A valuation-based method for ranking the intuitionistic fuzzy numbers

Ranking the intuitionistic fuzzy numbers plays an important role in the process of decision making in the intuitionistic fuzzy environment. This paper presents a valuation-based method for ranking the intuitionistic fuzzy numbers. For this purpose, first, a method for mapping the intuitionistic fuzzy numbers to the crisp values is proposed and the concept of spread value of intuitionistic fuzzy numbers is defined. Then, using these concepts, a ranking method for the intuitionistic fuzzy numbers is introduced. In order to provide a better understanding for the proposed method, the concept of valuation function is discussed and the corresponding formulas are derived for two common types of intuitionistic fuzzy numbers, i.e. the trapezoidal and the triangular numbers. A comparative example is also presented to demonstrate the validity and superiority of the proposed method.