International Journal of Fuzzy Mathematics and Systems. Volume 1, Number 1 (2011), pp. 47-58 © Research India Publications http://www.ripublication.com A Note on Fuzzy Goal Programming with Nested Priorities Babita Mishra and S.R. Singh * Department of Mathematics, Banaras Hindu University, Varanasi-221005, India *Corresponding Author E-mail: singh_shivaraj@rediffmail.com Abstract Rubin and Narsimhan [1984] proposed a method for formulating fuzzy priorities in goal programming. They used the concept that the membership function based on nested priorities has to be concave to solve the fuzzy goal programming problem by linear programming method. In this paper, we relax the condition of concave membership function by quasi concave membership function. We showed that the fuzzy goal programming problem with nested priorities can be solve by linear programming method using quasi concave membership function in a better way of attaining the goals. Keywords: Fuzzy priority, nested priority, piece wise linear membership function, concave membership function, quasi concave membership function. Introduction In fuzzy goal programming consideration of relative importance and priorities of different goals is crucial factor to obtain a suitable fuzzy decision satisfying the fuzzy goal in an optimal way. Narsimhan [14] considered this problem in fuzzy goal programming model and discussed its solution procedure. Hannan [4,5, 6] used conventional deviational variables into the model and showed that it can be solve by linear programming formulation. However both Narsimhan [14, 16] and Hannan[4,5,6] used only triangular or concave membership function. Nakamura [13] divided the quasi concave fuzzy multi objective problem as number of intersections between concave functions and convex functions and solved the sub problems by using linear programming. Inuiguchi [9] gave an algorithm for solution of fuzzy linear programming problem with piecewise linear membership functions and Yang et. al [17] gave a piecewise linear approximation method for fuzzy programming with non linear membership function. Li and Yu [11] proposed a method for solving a fuzzy