Adela Salvador

On t-norms based measures of specificity

This paper gives a general expression for families of measures of specificity of a fuzzy set or a possibility distribution based on three t-norms and a negation. Other known measures of specificity are particular cases of this expression and new examples are provided.

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.

Measures of specificity of fuzzy sets under T-indistinguishabilities

The concept of measure of specificity of fuzzy sets is extended in this paper to measure of specificity under the knowledge of T-indistinguishabilities. Four axioms of measure of specificity under T-indistinguishabilities are given. An algorithm to compute the inference independent set Tfr from a fuzzy set and a T-indistinguishability is used to measure the specificity of fuzzy sets under T-indistinguishabilities satisfying the axioms

T -fuzzy prime ideals

Abstract The purpose of this paper is to define, study and characterize the T -fuzzy prime ideals. T -fuzzy strongly prime ideals and T-S -fuzzy weakly prime ideals proving the inclusion relationships that are satisfied among them. The T -fuzzy comaximal ideals and fuzzy maximal ideals are also investigated.

Computing a T-transitive lower approximation or opening of a proximity relation

Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the more number of elicitations, the more probable inconsistency is. This is mostly the case within a fuzzy framework, even when the number of alternatives or object to be classified is relatively small. In this paper we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, being T any left-continuous t-norm. The computed approximation we propose will take O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors? knowledge, there are no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties.

A t-norm based specificity for fuzzy sets on compact domains

An expression for measuring the specificity of fuzzy sets on continuous domains is introduced. This expression is based on t-norms, negations and the Choquet integral. It is also proved that the new expression satisfies the given axioms for measure of specificity. New examples are provided.

On measuring μ - T -inconditionality of fuzzy relations

In this paper two methods are proposed to measure the μ-T-inconditionality character of any fuzzy relation for any continuous t-norm T, and it is studied when both methods result to be equivalent.

Hurst Coefficient in long time series of population size: Model for two plant populations with different reproductive strategies

Can the fractal dimension of fluctuations in population size be used to estimate extinction risk? The problem with estimating this fractal dimension is that the lengths of the time series are usually too short for conclusive results. This study answered this question with long time series data obtained from an iterative competition model. This model produces competitive extinction at different perturbation intensities for two different germination strategies: germination of all seeds vs. dormancy in half the seeds. This provided long time series of 900 years and different extinction risks. The results support the hypothesis for the effectiveness of the Hurst coefficient for estimating extinction risk.

Computing a T-transitive opening of a proximity

A fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation is given for any left-continuous t-norm, taking O(n(3)) time complexity, where n is the number of elements in the universe. It is proved that the computed fuzzy relation is a T-transitive opening when T is the minimum t-norm or a strictly growing t-norm. As far as we know, this is the first known algorithm that computes T-transitive openings preserving the reflexive and symmetric properties.

A new algorithm to compute low t-transitive approximation of a fuzzy relation preserving symmetry. comparisons with the t-transitive closure

It is given a new algorithm to compute a lower T-transitive approximation of a fuzzy relation that preserves symmetry. Given a reflexive and symmetric fuzzy relation, the new algorithm computes a T-indistinguishability that is contained in the fuzzy relation. It has been developed a C++ program that generates random symmetric fuzzy relations or random symmetric and reflexive fuzzy relations and computes their T-transitive closure and the new low T-transitive approximation. Average distances of the fuzzy relation with the T-transitive closure are similar than the average distances with the low T-transitive approximation.