Variance and Semi-Variances of Regular Interval Type-2 Fuzzy Variables

Abstract

In this paper, we define the variance and semi-variances of regular interval type-2 fuzzy variables (RIT2-FVs) as well as derive a calculation formula of them based on the credibility distribution. Following the relationship between the variance and the semi-variances of the regular symmetric triangular interval type-2 fuzzy variables (RSTIT2-FVs), a special type of interval type-2 fuzzy variable is discovered and proved. Furthermore, for applying the two measures, we propose the operational law for the variance and semi-variances of the linear function of mutually independent RSTIT2-FVs. Some numerical examples are illustrated. The consequences of examples prove that the formulas we proposed can be effectively applied to the calculation of the variance of RSTIT2-FVs. The results indicate that they play a great role in the application of variance of type-2 fuzzy sets in various fields.

Keywords

• interval type-2 fuzzy variable
• variance
• semi-variance
• operational law