Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables

Abstract

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.

Keywords

• interval type-2 fuzzy variable
• membership function
• expected value
• operational law