Solving the minimal solutions of max-product relation equation by graph method and branch method

Authors:
Zhonglin Chai
Affiliations:
Department of Mathematics, China Jiliang University, Hangzhou, China
Venue:
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part I
Year:
2011

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Abstract

Max-product fuzzy relation equations is one of the important classes of fuzzy relation equations. As max-min fuzzy relation equations, the main problem of solving max-product fuzzy relation equations is to find all its minimal solutions. Although some methods and algorithms have been proposed for finding them, they are still too complex in applications. In this paper, the properties of the equations' minimal solutions are studied, and two methods, graph method and branch method, are presented based on reference [1] to find the minimal solution of max-min fuzzy relation equations. Lastly, an example is given to illustrate the two methods.