Signed-Distance Measures Oriented to Rank Interval-Valued Fuzzy Numbers

Abstract

This paper proposes a class of signed-distance measures for interval-valued fuzzy numbers based on specific bivariate functions, called kernels, and $\alpha \beta$ -values of interval-valued fuzzy numbers. The main properties, such as robustness, of the proposed signed-distance measure are also studied in the space of interval-valued fuzzy numbers. Then, the proposed signed-distance is applied to rank a set of interval-valued fuzzy numbers using an axiomatic approach. The proposed method is examined and compared to several existing methods, and the feasibility and effectiveness of the proposed methods are cleared via numerical and theoretical comparisons. The results indicate that the proposed method is simple for ranking all kinds of $LR$ -interval-valued fuzzy numbers, and it can overcome drawbacks of the existing methods based on reasonable axioms expected for a ranking criterion in the space of interval-valued fuzzy numbers. Finally, the proposed method is applied to a case study related to a multicriteria group decision making.