Linear optimization of bipolar fuzzy relational equations with max-Łukasiewicz composition

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• 作者：Chia-Cheng Liu^a ; Yung-Yih Lur^a ; Yan-Kuen Wu ; ^b ; ^{ykw@vnu.edu.tw" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bipolar fuzzy relational equations ; Max-Łukasiewicz composition ; 0&ndash ; 1 integer linear programming problem
• 刊名：Information Sciences
• 出版年：2016
• 出版时间：10 September 2016
• 年：2016
• 卷：360
• 期：Complete
• 页码：149-162
• 全文大小：510 K

文摘

According to the literature, a linear optimization problem subjected to a system of bipolar fuzzy relational equations with max-Łukasiewicz composition can be translated into a 0–1 integer linear programming problem and solved using integer optimization techniques. However, the technique of integer optimization may involve hight computation complexity. To improve computational efficiency for solving such an optimization problem, this paper proves that each component of an optimal solution obtained from such an optimization problem can either be the corresponding component’s lower bound or upper bound value. Because of this characteristic, a simple value matrix with some simplified rules can be proposed to reduce the problem size first. A simple solution procedure is then presented for determining optimal solutions without translating such an optimization problem into a 0–1 integer linear programming problem. Two examples are provided to illustrate the simplicity and efficiency of the proposed algorithm.