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This paper discusses a nonlinear optimization problem with the system of max-Archimedean bipolar fuzzy relation equations as constraints. Some results related to the structure of the solution set of max-Archimedean bipolar fuzzy relation equations are proved. Using these results, a genetic algorithm is proposed to solve the problem for obtaining optimal or converging solutions. The effectiveness of the algorithm is also compared with other methods found in the literature. The previous methods require conversion of the problem into 0-1 mixed integer optimization problem solvable by some nonlinear optimization solvers and thereby, the computational work may increase with the size of the problem. Some test problems are developed to evaluate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper discusses a new method for finding the complete set of tolerable solutions of max-Archimedean interval-valued fuzzy relation equations. According to the literature, three types of solution sets, namely; tolerable solution set, united solution set and controllable solution set can be identified with interval-valued fuzzy relation equations. The structure and the properties of the tolerable solution set are studied. The complete set of tolerable solutions can be characterized by one maximum solution and finitely many minimal solutions. An efficient method based on the concept of covering is proposed which computes all minimal solutions. The concept of covering is useful for large size problems in terms of computation. The proposed method is illustrated with some examples. [ABSTRACT FROM AUTHOR]

This paper discusses the resolution of max-Archimedean bipolar fuzzy relation equations. In the literature, many methods have been proposed based on 0-1 integer programming problem or reduction methods for the optimization with bipolar fuzzy relation equations. A new concept based on the idea of covering and the notions of leading, non-leading variables are introduced in the present paper for finding the solutions of max-Archimedean bipolar fuzzy relation equations. It is shown that the problem of finding the complete solution set of the system of max-Archimedean bipolar fuzzy relation equations is equivalent to solving a covering problem and the solutions of such equations correspond to irredundant coverings of the covering problem. The proposed method is illustrated with some examples. [ABSTRACT FROM AUTHOR]