Fuzzy linear objective function optimization with fuzzy-valued max-product fuzzy relation inequality constraints

In this paper, we firstly consider an optimization problem with a linear objective function subject to a system of fuzzy relation inequalities using the max-product composition. Since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. An algorith...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 51; no. 9; pp. 1240 - 1250
Main Author: Abbasi Molai, Ali
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.05.2010
Elsevier
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Extension principle
Fuzzy relation inequality
Fuzzy set
Mathematical analysis
Mathematics
Membership function
Methods of scientific computing (including symbolic computation, algebraic computation)
Non-convex optimization
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Sciences and techniques of general use
Extension principle
Membership function
Non-convex optimization
Fuzzy set
Fuzzy relation inequality
Lower bound
Fuzzy system
Optimization method
Non linear programming
Algorithm
Linear model
Upper bound
Numerical analysis
Applied mathematics
Inequality constraint
Variational calculus
Mathematical model
Computer aided analysis
Mathematical programming
ISSN:0895-7177, 1872-9479
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Summary:In this paper, we firstly consider an optimization problem with a linear objective function subject to a system of fuzzy relation inequalities using the max-product composition. Since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. An algorithm is proposed to solve this problem using fuzzy relation inequality paths. Then, a more general case of the problem, i.e., an optimization model with one fuzzy linear objective function subject to fuzzy-valued max-product fuzzy relation inequality constraints, is investigated in this paper. A new approach is proposed to solve this problem based on Zadeh’s extension principle and the algorithm. This paper develops a procedure to derive the fuzzy objective value of the recent problem. A pair of mathematical program is formulated to compute the lower and upper bounds of the problem at the possibility level α . From different values of α , the membership function of the objective value is constructed. Since the objective value is expressed by a membership function rather than by a crisp value, more information is provided to make decisions.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2010.01.006