论文标题
关于Aczel-Alsina模糊关系方程的分辨率和线性编程问题
On the resolution and Linear programming problems subjected by Aczel-Alsina Fuzzy relational equations
论文作者
论文摘要
Aczel-Alsina T-norm属于严格的T-Norm家族，这些家族是各种模糊建模问题中最施加的模糊操作员。在本文中，我们研究了一个线性优化问题，其中可行区域被形成为由Aczel-Alsina t-norm定义的模糊关系方程（FRE）系统。由于可行解决方案集的FRE是非凸，并且所有最小解决方案的发现是NP硬化问题，因此可能不会直接采用常规方法。可行区域的分辨率得到了彻底研究。基于问题的某些理论属性，提出了一种算法以找到所有最佳解决方案，最后描述了一个示例以说明该算法。
Aczel-Alsina t-norm belongs to the family of strict t-norms that are the most applied fuzzy operators in various fuzzy modelling problems. In this paper, we study a linear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the Aczel-Alsina t-norm. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutions is an NP-hard problem, conventional methods may not be directly employed. The resolution of the feasible region is completely investigated. Based on some theoretical properties of the problem, an algorithm is presented to find all the optimal solutions, and finally an example is described to illustrate this algorithm.
