Similarity measures, penalty functions, and fuzzy entropy from new fuzzy subsethood measures. Issue 6 (29th January 2019)

• Record Type: Journal Article
• Authors: Santos, Helida; Couso, Inés; Bedregal, Benjamin; Takáč, Zdenko; Minárová, Mária; Asiaın, Alfredo; Barrenechea, Edurne; Bustince, Humberto
• Is Part Of: International journal of intelligent systems. Volume 34:Issue 6(2019)
• Page Start: 1281
• Page End: 1302
• Publication Date: 2019-01-29
• Subjects: fuzzy entropy -- fuzzy sets -- penalty functions -- similarity measures -- subsethood measure; Artificial intelligence -- Periodicals; Expert systems (Computer science) -- Periodicals; Intelligence artificielle -- Périodiques; Systèmes experts (Informatique) -- Périodiques; 006.3
• DOI: 10.1002/int.22096
• Languages: English
• ISSNs: 0884-8173

Abstract

Abstract: In this study, we discuss a new class of fuzzy subsethood measures between fuzzy sets. We propose a new definition of fuzzy subsethood measure as an intersection of other axiomatizations and provide two construction methods to obtain them. The advantage of this new approach is that we can construct fuzzy subsethood measures by aggregating fuzzy implication operators which may satisfy some properties widely studied in literature. We also obtain some of the classical measures such as the one defined by Goguen. The relationships with fuzzy distances, penalty functions, and similarity measures are also investigated. Finally, we provide an illustrative example which makes use of a fuzzy entropy defined by means of our fuzzy subsethood measures for choosing the best fuzzy technique for a specific problem.