Susana Cubillo

Computing with Antonyms

This work tries to follow some agreements linguistic seem to have on the semantical concept of antonym, and to model by means of a membership function an antonym aP of a predicate P, whose use is known by a given μP

When QM-operators are implication functions and conditional fuzzy relations

Some fuzzy reasoning systems base inference processes on fuzzy implication functions. Although there has been a great deal of work done on characterizing R‐ and S‐implications, little is known about QM‐implications in spite of their long history since they came to fuzzy logic by analogy with the quantum mechanic logic. This paper tackles the study of some characteristics of this type of operator. It focuses on the QM‐implication operator both as an implication function and also as a T‐conditional function, giving useful tools to characterize them. © 2000 John Wiley & Sons, Inc.

On conjectures in orthocomplemented lattices

Abstract A mathematical model for conjectures in orthocomplemented lattices is presented. After defining when a conjecture is a consequence or a hypothesis, some operators of conjectures, consequences and hypotheses are introduced and some properties they show are studied. This is the case, for example, of being monotonic or non-monotonic operators. As orthocomplemented lattices contain orthomodular lattices and Boolean algebras, they offer a sufficiently broad framework to obtain some general results that can be restricted to such particular, but important, lattices. This is, for example, the case of the structures theorem for hypotheses. Some results are illustrated by examples of mathematical or linguistic character, and an appendix on orthocomplemented lattices is included.

On consequence in approximate reasoning

ABSTRACT The purpose of this paper is to explore the notion of consequence in Approximate Reasoning. While logical consequence has an standard (semantic and syntactic) definition in Exact Logic, several different definitions of that concept can be considered in the Approximate Reasoning framework. In this paper some definitions are compared with consequences derived from inference methods used in Artificial Intelligence. We will show that some inference methods are not covered by that definitions. Finally a more general concept of Approximate Consequence is introduced covering a wide variety of such inference methods.

Conjunction and disjunction on ([0,1], ≤)

Abstract In classical logic the proposition “p and q” is true if and only if p is true and q is true. In multi-valued logic, to functionally obtain the truth value of “p and q”, t-norms are used, but there are many situations in real life in which another functions are also used. This paper contains two definitions of conjunction including large families of possible conjunction functions. Furthermore, a new definition of local conjunction is given, and symmetrically, some definitions of disjunctions and of local disjunction. In particular, quasiarithmetic and weighted means are studied.

A method to make some fuzzy relations T-transitive

A new method is given for a finite reflexive relation with a fixed set of properties and a t‐norm T, so that a different, but similar, T‐transitive relation could be found. The transitive closure is greater than the given relation; however, the T‐transitivized relation defined in this article is less than or equal to the original one, while reaching or maintaining, in this case, the T‐conditionality. The algorithm also verifies if a relation is T‐transitive. ©1999 John Wiley & Sons, Inc.

Negations on type-2 fuzzy sets

Abstract So far, the negation that usually has been considered within the type-2 fuzzy sets (T2FSs) framework, and hence T2FS truth values M (set of all functions from [ 0 , 1 ] to [ 0 , 1 ] ), was obtained by means of Zadehs extension principle and calculated from standard negation in [ 0 , 1 ] . But there has been no comparative analysis of the properties that hold for the above operation and the axioms that any negation in M should satisfy. This suggests that negations should be studied more thoroughly in this context. Following on from this, we introduce in this paper the axioms that an operation in M must satisfy to qualify as a negation and then prove that the usual negation on T2FSs, in particular, is antimonotonic in L (set of normal and convex functions of M ) but not in M . We propose a family of operations calculated from any suprajective negation in [ 0 , 1 ] and prove that they are negations in L . Finally, we examine De Morgans laws for some operations with respect to these negations.

Measuring incompatibility between Atanassov's intuitionistic fuzzy sets

The aim of this paper is to establish an axiomatic definition of incompatibility measure in the framework of Atanassovs intuitionistic fuzzy sets and use geometrical methods to build some families of such incompatibility measures. First, we construct several functions to measure incompatibility for an intuitionistic t-norm that can be represented by an adequate t-norm and t-conorm. Additionally, we establish some relations between some particular cases of these functions. Similarly, we then obtain incompatibility measures for a family of non-representable intuitionistic t-norms.

SELF-CONTRADICTION AND CONTRADICTION BETWEEN TWO ATANASSOV'S INTUITIONISTIC FUZZY SETS

The paper focuses on the study of the contradiction between two Atanassovs intuitionistic fuzzy sets. First, taking into account some characterizations obtained in previous papers, some functions are defined in order to measure the degrees of contradiction. Besides the principal properties of these measures are pointed out. Finally, some results relating self-contradiction and contradiction between two Atanassovs intuitionistic fuzzy sets are achieved.

On modus ponens generating functions

This paper investigates the use of functions other than t-norms to model the Modus Ponens rule in a fuzzy inference process. For that purpose, new definitions for fuzzy inference related concepts a...