Optimization of fuzzy relational equations with a linear convex combination of max-min and max-average compositions

• Published in: 2007 IEEE International Conference on Industrial Engineering and Engineering Management pp. 832 - 836
• Main Authors: Yan-Kuen Wu, Wen-Wei Yang
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2007
• Subjects: Cost function; Differential algebraic equations; Differential equations; Fuzzy optimization; Fuzzy relational equations; Fuzzy sets; Fuzzy systems; Industrial relations; Linear programming; Max-average composition; Max-min composition; Optimization methods; Uncertainty; Vectors
• ISBN: 1424415284; 9781424415281
• ISSN: 2157-3611
• DOI: 10.1109/IEEM.2007.4419307

Max-min and max-product compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations. Both are members in the class of max-t-norm composition. In this study, a linear convex combination of max-min and max-average compositions is considered for the same optimization model, which does not belong to the max-t- norm composition. However, this convex combined composition generates some properties of the solution set that are similar to the max-product composition, but different with max-min composition. Hence, the method applied to optimize the linear programming problem with max-product composition can be employed again to solve the same problem. Moreover, this study will show that the tabular method provided by Ghodousian and Khorram can not guarantee to obtain an optimal solution for the same optimization model.