Date of publication: 2008-01

XIV Congreso Español sobre Tecnologías y Lógica Fuzzy (ESTYLF 2008)

p. 401-404

Abstract:

En este trabajo se estudia la posibilidad de introduir conceptos de teoría de conjuntos borrosos en los currículos correspondientes a distintos niveles de enseñanza. Se hace especial hincapié en la enseñanza de las relaciones borrosas presentando un entorno Excel© como soporte docente y de experimentación.]]>

International journal of approximate reasoning

Vol. 46, num. 3, p. 511-524

DOI: 10.1016/j.ijar.2007.01.003

Date of publication: 2007-12

Abstract:

Lipschitzian and kernel aggregation operators with respect to natural T-indistinguishability operators ET and their powers are studied. A t-norm T is proved to be ET-lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T.]]>

Date of publication: 2007-09

EUSFLAT07

p. 127-133

Abstract:

Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator with respect to T.]]>

IEEE International Conference on Fuzzy Systems

p. 1060-1065

Abstract:

Lipschitzian and kernel aggregation operators with respect to the natural T-indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ETLipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T.]]>

5th Mathematics & Design International Conference

p. 1-21

XIII Congreso Español sobre Tecnologías y Lógica Fuzzy

Presentation's date: 2006-09-20

International journal of intelligent systems

Vol. 21, num. 8, p. 857-873

Date of publication: 2006-08

Abstract:

This article gives a new approach to aggregating assuming that there is an indistinguishability operator or similarity defined on the universe of discourse. The very simple idea is that when we want to aggregate two values a and b we are looking for a value l that is as similar to a as to b or, in a more logical language, the degrees of equivalence of l with a and b must coincide. Interesting aggregation operators on the unit interval are obtained from natural indistinguishability operators associated to t-norms that are ordinal sums.

This article gives a new approach to aggregating assuming that there is an indistinguishability operator or similarity defined on the universe of discourse. The very simple idea is that when we want to aggregate two values a and b we are looking for a value l that is as similar to a as to b or, in a more logical language, the degrees of equivalence of l with a and b must coincide. Interesting aggregation operators on the unit interval are obtained from natural indistinguishability operators associated to t-norms that are ordinal sums.]]>

IEEE World Congress on Computational Intelligence

Presentation's date: 2006-07-16

International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

p. 2416-2421

XIII Congreso Español sobre Tecnologías y Lógica Fuzzy

p. 129-134

IEEE World Congress on Computational Intelligence

p. 9019-9025

Conference of the European Society for Fuzzy Logic and Technology

Presentation's date: 2005-09-07

IEEE International Conference on Fuzzy Systems

Presentation's date: 2005-05-22

Conference of the European Society for Fuzzy Logic and Technology

p. 303-308

IEEE International Conference on Fuzzy Systems

p. 658-662

XII Congreso Español Sobre Tecnologías y Lógica Fuzzy

Presentation's date: 2004-09-15

Fuzzy sets and systems

Vol. 146, num. 1, p. 27-41

DOI: 10.1016/j.fss.2003.11.004

Date of publication: 2004-08

Abstract:

This paper studies some geometric aspects of indistinguishability operators (also called similarities and fuzzy equivalences). Concretely, it will be focused on the (geometric) group associated to a T-indistinguishability operator E on X (i.e., the group of all bijective maps View the MathML source such that E(x,y)=E(h(x),h(y))¿x,y¿X). The cases for E being one dimensional and invariant under translations on the real line will be completely studied. This last property will be generalized to any group and there will be stated a bijection between indistinguishability operators invariant under translations on a group and its normal fuzzy subgroups.

