E. Barrenechea

Comments on “Interval Type-2 Fuzzy Sets are Generalization of Interval-Valued Fuzzy Sets: Towards a Wide View on Their Relationship”

This letter makes some observations about “Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: Towards a wide view on their relationship,” IEEE Trans. Fuzzy Systems that further support the distinction between an interval type-2 fuzzy set (IT2 FS) and an interval-valued fuzzy set (IV FS), points out that all operations, methods, and systems that have been developed and published about IT2 FSs are, so far, only valid in the special case when IT2 FS = IVFS, and suggests some research opportunities.

Solving multi-class problems with linguistic fuzzy rule based classification systems based on pairwise learning and preference relations

This paper deals with multi-class classification for linguistic fuzzy rule based classification systems. The idea is to decompose the original data-set into binary classification problems using the pairwise learning approach (confronting all pair of classes), and to obtain an independent fuzzy system for each one of them. Along the inference process, each fuzzy rule based classification system generates an association degree for both of its corresponding classes and these values are encoded into a fuzzy preference relation. Our analysis is focused on the final step that returns the predicted class-label. Specifically, we propose to manage the fuzzy preference relation using a non-dominance criterion on the different alternatives, contrasting the behaviour of this model with both the classical weighted voting scheme and a decision rule that combines the fuzzy relations of preference, conflict and ignorance by means of a voting strategy. Our experimental study is carried out using two different linguistic fuzzy rule learning methods for which we show that the non-dominance criterion is a good alternative in comparison with the previously mentioned aggregation mechanisms. This empirical analysis is supported through the corresponding statistical analysis using non-parametrical tests.

INTUITIONISTIC FUZZY IMPLICATION OPERATORS — AN EXPRESSION AND MAIN PROPERTIES

In this paper we present the definition and properties of intuitionistic fuzzy implication operators. We study the expression obtained from said operators when fuzzy implication and coimplication operators are applied to different aggregations of degrees of truth and non-truth of the propositions.

WEAK FUZZY S-SUBSETHOOD MEASURES: OVERLAP INDEX

Starting from the definitions of the weak fuzzy subsethood measure (V.R. Young, Fuzzy subsethood. Fuzzy Sets and Systems, 77 (1996) 371–384) and of strong fuzzy inclusion, (D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York, Academic Press, 1980) we define weak fuzzy S-subsethood measures. We analyze their axiomatization and present various constructions obtained by aggregating implication operators with special properties. We conclude by presenting the conditions under which we can construct fuzzy entropies and overlap indices from these measures.

A method for constructing V. Young's fuzzy subsethood measures and fuzzy entropies

In the first part of the paper we show the three most important axiomatizations of the concept of subsethood measure. Then we present the reasons why we focus on the definition given by V. Young. Next we study a method for constructing said measures and we analyze the conditions in which they satisfy the axioms of Sinha and Dougherty. Afterwards we study the way of obtaining fuzzy entropies that fulfil the valuation property from said subsethood measures

Ignorance-Based Fuzzy Clustering Algorithm

In this work an ignorance-based fuzzy clustering algorithm is presented. The algorithm is based on the Entropy-based clustering algorithm proposed by Yao et al. [1]. In our proposal, we calculate the total ignorance instead of using the entropy at each data point to select the data point as the first cluster center. The experimental results show that the ignorance-based clustering improves the data classification made by the EFC in image segmentation.

Laws for conjunctions and disjunctions in interval type 2 fuzzy sets

In this paper we study in depth certain properties of interval type 2 fuzzy sets. In particular we recall a method to construct different interval type 2 fuzzy connectives starting from an operator. We further study the law of contradiction and the law of excluded middle for these sets. Furthermore we analyze the properties: idempotency, absorption, and distributiveness.

From Trillas’ Negations and Antonyms to a Set Representation of Contradiction Within Bipolar and Other Extensions of Fuzzy Sets

In 1979, Enric Trillas started to interest in in fuzzy connectives. His first paper on this topic was ”Funciones de negacin en la teora de subconjuntos difusos” ([9]) (Negation functions in the theory of fuzzy subsets), which appeared in Spanish in the Stochastica journal. This work, focused on the characterization of strong negations, has been so relevant for the development of fuzzy theory that it was translated into English and widely cited in the last 35 years.