Some Results of the Bipolar Max-product Fuzzy Relational Equations
نویسندگان
چکیده
In the literature, some studies have shown that determining the consistency of bipolar fuzzy relational equations is NP-complete. Namely, the solution procedure for solving a system of bipolar fuzzy relational equations with max-product composition contains a high computational complexity. In this study, some sufficient conditions for consistency of bipolar fuzzy relational equations are proposed to reduce the difficulty of detecting the case of an empty solution set. Numerical examples illustrate that the proposed properties are simple to use and do not require to generate the set of possible feasible solution pairs.
منابع مشابه
Some Properties of Bipolar Max-min Fuzzy Relational Equations
In the literature, the solution set of a system of bipolar fuzzy relational equations with max-min composition can be characterized by a finite set of maximal and minimal solution pairs. However, some researches presented that determining the consistency of a system of bipolar fuzzy relational equations is NP-complete. Namely, the solution procedure for solving a system of bipolar fuzzy relatio...
متن کاملPosynomial geometric programming problem subject to max–product fuzzy relation equations
In this article, we study a class of posynomial geometric programming problem (PGPF), with the purpose of minimizing a posynomial subject to fuzzy relational equations with max–product composition. With the help of auxiliary variables, it is converted convert the PGPF into an equivalent programming problem whose objective function is a non-decreasing function with an auxiliary variable. Some pr...
متن کاملRESOLUTION OF NONLINEAR OPTIMIZATION PROBLEMS SUBJECT TO BIPOLAR MAX-MIN FUZZY RELATION EQUATION CONSTRAINTS USING GENETIC ALGORITHM
This paper studies the nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set of the problems is non-convex, in a general case. Therefore, conventional nonlinear optimization methods cannot be ideal for resolution of such problems. Hence, a Genetic Algorithm (GA) is proposed to find their optimal solution. This algorithm uses th...
متن کاملSolving a non-convex non-linear optimization problem constrained by fuzzy relational equations and Sugeno-Weber family of t-norms
Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-conorms were suggested as addition rules by Sugeno for so-called $lambda$–fuzzy measures. In this paper, we study a nonlinear optimization problem where the fea...
متن کاملOn the optimization of Dombi non-linear programming
Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, we study a nonlinear optimization problem in which the constraints are defined as fuzzy relational equations (FRE) with the Dombi...
متن کامل