Convergence of max-arithmetic mean powers of a fuzzy matrix

Authors:
Yung-Yih Lur;Yan-Kuen Wu;Sy-Ming Guu
Affiliations:
Department of Industrial Management, Vanung University, Taoyuan 320, Taiwan, ROC;Department of Industrial Management, Vanung University, Taoyuan 320, Taiwan, ROC;Department of Business Administration, Yuan Ze University, Taoyuan 320, Taiwan, ROC
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

Fuzzy matrices provide convenient representations for fuzzy relations on finite universes. In the literature, the powers of a fuzzy matrix with max-min/max-product/max-Archimedean t-norm compositions have been studied. It turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved. In this paper, the max-arithmetic mean composition is considered for the fuzzy relations. We show that the max-arithmetic mean powers of a fuzzy matrix always are convergent.