The trapezoidal fuzzy soft set and its application in MCDM

Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. Since the trapezoidal fuzzy number, as a vital concept of fuzzy set, can express linguistic assessments by transforming them into numerical variables objectively, this paper aims to extend classical soft sets to trapezoidal fuzzy soft sets based on trapezoidal fuzzy numbers. Then, some operations on a trapezoidal fuzzy soft set are defined, such as complement operation, AND operation, and OR operation. Finally, a Multiple Criterion Decision-Making (MCDM) problem under a fuzzy environment is analyzed by trapezoidal fuzzy soft sets with the demonstration of a numerical example. This paper also uses traditional fuzzy soft sets to deal with the MCDM problem. The result shows that the method provided by this paper outperforms the traditional one. (C) 2012 Elsevier Inc. All rights reserved.