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 Systems with Applications 36 (2009) 6833-6842) is incorrect. The main aim of this paper is to prop...

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...

Abstract. The fuzzy set theory has been applied in many fields such as management, engineering etc. In modern management applications ranking using fuzzy numbers are the most important aspect in decision making process. This paper proposes a new method on the incentre of centroids and uses of Euclidean distance to ranking generalized hexagonal fuzzy numbers. We have used a ranking method for or...

In most of the commonly used approaches, the ranking of generalized fuzzy numbers is calculated based on the only one criterion i.e., rank criteria. However, there are some weaknesses associated with this criterion. In this paper, we discuss the insufficiency of considering only rank for the ordering of generalized fuzzy numbers. Some shortcomings in existing ranking methods have been pointed o...

The new concept of a Z – number has been recently introduced in decision making analysis. This concept is capable of effectively dealing with uncertainty in information about a decision. As this concept is relatively new in fuzzy sets, its underlying theoretical aspects have not been established yet. In this paper, a multi-layer methodology for ranking Z – numbers is proposed for the first time...

Triangular intuitionistic fuzzy numbers (TIFNs) is a special case of intuitionistic fuzzy (IF) set and the ranking of TIFNs is an important problem. The aim of this paper is to develop a new methodology for ranking TIFNs by using multiattribute decision making methods (MADM). In this methodology, the value and ambiguity indices of TIFNs may be considered as the attributes and the TIFNs in compa...

today, the knowledge of regions’ strong and weak points and the existing gaps between regions is necessary for better planning and programming to deal with them. using such indexes as economic, sociologic, cultural, sanitary and other indexes which can be good criteria for the position and place determination of these quotients, is the main solving problem factor to achieve economic welfare, so...

in this paper, by using a new approach on distance between two fuzzy numbers, we construct a new ranking system for fuzzy number which is very realistic and also matching our intuition as the crisp ranking system on r.

In this paper I will introduce the trapezoidal intuitionistic fuzzy numbers (IF numbers) and will prove some operations for them. Also I am going to propose a new ordering method for IF numbers in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse fuzzy membership and non-membership...