A characterization of the extension principle
Fuzzy Sets and Systems - Special issue: Dedicated to the memory of Richard E. Bellman
A general model for fuzzy linear programming
Fuzzy Sets and Systems
Linear programming problems and ranking of fuzzy numbers
Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Solving fuzzy relation equations with a linear objective function
Fuzzy Sets and Systems
Optimization of fuzzy relation equations with max-product composition
Fuzzy Sets and Systems
Fuzzy Mathematical Programming: Methods and Applications
Fuzzy Mathematical Programming: Methods and Applications
A Note on Fuzzy Relation Programming Problems with Max-Strict-t-Norm Composition
Fuzzy Optimization and Decision Making
Fuzzy Optimization and Decision Making
Information Sciences: an International Journal
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition
Fuzzy Optimization and Decision Making
Computers and Industrial Engineering
The use of parametric programming in fuzzy linear programming
Fuzzy Sets and Systems
An accelerated approach for solving fuzzy relation equations with a linear objective function
IEEE Transactions on Fuzzy Systems
The quadratic programming problem with fuzzy relation inequality constraints
Computers and Industrial Engineering
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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 @a. From different values of @a, 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.