algebras, called equivalential equality algebras is closely related to BCK-algebras with meet. We show that the variety of equality algebras has nice properties: We shall investigate their congruences and filters and prove that the...

On EQ-Fuzzy Logics with Delta Connective

Martin Dyba, Vilém Novák
In this paper, extension of the EQ-logic by the connective is introduced. The former is a new kind of many-valued logic which based on EQ-algebra of truth values, i.e. the algebra in which fuzzy equality is the fundamental operation and implication is derived from it. First, we extend the EQ-algebra...

Axiomatic Extensions of Höhle's Monoidal Logic

Esko Turunen
We introduce an axiomatic extension of H¨ohle's Monoidal Logic called Semi­divisible Monoidal Logic, and prove that it is complete by showing that semi­divisibility is preserved in MacNeille completion. Moreover, we introduce Strong semi­ divisible Monoidal Logic and conjecture that a predicate formula...

Filters in algebras of fuzzy logics

Martin Víta, Petr Cintula
This paper presents a generalization of many particular results about special types of filters (e.g., (positive) implicative, fantastic) on algebras of nonclassical (mostly fuzzy) logics. Our approach is rooted in the framework of Abstract Algebraic Logic, and is based on the close connection between...

Non-deterministic Connectives in Propositional Gödel Logic

Ori Lahav, Arnon Avron
We define the notion of a canonical Gödel system in the framework of single-conclusion hypersequent calculi. A corresponding general (nondeterministic) Gödel valuation semantics is developed, as well as a (non-deterministic) linear intuitionistic Kripke-frames semantics. We show that every canonical...

Nilpotent Minimum Fuzzy Description Logics

Brunella Gerla, Massimo Dalla Rovere
We define the fuzzy description logic ALCHNM based on the t-norm of Nilpotent Minimum and we prove its reduction to the crisp description logic ALCH. Hence we prove decidability results for ALCHNM.

Fuzzy Type Theory, Descriptions, and Partial Functions

Vilém Novák.
This paper studies the possibility to deal with partial functions in fuzzy type theory. Among various ways how to represent them we chose introduction of a special value "undefined" laying outside the corresponding domain. In FTT, we can quite naturally utilize the description operator by extending...

A logic of the similarity with prototypes and its relationship to fuzzy logic

Thomas Vetterlein
Fuzzy sets are widely used to model vague properties. According to a common understanding, a fuzzy set represents the degrees of similarity of precisely specified objects with the prototypes of the considered vague property. We propose a logic based on this idea, using an entailment relation which was...

Fuzzy attribute logic with model constraints

Radim Belohlavek, Vilem Vychodil
Presented are preliminary results on ordinary-style and graded-style completeness results for fuzzy attribute logic with models constrained by fuzzy closure operators with hedges.

Computation with fuzzy quantities

Mirko Navara
Solving systems of equations (even linear ones) in standard fuzzy arithmetic may be a problem. We suggest an alternative approach which transfers the task to a linear space where the solution may be standard. Fuzzy intervals form a proper subset (in fact, a cone) in this linear space.

A new method of generating fuzzy implications from given ones

Sebastià Massanet, Joan Torrens
In this paper, a new construction method of a fuzzy implication from two given ones, called e-generation method, is introduced. This method allows to con- trol, up to a certain level, the increasingness on the second variable of the fuzzy implication through an adequate scaling on that variable of the...

R-implications and the Exchange Principle:A Complete Characterization

Balasubramaniam Jayaram, Michal Baczynski, Radko Mesiar
It is well-known that the residual IT of a leftcontinuous t-norm T satisfies the exchange principle (EP), viz., IT (x, IT (y, z)) = IT (y, IT (x, z)) for all x, y, z [0, 1]. However, the left-continuity of T is only sufficient and not necessary, as many examples in the literature illustrate. In this...

Dependencies between fuzzy conjunctions and implications

Anna Krol
This paper deals with some dependencies between fuzzy conjunctions and fuzzy implications. More precisely, a fuzzy implication generated from a fuzzy conjunction and a fuzzy conjunction induced by a fuzzy implication is considered. In the case of a fuzzy conjunction only border conditions and monotonicity...

