A goal programming approach for fuzzy multiobjective fractional programming problems

Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007 ), there may exist a situation where a decision...

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Bibliographic Details
Published in:International journal of systems science Vol. 40; no. 8; pp. 867 - 874
Main Author: Chang, Ching-Ter
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis Group 01.08.2009
Taylor & Francis
Subjects:
Applied sciences
Decision theory. Utility theory
Exact sciences and technology
fractional programming
fuzzy programming
goal programming
Mathematical programming
Operational research and scientific management
Operational research. Management science
Membership function
Mixed programming
Decision making
Multiobjective programming
Fuzzy programming
Goal programming
Fuzzy logic
Zero one programming
Problem solving
Objective function
Fractional programming
Achievement
Rational function
Mathematical programming
ISSN:0020-7721, 1464-5319
Online Access:Get full text
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Summary:Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007 ), there may exist a situation where a decision-maker would like to make a decision on FMOFP involving the achievement of fuzzy goals, in which some of them may meet the behaviour of fuzzy programming (i.e. level achieved) or the behaviour of binary programming (i.e. completely not achieved). This is turned into a fuzzy multiple objective mixed binary fractional programming (FMOMBFP) problem. However, to the best of our knowledge, this problem is not well formulated by mathematical programming. Therefore, this article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required. In addition, achieving the highest membership value of each fuzzy goal defined for the fractional objective function, the proposed method can alleviate the computational difficulties when solving the FMOMBFP problem. To demonstrate the usefulness of the proposed method, a real-world case is also included.
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ISSN:0020-7721
1464-5319
DOI:10.1080/00207720902974538