A Novel Similarity Measure for Generalized Trapezoidal Fuzzy Numbers and its Application to Decision-Making

Abstract

Similarity measures of fuzzy numbers have been widely applied in various areas. In the last decade, many similarity measures of generalized fuzzy numbers were proposed. However, there are two main limitations in existing similarity measures: 1) they cannot correctly calculate the degree of similarity between two generalized trapezoidal fuzzy numbers in some cases; and 2) the definitions of recently developed similarity measures are complicated and difficult to interpret. In this paper, a novel approach to similarity measurement between generalized trapezoidal fuzzy numbers is proposed. The proposed similarity measure has a simple definition and is easier to understand intuitively. Furthermore, we analyze its properties and compare it with existing similarity measures. The results show that the proposed measure outperforms existing similarity measures. Finally, we apply the proposed similarity measure to develop a fuzzy-logic-based approach for new product go/nogo decision-making at the front end. The proposed fuzzy software quality evaluation method is more flexible and more intelligent than existing methods due to the fact that it considers the degrees of confidence of evaluators’ opinions.