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

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156 articles

Redundancies in systems of fuzzy/linguistic IF-THEN rules

Antonin Dvorak, Martin Stepnicka, Lenka Vavrícková
In this paper we will investigate which fuzzy/linguistic rules are redundant in systems of such rules called linguistic descriptions. We present a formal definition of redundancy and show that rules which are seemingly redundant can be in fact indispensable. These results apply for IF-THEN rules which...

Combination of interval analysis and PSO for optimization

Clément Solau, Bruno Marhic, Arnaud Delahoche, Claude Clérentin, Anne-Marie Joly-Desodt, David Menga
In this paper, a constrained optimization method for various functions such as non differentiable ones based on interval analysis is proposed. The process can be broken down into two distinct parts: the first one that approximates the space satisfying the constraints and the second one that is exclusively...

Determining the accuracy in image supervised classification problems

Daniel Gomez, Javier Montero
A large number of accuracy measures for crisp supervised classification have been developed in supervised image classification literature. Overall accuracy, Kappa index, Kappa location, Kappa histo and user accuracy are some well-known examples. In this work, we will extend and analyze some of these...

Transitive Openings

Dionis Boixader, Jordi Recasens
Though the transitive closure of a reflexive and symmetric fuzzy relation R is unique and there are several algorithms to calculate it, there can be many transitive openings (maximal T-indistinguishability operators among the ones smaller than or equal to R). This paper presents a method to calculate...

A Unified Model for Fuzzy Aggregation Operators and its Application in Group Decision Making

José M. Merigó
We develop a new model for fuzzy decision making based on the use of several sources of information in the analysis. We introduce the fuzzy unified aggregation operator (FUAO). It is an aggregation operator that unifies other aggregation operators in the same formulation and considering the degree of...

Solution of Fuzzy Differential Equations with generalized differentiability using LU-parametric representation

Barnabas Bede, Luciano Stefanini
fuzzy numbers and fuzzy-valued functions, to obtain valid approximations of fuzzy generalized derivative and to solve fuzzy differential equations. The main result is that a fuzzy differential initial-value problem can be translated into a system of in nitely many ordinary differential equations and,...

Closing and Opening based on discrete t-norms. Applications to natural Image Analysis

Manuel González-Hidalgo, Sebastià Massanet
This paper delves deeply into the recently introduced mathematical morphology based on discrete t-norms. Closing and opening operators and the concepts of open and closed objects are introduced. All the properties satisfied by nilpotent t-norms, even the generalized idempotence, hold too. After that,...

F-boxes for filtering

Olivier Strauss, Sebastien Destercke
Selecting a particular summative kernel (i.e., formally equivalent to a probability distribution) when filtering a digital signal can be a difficult task. An obvious solution to this problem is to filter with multiple kernels rather than with a single one, but the computing cost of such a solution can...

Different interpretations of fuzzy gradual-inclusion-based IR models

Laurent Ughetto, Vincent Claveau
Recently, a theoretical fuzzy IR system, based on gradual inclusion measures, has been proposed [1]. In this model, derived from the division of fuzzy relations, the gradual inclusion of a query in a document is modeled by a fuzzy implication. In previous papers, we have shown that, under some assumptions,...

Preservation of Intuitionistic Fuzzy Preference Relations

Pawel Drygas
In this paper we consider some properties of intuitionistic fuzzy preference relations. We pay attention to preservation of intuitionistic fuzzy preference relations by aggregation operations. In particular, we know, that a special kind of aggregation operations (lattice operations) do not preserve...

Fuzzy inference systems for synthetic monthly inflow time series generation

Ivette Luna, Rosangela Ballini, Secundino Soares, Donato Da Silva Filho
Inflow data plays an important role in water and energy resources planning and management. In general, due to the limited availability of historical inflow data, synthetic streamflow time series have been widely used for several applications such as mid- and long-term hydropower scheduling and the identification...

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....

On the transitive closure of reciprocal [0, 1]-valued relations

Steven Freson, Hans De Meyer, Bernard De Baets
We build a theoretical framework that enables to extend the concept of transitive closure to the class of complete crisp relations, the class of reciprocal 3-valued relations and the class of reciprocal [0, 1]valued relations. We present algorithms to compute the transitive closure of reciprocal [0,...

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...

Ranking fuzzy numbers using fuzzy maximizing-minimizing points

S. Salahshour, S. Abbasbandy, T. Allahviranloo
Up to now, several approaches have been proposed for ranking of fuzzy numbers using maximizing set and minimizing sets. Often, the reference points are created by real numbers. In this paper, we proposed new reference points so called fuzzy maximizing-minimizing points. To this purpose, we used the...

Design of unknown input fuzzy observer for vehicle dynamics estimation with road geometry consideration

Hamid Dahmani, Mohammed Chadli, Abdelhamid Rabhi, Achmed El Hajjaji
A methodology for estimating vehicle dynamics whith road geometry consideration is presented in this paper. Vehicle sideslip and roll parameters are estimated in the presence of the road bank angle and the road curvature as unknown inputs. The unknown inputs are then estimated using the observer results....

Trapezoidal approximations of fuzzy numbers with restrictions on the support and core

Przemyslaw Grzegorzewski, Karolina Pasternak-Winiarska
Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New operators that fulfill additional requirements for the core and support of the fuzzy number are suggested. These supplementary conditions guarantee the proper interpretation of the solution...

Imprecise linear filtering: a second step

Olivier Strauss, Agnès Rico
Linear digital signal processing consists in convoluting the input sampled signal with the discrete version of the impulse response of a filter designed by an expert. More than often, a unique impulse response does not represent the complete knowledge of the expert who should have proposed more than...

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...

