Coherence Measures on Finite Fuzzy Sets

Abstract

Comparison tools for fuzzy sets are an indispensable topic. Mostly of this tools deal with fuzzy sets from the view of similarity, order and so forth. A comparison tool based on coherence intuitive concept is presented. For constructing this concept, one start from three basics properties. A development of this tool is presented, equally coherence measures are connected with Fishburn-Yager's ambiguity measures. Two methods for constructing coherence measures are shown: one from ambiguity measures and other from metrics on [0,1 ] m . Concretely, has been constructed various coherence measures from different ambiguity measures and different metrics. Equivalency between some coherence measures has been shown. This paper finish with numeric examples presented in order to check coherence measures displayed.

Fuzzy coherence measures

“…As we have previously stated, these three generalizations make up and provide us with a framework common to the different previous contributions by the authors. 1,2 These generalizations have also generalized and unified the approximations carried out in this same context by other authors. [5][6][7] Particularly, some of the properties pointed out in Ref.…”

“…1 and 2 was to offer a similarity tool, for comparing fuzzy sets, sensible to the fuzziness of the considered sets. In this way, from a very simple axiomatic, the definition of coherence measures was shown for both finite 1 and nonfinite 2 sets X. Despite the rigorous study taken in Ref.…”

“…Despite the rigorous study taken in Ref. 1 and then in Ref. 2, the integration of these measures in a common shared theoretical framework is still pending.…”

Coherence measures and their relation to fuzzy similarity and inconsistency in knowledge bases

“…In the case of similarity, two very different conceptions of similarity have been identified, one ignoring the degree of fuzziness of the sets and the other incorporating it. It has been shown how measures of the first type can be converted to measures of the second type and that the second type is closely related to the notion of a coherence measure proposed by Sancho-Royo and Verdegay (2000). Furthermore, a notion of fuzzy-independence was defined relative to a similarity measure of the first type and it was shown that when such a similarity measure is used to generate a similarity measure of the second type, the former measure is insensitive to fuzzy-dependence while the latter is not.…”

Rectification of Preferences in a Fuzzy Environment

“…We then propose that the confidence measure we are looking for can be analyzed as a coherence measure. Recall that ambiguity [8] and coherence measures [20] are explicitly related by extension theorems proven for any strong negation (such that a kbijection verifying n(x)=k-1(k(1)-k(x)) exists, see [5], [20], [21]). These coherence measures evaluate how fuzzy and similar are any pair of fuzzy sets, where the degree of fuzziness is characterized by F1-F3.…”