Fuzzy risk analysis based on measures of similarity between interval-valued fuzzy numbers

Abstract

In this paper, we present a new method for handling fuzzy risk analysis problems based on measures of similarity between interval-valued fuzzy numbers. First, we propose a similarity measure to calculate the degree of similarity between interval-valued fuzzy numbers. The proposed similarity measure uses the concept of geometry to calculate the center-of-gravity (COG) points of the lower fuzzy numbers and the upper fuzzy numbers of interval-valued fuzzy numbers, respectively, to calculate the degree of similarity between interval-valued fuzzy numbers. We also prove some properties of the proposed similarity measure. Then, we use the proposed similarity measure for interval-valued fuzzy numbers for handling fuzzy risk analysis problems. The proposed method is more flexible and more intelligent than the methods presented in [S.J. Chen, S.M. Chen, Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, IEEE Transactions on Fuzzy Systems 11 (1) (2003) 45–56; S.M. Chen, Evaluating the rate of aggregative risk in software development using fuzzy set theory, Cybernetics and Systems 30 (1) (1999) 57–75; S.M. Chen, New methods for subjective mental workload assessment and fuzzy risk analysis, Cybernetics and Systems 27 (5) (1996) 449–472; H.M. Lee, Applying fuzzy set theory to evaluate the rate of aggregative risk in software development, Fuzzy Sets and Systems 79 (3) (1996) 323–336; K.J. Schmucker, Fuzzy Sets, Natural Language Computations, and Risk Analysis, Computer Science Press, MD (1984)] due to the fact that it uses interval-valued fuzzy numbers rather than fuzzy numbers or generalized fuzzy numbers for handling fuzzy risk analysis problems. It provides us with a useful way for handling fuzzy risk analysis problems.