Convex-cone-based comparisons of and difference evaluations for fuzzy sets. (3rd July 2018)

• Record Type: Journal Article
• Authors: Ike, Koichiro; Tanaka, Tamaki
• Is Part Of: Optimization. Volume 67:Number 7(2018)
• Page Start: 1051
• Page End: 1066
• Publication Date: 2018-07-03
• Subjects: Fuzzy set -- set relation -- scalarization -- calculation method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1432608
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: This paper focuses on how to compare two fuzzy sets and, from the viewpoint of set optimization, proposes eight types of fuzzy-set relations based on a convex cone as new comparison criteria of fuzzy sets. Then, difference evaluation functions for fuzzy sets are introduced. Under suitable assumptions of certain compactness and stability of fuzzy sets, we show that these functions correspond well to the fuzzy-set relations. In addition, through transforming these functions stepwise, we deal with numerical calculation methods of them in particular cases. Consequently, we can judge whether each fuzzy-set relation holds or not for given two fuzzy sets with the aid of computers.