Reducing the search space of a linear fractional programming problem under fuzzy relational equations with max-Archimedean t-norm composition

Authors:
Yan-Kuen Wu;Sy-Ming Guu;Julie Yu-Chih Liu
Affiliations:
Department of Industrial Management, Vanung University, Taoyuan 320, Taiwan, ROC;Department of Business Administration, Yuan Ze University, Taoyuan 320, Taiwan, ROC;Department of Information Management, Yuan Ze University, Taoyuan 320, Taiwan, ROC
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

Prior studies have demonstrated that one of the minimal solutions of a fuzzy relational equation with the max-Archimedean t-norm composition is an optimal solution of a linear objective function with positive coefficients. However, this property cannot be adopted to optimize the problem of a linear fractional objective function. This study presents an efficient method to optimize such a linear fractional programming problem. First, some theoretical results are developed based on the properties of max-Archimedean t-norm composition. The result is used to reduce the feasible domain. The problem can thus be simplified and converted into a traditional linear fractional programming problem, and eventually optimized in a small search space. A numerical example is provided to illustrate the procedure.