An Approximation Approach for Representing S-Shaped Membership Functions

作者：Chang Ching Ter^*

来源：IEEE Transactions on Fuzzy Systems, 2010, 18(2): 412-424.

DOI：10.1109/TFUZZ.2010.2042961

• Binary variable
• fuzzy-goal programming (FGP)
• fuzzy-linear programming (FLP)
• membership MF)
• piecewise-linear PLF)

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 linear-programming 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 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.

• 出版日期2010-4
• 单位长春大学