Thick gradual intervals: An alternative interpretation of type-2 fuzzy intervals and its potential use in type-2 fuzzy computations. (October 2019)

• Record Type: Journal Article
• Authors: Boukezzoula, Reda; Jaulin, Luc; Foulloy, Laurent
• Is Part Of: Engineering applications of artificial intelligence. Volume 85(2019)
• Page Start: 691
• Page End: 712
• Publication Date: 2019-10
• Subjects: Type-1 and type-2 fuzzy intervals -- Thick intervals and thick gradual intervals -- Fuzzy arithmetic and gradual arithmetic -- Interval arithmetic -- T2FI regression -- T2FI aggregation operators; Engineering -- Data processing -- Periodicals; Artificial intelligence -- Periodicals; Expert systems (Computer science) -- Periodicals; Ingénierie -- Informatique -- Périodiques; Intelligence artificielle -- Périodiques; Systèmes experts (Informatique) -- Périodiques; Artificial intelligence; Engineering -- Data processing; Expert systems (Computer science); Periodicals; 620.00285
• DOI: 10.1016/j.engappai.2019.07.014
• Languages: English
• ISSNs: 0952-1976

Abstract

Abstract: This paper proposes a new interpretation of type-2 fuzzy intervals (T2FIs) through the joint use of gradual intervals (GIs) and thick intervals (TIs). In this framework, a T2FI is viewed as a thick gradual interval (TGI). This new representation gives an original concept for the manipulation of T2FIs according to the thick gradual representation. Furthermore, this vision allows an extension of the interval arithmetic arsenal and reasoning to the framework of T2FIs. The proposed approach can be regarded as more computationally viable, which will make T2FIs computations more useful in applied scenarios. As an illustration, the proposed concept is used to implement the elementary arithmetic operations on T2FIs. The potentialities of the TGI approach have been validated in the frameworks of T2FI aggregation operators and T2FI regression.