Method for solving quasi-concave and non-concave fuzzy multi-objective programming problems

This paper proposes a method based on linear programming techniques to treat quasi-concave and non-concave fuzzy multi-objective programming (FMOP) problems. The proposed method initially presents a piecewise linear expression to interpreting a quasi-concave membership function. Then we find the con...

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Bibliographic Details
Published in:Fuzzy sets and systems 2001-09, Vol.122 (2), p.205-227
Main Authors: Yu, Chian-Son, Li, Han-Lin
Format: Article
Language:English
Subjects:
Fuzzy multi-objective programming
Linear programming
Non-concave
Piecewise
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Summary:This paper proposes a method based on linear programming techniques to treat quasi-concave and non-concave fuzzy multi-objective programming (FMOP) problems. The proposed method initially presents a piecewise linear expression to interpreting a quasi-concave membership function. Then we find the convex-type break points and transform all quasi-concave membership functions into concave functions. After that, the converted program is solved by linear programming techniques to obtain a global optimum. In addition to not containing any of the zero–one variables, the proposed method does not require dividing the quasi-concave FMOP problem into large sub-problems as in conventional methods. The extension of the proposed method can treat general non-concave FMOP problems by merely adding less number of zero–one variables.
ISSN:0165-0114
1872-6801
DOI:10.1016/S0165-0114(99)00163-3