A Superior Goal Programming Approach for S-Shaped Membership Function and Its Applications

In general, to formulate fuzzy linear programming problem with n S-shaped utility (membership) functions, n or more extra binary variables are required in the traditional methods because S-shaped curve is neither convex nor concave everywhere (Yang et al. 1991, Lin and Chen 2002, Chang 2007). As shown by Keha et al. (2004), adding binary variables do not improve the bound of the linear programming relaxation. On the contrary, the binary variables will increase the computational burden in the solution process, if problem size gets large. Therefore, the formulation without binary variables seems to be more efficient. Following this, the study proposes a novel approach to formulate S-shaped membership function without adding any extra binary variable. That is, the formulated fuzzy linear programming problem with S-shaped membership functions represents a linear form which can be easily solved using common linear programming packages. This improves the efficiency of fuzzy linear programming in solving decision / management problems with S-shaped membership function. Finally, computational experience is provided to demonstrate the superiority of the proposed models. An illustrative example is also provided to show the usefulness of the proposed method.

Project ID:PF10001-0896
External Project ID:NSC99-2410-H182-015-MY3