Convergence of powers for a fuzzy matrix with convex combination of max-min and max-arithmetic mean operations

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:
Information Sciences: an International Journal
Year:
2009

Citing 12
Cited 1

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Convergence of max-arithmetic mean powers of a fuzzy matrix

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Convergence of powers of a fuzzy transitive matrix

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Abstract

Fuzzy matrices have been proposed to represent fuzzy relations on finite universes. Since Thomason's paper in 1977 showing that powers of a max-min fuzzy matrix either converge or oscillate with a finite period, conditions for limiting behavior of powers of a fuzzy matrix have been studied. It turns out that the limiting behavior depends on the algebraic operations employed, which usually in the literature includes max-min/max-product/max-Archimedean t-norm/max t-norm/max-arithmetic mean operations, respectively. In this paper, we consider the powers of a fuzzy matrix with convex combination of max-min and max-arithmetic mean operations. We show that the powers of such a fuzzy matrix are always convergent.