A Novel Inverse Credibility Distribution Approach for the Membership Functions of LR Fuzzy Intervals: A Case Study on a Completion Time Analysis

Abstract

Fuzzy arithmetic is of great significance in dealing with vague information, especially the basic arithmetic operations (i.e., ⊕, ⊖, ⊗, ⊙). However, the classical and widely accepted accurate and approximate approaches, the interval arithmetic approach and standard approximation method, cannot output accurate or well-approximated expressions of the membership function, which may prevent decision makers from making the right decisions in real applications. To tackle this problem, this paper first discusses the relationships among the membership function, the credibility distribution, and the inverse credibility distribution and summarizes the relationships as several theorems. Then, by means of the theorems and the newly proposed operational law, this paper proposes an inverse credibility distribution approach that can output the accurate expression of the membership function for continuous and strictly monotone functions of regular LR fuzzy intervals. To better demonstrate the effectiveness of the raised approach, the commonly-used LR fuzzy interval, the symmetric trapezoidal fuzzy number, is employed, and several comparisons with the other two methods are made. The results show that the proposed approach can output an exact or well-approximated expression of the membership function, which the others cannot. In addition, some comparisons of the proposed approach with other methods are also made on a completion time analysis of a construction project to show the effectiveness of the proposed approach in real applications.