Obtaining representable coimplications from aggregation and dual operators

Renata Reiser, Benjamin Bedregal
The aim of this work is to study N-dual structures of representable implications generated from a set M of aggregation functions and pairs of mutual dual functions, founded on the isomorphism between the unit interval and special instances of the Goguen's L-fuzzy sets. We discuss under which conditions...

Distributive equation of implications based on continuous triangular norms

Feng Qin, Michal Baczynski, Aifang Xie
In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equations of implications. In details, by means of the section of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(x, T1(y, z))...

Probabilistic Implications

Przemyslaw Grzegorzewski
A new family of implication operators, called probabilistic implications, is introduced. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that some well-known fuzzy implications appear as a particular probabilistic...

Fuzzy implications defined on the set of discrete fuzzy numbers

Juan Vicente Riera, Joan Torrens
Given an implication function I defined on the finite chain L = {0, ..., n}, a method for extending I to the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L (denoted by AL

On lattice structure and implications on ordered fuzzy numbers

Magdalena Kacprzak, Witold Kosinski
Ordered fuzzy numbers (OFN) invented by the second author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. The definition of OFN uses the extension of the parametric representation of convex fuzzy...

A Fuzzy Rule Mining Approach involving Absent Items

Miguel Delgado, Maria Dolores Ruiz, Daniel Sanchez, José Maria Serrano
In this paper we present how to extract fuzzy association rules involving both the presence and the absence of items using a fuzzy rule mining procedure introduced by the authors in previous works. The rule mining procedure is based on the GUHA logical model, fuzzified via a recently proposed representation...

Membership-based clustering of heterogeneous fuzzy data

Gernot Herbst, Arne-Jens Hempel, Rainer Fletling, Steffen F. Bocklisch
This article contributes to clustering and fuzzy modelling of data such that specific characteristics of each datum can be incorporated. Particularly, each object may exhibit an individual area of influence in its feature space, for which it is representative. For such objects, a similarity measure is...

Cluster Tendency Assessment for Fuzzy Clustering of Incomplete Data

Ludmila Himmelspach, Daniel Hommers, Stefan Conrad
The quality of results for partitioning clustering algorithms depends on the assumption made on the number of clusters presented in the data set. Applying clustering methods on real data missing values turn out to be an additional challenging problem for clustering algorithms. Fuzzy clustering approaches...

M-Estimator induced Fuzzy Clustering Algorithms

Roland Winkler, Frank Klawonn, Rudolf Kruse
M-estimators can be seen as a special case of robust clustering algorithms. In this paper, we present the reversed direction and show that clustering algorithms can be constructed by using M-estimators. A clever normalization is used to link the values of several M-estimator prototypes together in one...

Fuzzy Inference System based Contrast Enhancement

Balasubramaniam Jayaram, Kakarla Narayana, V. Vetrivel
In this work, we propose a fuzzy inference system based contrast enhancement of gray level images. We propose a new method of generating the fuzzy if-then rules specific to a given image based on the local information available to be used by a fuzzy inference system. To this end, we only generate a...

Towards an objective edge detection algorithm

Manuel González-Hidalgo, Sebastià Massanet
In this paper a comparative analysis of different techniques in order to transform a gray-scale edge image to a thin binary edge image is performed. Several thresholding methods and thinning methods are compared. The comparison is made according to some performance measures, such as Pratt's figure of...

Generation of fuzzy edge images using trapezoidal membership functions

Carlos Lopez-Molina, Humberto Bustince, Javier Fernandez, Bernard De Baets
The fuzzy representation of the edges has been widely studied in different works. Generally, for each pixel, the authors use membership degrees linearly proportional to the magnitude of the gradient at that position of the image. This would be equivalent to using a triangular membership functions on...

Two different approaches to handle landmark location uncertainty in skull-face overlay:coevolution vs fuzzy landmarks

Óscar Ibáñez, Óscar Cordón, Sergio Damas
Craniofacial superimposition is a forensic process where photographs or video shots of a missing person are compared with the skull that is found. By projecting both photographs on top of each other (or, even better, matching a scanned three-dimensional skull model against the face photo/video shot),...