Probability on Effect Algebras

Mája Kuková, Alzbeta Michalíková, Belo Riecan
Effect algebras ([1], [2]) and D-posets ([3]) are equivalent systems important in quantum structures. In the paper an independent sequence of observables is defined by such a way that a very general version of the central limit theorem may be proved.

Unended Reflections on Family Resemblance and Predicates Linguistic Migration

Itziar Garcia-Honrado, Enric Trillas
This paper takes into account the Wittgenstein's idea of family resemblance as a particular crisp relation between some fuzzy sets, that is, between some representations of predicates use from its use. It is shown that all uses of the same predicate actually do have some kind of family resemblance,...

Intuitionistic fuzzy preference relations

Urszula Dudziak, Barbara Pekala
We consider properties of intuitionistic fuzzy preference relations. We study preservation of a preference relation by lattice operations, composition and some Atanassov's operators like F,, P,, Q,, where , [0, 1]. We also define semi-properties of intuitionistic fuzzy relations, namely reflexivity,...

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...

Fuzzy logic in competence management

Raymond Houé, Bernard Grabot, Germaine Tchuente
Industrial performance has for a long time been considered as a result of technical resources optimization. During the recent decades, competencybased approach has emerged as a promising concept for taking into account human skills/knowledge/abilities while addressing organizational goals and constraints....

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.

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...

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.

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....

MRP with imprecise demand and uncertain lead time

Romain Guillaume, Caroline Thierry, Bernard Grabot
Taking into account the uncertainty of real data in the planning process is a real challenge for nowadays companies. It is suggested in this communication to take into account the demand uncertainty, but also the uncertainty on the lead times, for deciding which quantities of components should be released,...

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...

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...

A MCDM approach for evaluating company's environmental practices

Rocio de Andrés Calle, Teresa González-Arteaga, Luis Martínez López
The need of organizations to evaluate their environmental practices is increasing, but there are many possibilities to do it. In this paper a decision model is proposed to evaluate company's environmental practice taking into account different collectives of reviewers related to the company's activity....

Intersection and union of type-2 fuzzy sets and connection to (1, 2)-double cuts

Zdenko Takac
It is known that the standard intersection and union of type-1 fuzzy sets (i.e., the intersection and union under the minimum t-norm and maximum tconorm) are the only cutworthy operations for type-

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...

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...

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...

Multi-criteria Group Decision Supplier Selection Problem using Fuzzy TOPSIS Based Approch

Akram Zuoggari, Lyes Benyoucef
This paper presents a new decision making approach for group multi-criteria supplier selection problem, which clubs supplier selection process with order allocation for dynamic supply chains to cope market variations. More specifically, the developed approach imitates the knowledge acquisition and manipulation...

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.

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...

Fuzzy Function: Theoretical and Practical Point of View

Irina Perfilieva
The aim of this investigation is to reconsider two notions of fuzzy function, namely: a fuzzy function as a special fuzzy relation and a fuzzy function as a mapping between fuzzy spaces. We propose to combine both notions in such a way that a fuzzy function as a relation determines a fuzzy function...

Fuzzy methods for database protection

Vicenc Torra, Daniel Abril, Guillermo Navarro-Arribas
Data privacy has become an important topic of research. Ubiquitous databases and the eclosion of web technology eases the access to information. This information can be related to individuals, and, thus, sensitive information about users can be easily accessed by interested parties. Data privacy focuses...

Quasi-arithmetic means and OWA functions in interval-valued and Atanassov's intuitionistic fuzzy set theory

Glad Deschrijver
In this paper we propose an extension of the wellknown OWA functions introduced by Yager to interval-valued (IVFS) and Atanassov's intuitionistic (AIFS) fuzzy set theory. We first extend the arithmetic and the quasi-arithmetic mean using the arithmetic operators in IVFS and AIFS theory and investigate...

Linguistic Summarization of Time Series Data using Genetic Algorithms

Rita Castillo-Ortega, Nicolás Marín, Daniel Sánchez, Andrea G.B. Tettamanzi
In this paper, the use of an evolutionary approach when obtaining linguistic summaries from time series data is proposed. We assume the availability of a hierarchical partition of the time dimension in the time series. The use of natural language allows the human users to understand the resulting summaries...

Supplementarity measures on fuzzy sets

Susana Cubillo, Elena E. Castiñeira, Wilmer Montilla
In this paper, we tackle the study of so-called supplementarity measures. They are introduced axiomatically and are then related to incompatibility measures by antonyms. To do this, we have to establish what we mean by antonymous measure. We then prove that, under certain conditions, supplementarity...

On the convergence of HLMS Algorithm

Murillo Javier, Serge Guillaume, Elizabeth Tapia, Bulacio Pilar
In multicriteria decision making, the study of attribute contributions is crucial to attain correct decisions. Fuzzy measures allow a complete description of the joint behavior of attribute subsets. However, the determination of fuzzy measures is often hard. A common way to identify fuzzy measures is...

Fuzzy Measures on Finite Scales as Families of Possibility Measures

Didier Dubois
We show that any capacity or fuzzy measure ranging on a qualitative scale can be viewed both as the lower bound of a set of possibility measures, and the upper bound of a set of necessity measures. An algorithm is provided to compute the minimal set of possibility measures dominating a given capacity....

Axiomatizations of the discrete Choquet integral and extensions

Miguel Couceiro, Jean-Luc Marichal
Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and...

On the connection between probability boxes and possibility measures

Matthias C. M. Troffaes, Enrique Miranda, Sebastien Destercke
We explore the relationship between p-boxes on totally preordered spaces and possibility measures. We start by demonstrating that only those p-boxes who have 0–1- valued lower or upper cumulative distribution function can be possibility measures, and we derive expressions for their natural extension...