Optimizing a Linear Fractional Programming Problem with Max-Product Fuzzy Relational Equation Constraints

求解具最大－積模糊關係方程式的線性分數規劃問題

吳炎崑(Yan-Kuen Wu)

《工業工程學刊》 25卷4期 (2008/07) Pp. 314-325

https://doi.org/10.29977/JCIIE.200807.0006

摘要

本文主要探討線性分數規劃以最大－積模糊關係方程式爲限制條件的最佳化問題，研究此一以往未曾被討論過的新課題，本文提出三個成果：一、利用最大-積模糊關係方程式其可行解的性質，提出求解此類線性分數規劃問題的一些理論結果。二、運用這些結果簡化問題的可行域，並將簡化後的問題轉換成傳統的線性分數規劃模式。三、取代一般尋找原問題所有最小解，再由所有最小解中找出最佳解的方式，提出求解此類問題較高效率的演算法。爲了說明如何求解具最大－積模糊關係方程式的線性分數規劃問題，文中提供求解程序與演算實例。

關鍵字

線性分數規劃問題 ； 模糊關係方程式 ； 最大－積型式

並列摘要

This study investigates a new framework that a linear fractional programming problem is subject to fuzzy relational equations with max-product composition. Three folds are presented. First, some theoretical results are developed to optimize such a linear fractional programming problem based on the properties of max-product composition. Second, the results are adopted to reduce the feasible domain. The problem can thus be simplified and converted into a traditional linear fractional programming problem. Third, a procedure is presented to solve this optimization problem without looking for all potential minimal solutions. Numerical examples are provided to illustrate the procedure.

並列關鍵字

linear fractional programming problem ； fuzzy relational equations ； max-product composition

參考文獻

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