Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Syst Appl 36:6833–6842, 2009) is incorrect. The main aim of this paper is to propose a new approac...

Ranking of fuzzy numbers is not an easy task as fuzzy numbers are represented by possibility distributions and they can overlap with each other. Since it was introduced, various approaches on ranking fuzzy numbers have been proposed. The recent ranking fuzzy numbers proposed by Wang and Li is claimed to be the improved version in ranking. However, the method was never been simplified and tested...

This paper presents an area-based approach to ranking fuzzy numbers in fuzzy decision making. To ensure that all the information that a fuzzy number has is adequately considered, the concepts of the absolute area and the degree of deviation of a fuzzy number are integrated into the process of comparing and ranking fuzzy numbers. To help the decision maker better address the risk inherent in the...

Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking...

The order relation of fuzzy number is important in decision making and optimization modeling, and ranking fuzzy numbers is difficult in nature. Ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) is more difficult due to the fact that the TrIFNs are a generalization of the fuzzy numbers. The aim of this paper is to develop a new methodology for ranking TrIFNs. We define the value-index an...

Since much of human reasoning is based on imprecise, vague and subjective values, most of decision-making processing, in reality, requires handling and evaluation of fuzzy numbers. Zadeh’s (Zadeh 1965) fuzzy logic has given analysts a tool to present the human behavior more precisely, especially where relatively few data exist, and where the expert knowledge about the system is vague and lingui...