关于Aczel-Alsina Fuzzy关系方程的解和线性规划问题
On the resolution and Linear programming problems subjected by Aczel-Alsina Fuzzy relational equations
摘要：
Aczel-Alsina t-范数属于严格t-范数家族，是各种模糊建模问题中最常用的模糊算子。在本文中，我们研究了一个线性最优化问题，其中的可行域形成为一个系统的模糊关系方程（FRE）定义的Aczel-Alsina t-范数。由于FREs的可行解集是非凸的，并且所有最小解的寻找是NP难问题，因此不能直接采用常规方法。全面研究了可行域的分辨率。基于问题的一些理论性质，给出了一个求所有最优解的算法，最后给出了一个例子来说明该算法。
英文摘要：
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.
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