The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.

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...

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...

Although simple additive weighting method (SAW) is the most popular approach for classical multiple attribute decision making (MADM), it is not practical any more if information is fuzzy. The existing methods of Fuzzy Simple Additive Weighting method (FSAW) apply defuzzification which distorts fuzzy numbers. Furthermore, most of the methods usually require lengthy and laborious manipulations. I...

We present some interesting properties related to the area compensation procedure to compare fuzzy numbers. It has been proved that this method produces more than a fuzzy interval order: it induces a ranking of fuzzy numbers. Some further results are given about the transitivity property and about computational aspects. Extensions to non-normal fuzzy numbers and fuzzy quantities are also proposed.

In this paper, we investigate an assignment problem in which cost coefficients are triangular intuitionistic fuzzy numbers. In conventional assignment problem, cost is always certain. This paper develops an approach to solve an intuitionistic fuzzy assignment problem where cost is not deterministic numbers but imprecise ones. Here, the elements of the costs (profits) matrix of the assignment pr...

Two families of metrics in space of intuitionistic fuzzy numbers are considered. A method of ranking intuitionistic fuzzy numbers based on these metrics is also suggested and invesigated.

We find necessary and sufficient conditions for a ranking index defined on the set of triangular fuzzy numbers as a linear combination of its components to rank effectively. Then, based on this result, we characterize the class of ranking indices which generates orderings on triangular fuzzy numbers satisfying the basic requirements by Wang and Kerre in a slightly modified form.

In this paper, we want represented a method for ranking of two exponential trapezoidal fuzzy numbers. A median value is proposed for the ranking of exponential trapezoidal fuzzy numbers. For the validation the results of the proposed approach are compared with different existing approaches.

In this paper, we want proposed a new method for ranking in areas of two generalized trapezoidal fuzzy numbers. A simpler and easier approach is proposed for the ranking of generalized trapezoidal fuzzy numbers. For the confirmation this results, we compared with different existing approaches. 2010 AMS CLASSIFICATION: 47S20, 03E72.