An enhanced two-step method for ranking generalized trapezoidal fuzzy numbers and its application to economic evaluation of projects

Today, the advancement of intelligent inference models and systems for addressing decision-making problems has brought the issue of accurately prioritizing and ranking decision options to the forefront. Additionally, the increasing use of fuzzy numbers and fuzzy sets in modeling complex problems has made fuzzy number rankings essential in management sciences and fuzzy decision-making scenarios. Various methods have been proposed to tackle fuzzy number ranking challenges. In this context, researchers have utilized different characteristics of fuzzy numbers, such as the center of gravity (CoG), the spread of fuzzy numbers, and their perimeter, among other features. However, many existing methods for addressing specific decision-making problems struggle to rank fuzzy numbers accurately. Unfortunately, the output results from these methods often contradict human intuition and perception. This paper presents an enhanced two-step method that is based on the value and degree of ambiguity of generalized trapezoidal fuzzy numbers. Additionally, this proposed method introduces distinct indices for the left and right extensions of fuzzy numbers, thereby addressing the shortcomings of previous approaches. The method ultimately ranks the fuzzy numbers in two stages. In the first stage, the rating index for the fuzzy numbers is calculated based on their value and ambiguity. If the ranking indices are equal in this stage, the final ranking is determined in the second stage based on the left and right extensions of the fuzzy numbers. Using sixteen different sets of generalized trapezoidal fuzzy numbers, the strength and effectiveness of the proposed method are compared to previous studies. Finally, the proposed method is applied to the economic evaluation of projects through the use of fuzzy net present value (FNPV). An example is also provided to demonstrate the performance of this method.