论文标题
DOMBI FRES上的Dombi模糊关系方程的分辨率和简化
Resolution and simplification of Dombi-fuzzy relational equations and latticized optimization programming on Dombi FREs
论文作者
论文摘要
在本文中，我们介绍了一种晶格的优化问题，其目标函数是最大组件函数，可行区域被定义为Dombi t-norm定义的模糊关系相等性（FRE）系统。 T-norms的Dombi家族包括一个连续严格的T-Norms的参数家族，其成员正在增加参数的功能。当参数从零变为无穷大时，这个T-norm家族涵盖了T-norms的全部频谱。由于可行解决方案集是非凸的，因此所有最小解决方案的发现是NP硬化问题，因此设计有效的解决方案程序来解决此类问题并不是一件微不足道的工作。得出了一些必要和足够的条件，以确定问题的可行性。可行的溶液集以有限数量的封闭凸单元而表征。提出了一种用于解决此非线性问题的算法。事实证明，算法可以找到确切的最佳解决方案，并提出一个示例以说明所提出的算法。
In this paper, we introduce a type of latticized optimization problem whose objective function is the maximum component function and the feasible region is defined as a system of fuzzy relational equalities (FRE) defined by the Dombi t-norm. 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. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutions is an NP-hard problem, designing an efficient solution procedure for solving such problems is not a trivial job. Some necessary and sufficient conditions are derived to determine the feasibility of the problem. The feasible solution set is characterized in terms of a finite number of closed convex cells. An algorithm is presented for solving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.
