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1 Journal of Mathematics and Applications

1 2011

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Ranking of generalized fuzzy numbers with generalized fuzzy simplex algorithm

Kumar A., Singh P.

Journal of Mathematics and Applications

2011

Vol. 34

53--73

Ranking of fuzzy numbers play an important role in decision making problems. Fuzzy numbers must be ranked before an action is taken by a decision maker. Jain (Decision-making in the presence of fuzzy variables, IEEE Transactions on Systems, Man and Cybernetics 6 (1976) 698-703) proposed the concept of ranking function for comparing normal fuzzy numbers. Chen (Operations on fuzzy numbers with function principal, Tamkang Journal of Management Science 6 (1985) 13-25) pointed out that in many cases it is not to possible to restrict the membership function to the normal form and proposed the concept of generalized fuzzy numbers. Chen and Chen (Fuzzy risk analysis based on the ranking generalized fuzzy numbers with different heights and different spreads, Expert Systems with Applications 36 (2009) 6833-6842) pointed out the shortcomings of the existing methods for the ranking of generalized fuzzy numbers and proposed a new method. In this paper the shortcomings of the Chen and Chen method are pointed out and a new method is proposed for the ranking of generalized fuzzy numbers. Also using the proposed ranking method, a generalized simplex algorithm is proposed for solving a special type of fuzzy linear programming (FLP) problems. To illustrate the proposed algorithm a numerical example is solved and the advantages of the proposed algorithm are discussed. Since the proposed algorithm is a direct extension of classical algorithm so it is very easy to understand and apply the proposed algorithm to find the optimal solution of FLP problems occurring in the real life situations.