An approximation approach for representing S-shaped membership functions

Authors:
Ching-Ter Chang
Affiliations:
Department of Information Management, Chang Gung University, Tao-Yuan, Taiwan
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2010

Citing 14
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Abstract

In general, to formulate a fuzzy-linear-programming problem with n S-shaped utility (membership) functions, traditional methods require n or more extra binary variables because S-shaped curves are neither convex nor concave in all places. Adding binary variables does not improve the bound of the linearprogramming relaxation. On the contrary, added binary variables increase the computational burden in the solution process if problems get large. Therefore, a formulation without binary variables should be more efficient. Accordingly, this study proposes a piecewise-linear approach to formulate an S-shaped membership function (MF) without adding any extra binary variables, which improves the efficiency of fuzzy-linear programming in solving decision/ management problems with S-shaped MFs. Finally, a computational experiment is provided to demonstrate the superiority of the proposed models. An illustrative example is also provided to show the usefulness of the proposed method.