Fuzzy goal programming: Complementary slackness conditions and computational schemes

Goal programming (GP) is an important category in linear programming and multiobjective versions, which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem. In this paper, we deal with fuzzy goal programming (FGP), which is a genera...

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Bibliographic Details
Published in:Applied mathematics and computation 2006-08, Vol.179 (2), p.506-522
Main Authors: Hashemi, S. Mehdi, Ghatee, Mehdi, Hashemi, Behnam
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Complementary slackness conditions
Convex combination
Duality theorems
Exact sciences and technology
Fuzzy extensions of relations
Fuzzy goal programming (FGP)
Goal
Interior point algorithms
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Optimistic and pessimistic solutions
Sciences and techniques of general use
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Summary:Goal programming (GP) is an important category in linear programming and multiobjective versions, which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem. In this paper, we deal with fuzzy goal programming (FGP), which is a generalized problem in vague nature, where parameters, relations and goals are given as fuzzy quantities with respect to imprecise data. Recently, Inuiguchi et al. [M. Inuiguchi, J. Ramik, T. Tanio, M. Vlach, Satisficing solutions and duality in interval and fuzzy linear programming, Fuzzy Sets and Systems, 135 (2003) 151–177.] have proved some important dual theorems on FGP, which are very close to the same crisp versions. In continuation to their works, based on fuzzy extensions of relations, we get complementary slackness conditions for FGP, which have an essential role in many optimization techniques. Moreover, we obtain the most optimistic and pessimistic satisficing solutions, employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty. Our practical schemes implement an efficient interior point algorithm as sub-procedure, so they are polynomial-time algorithms.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2005.11.121