Maximizing a monomial geometric objective function subject to bipolar max-product fuzzy relation constraints
Maximizing a monomial geometric objective function subject to bipolar max-product fuzzy relation constraints
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DOI：
10.3233/jifs-151820
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Aliannezhadi;Shadi Shahab Ardalan;A. A. Molai-A.
中科院分区：
文献类型：
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作者：
S. Aliannezhadi;Shadi Shahab Ardalan;A. A. Molai-A.
研究了双极最大积模糊关系约束下单项几何目标函数的最大化问题。首先，证明了双极最大乘积模糊关系不等式（FRI）系统可以等价地转化为双极最大乘积模糊关系方程（FRE）系统。因此，在双极最大乘积FRE系统的情况下，确定了问题的可行域的结构。在一般情况下，证明了它的解集是非凸的。给出了其可行域解存在的充分条件。根据可行域的结构和目标函数的性质，设计了一种求解优化问题的算法。并通过经济学和覆盖问题领域的应用实例说明了其重要性。文中给出了一些数值例子来说明上述观点。
In this paper, the problem of maximizing a monomial geometric objective function subject to bipolar max-product fuzzy relation constraints is studied. First of all, it is shown that the bipolar max-product Fuzzy Relation Inequality (FRI) system can equivalently be converted to a bipolar max-product Fuzzy Relation Equation (FRE) system. Hence, the structure of feasible domain of the problem is determined in the case of the bipolar max-product FRE system. It is shown that its solution set is non-convex, in a general case. Some sufficient conditions are proposed for solution existence of its feasible domain. An algorithm is designed to solve the optimization problem with regard to the structure of its feasible domain and the properties of the objective function. Its importance is also illustrated by an application example in the area of economics and covering problem. Some numerical examples are given to illustrate the above points.