This paper studies some geometric aspects of indistinguishability operators (also called similarities and fuzzy equivalences). Concretely, it will be focused on the (geometric) group associated to a T-indistinguishability operator E on X (i.e., the group of all bijective maps View the MathML source such that E(x,y)=E(h(x),h(y))∀x,y∈X). The cases for E being one dimensional and invariant under translations on the real line will be completely studied. This last property will be generalized to any group and there will be stated a bijection between indistinguishability operators invariant under translations on a group and its normal fuzzy subgroups.]]>

IEEE International Conference on Fuzzy Systems

Presentation's date: 2004-07-26

International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

p. 635-640

International Conference Virtual City and Territory

p. 1-14

International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

p. 635-640

IEEE International Conference on Fuzzy Systems

p. 1567-1571

DOI: 10.1109/FUZZY.2004.1375410

Abstract:

A new way to generate indistinguishability operators coherent with the underlying ordering structure of the real Dine is given in the sense that this structure should be compatible with the betweenness relation generated by the relation. A new way to generate indistinguishability operators coherent with the underlying ordering structure of the real line is given in the sense that this structure should be compatible with the between ness relation generated by the relation.]]>

International Conference of Mathematics and Design

p. 73-82

International Conference Virtual City and Territory

p. 1-14

XII Congreso Español Sobre Tecnologías y Lógica Fuzzy

p. 125-128

International journal of intelligent systems

Vol. 18, num. 12, p. 1193-1214

DOI: 10.1002/int.10141

Date of publication: 2003-12

Abstract:

This article studies the aggregation of transitive fuzzy relations. We first find operators that preserve transitivity and then extend the results to aggregating operators. As special cases, means and some kind of suitable ordered weighted averaging (OWAs) are used to aggregate transitive fuzzy relations with respect to an Archimedean t-norm. Three families of transitive relations that allow us to modify the entries of a given relation R continuously towards the smallest and the greatest ones in our universe are given. Aggregation of nonfinite families of transitive relations also is studied and applied to calculate the degree of inclusion or similarity of fuzzy quantities (fuzzy subsets of an interval of the real line). © 2003 Wiley Periodicals, Inc.]]>

10th IFSA World Congress

Presentation's date: 2003-06-29

10th IFSA World Congress

p. 85-88

3er Internacional Conference on Fuzzy Logia and Technology

p. 429-432

XI congreso español sobre tecnologías y lógica fuzzy

Presentation's date: 2002-09-17

XI congreso español sobre tecnologías y lógica fuzzy

p. 327-331

Presentation's date: 2002-09-17

Date of publication: 2002-09

International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

Presentation's date: 2002-07-01

Date of publication: 2002-04

Date of publication: 2002-04

Soft computing

Vol. 6, num. 1, p. 14-20

DOI: 10.1007/s005000100123

Date of publication: 2002-02

Abstract:

In this paper, some geometric aspects of indistinguishability operators are studied by using the concept of morphism between them. Among all possible types of morphisms, the paper is focused on the following cases: Maps that transform a T-indistinguishability operator into another of such operators with respect to the same t-norm T and maps that transform a T-indistinguishability operator into another one of such operators with respect to a different t-norm T ′. The group of isometries of a given T-indistinguishability operator is also studied and it is determined for the case of one-dimensional operators, in particular for the natural indistinguishability operators E T on [0, 1]. Finally, the indistinguishability operators invariant under translations on the real line are characterized.]]>

International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

p. 157-162

XI congreso español sobre tecnologías y lógica fuzzy

p. 550-560

International Conference in Fuzzy Logic and Technology

Presentation's date: 2001-09-05

Joint 9th IFSA World Congress and 20th NAFIPS International Conference

Presentation's date: 2001-07-25

Fuzzy sets and systems

Vol. 120, num. 3, p. 415-422

DOI: 10.1016/S0165-0114(99)00133-5

Date of publication: 2001-06

Abstract:

Indistinguishability operators fuzzify the concept of equivalence relation and have been proved a useful tool in theoretical studies as well as in di0erent applications such as fuzzy control or approximate reasoning. One interesting problem is their construction. There are di0erent ways depending on how the data are given and on their future use. In this paper, the length of an indistinguishability operator is de2ned and it is used to relate its generation via max-T product and via the representation theorem when T is an Archimedean t-norm. The link is obtained taking into account that indistinguishability operators generate betweenness relations. The study is also extended to decomposable operators.]]>