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

• 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
• DOI: 10.1016/j.mcm.2010.01.006

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.