A new method namely, level-sum method based on the multi-objective linear programming and the simplex method is proposed for computing an optimal fuzzy solution to a fuzzy linear programming problem inwhich fuzzy ranking functions are not used. The level-sum method is illustrated by numerical examples.

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Abstract:A new approach, namely sum of objectives (SO) method is proposed to finding a fair solution to multi-objective programming problems. The proposed method is very simple, easy to use and understand and also, common approaches. It is illustrated with the help of numerical examples. The fair solution serves more better than efficient solution for decision makers when they are handling multiple objective decision making problems. Mathematics subject classification: 65K05, 90C29.

A new method namely, denominator objective restriction method based on simplex method is proposed for solving linear fractional programming problems. Further, another method namely, decomposition-restriction method based on decomposition principle and the denominator objective restriction method is proposed for obtaining an optimal fuzzy solution to the fully fuzzy linear fractional programming problem. The procedures for the proposed methods are illustrated with the numerical examples.