An Approximation Approach for Representing S-Shaped Membership Functions

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 lin...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems Vol. 18; no. 2; pp. 412 - 424
Main Author: Chang, Ching-Ter
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximation
Binary variable
Computation
Computational efficiency
Delta modulation
Functional programming
Fuzzy sets
fuzzy-goal programming (FGP)
fuzzy-linear programming (FLP)
Linear programming
Management
Mathematical analysis
Mathematical models
membership function (MF)
Natural languages
Packaging
Piecewise linear approximation
Piecewise linear techniques
piecewise-linear function (PLF)
Programming
Utilities
Utility programs
ISSN:1063-6706, 1941-0034
Online Access:Get full text
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Summary: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 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.
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2010.2042961