Abstract
In the literature, the powers of a square fuzzy matrix with respect to the max-weighted power mean composition have been shown to always converge. This study considers the max-weighted power mean composition for a sequence of fuzzy matrices. It reveals that the repeated compositions of a sequence of n fuzzy matrices oscillate among n fuzzy matrices once the number of compositions exceeds a certain threshold. The previous finding can be considered as a special case of this study with n = 1.
Highlights
In fuzzy set theory, fuzzy relations describe vague relationships among elements.the composition of fuzzy relations provides a way to infer new fuzzy relations.A fuzzy relation can be represented using a fuzzy matrix, where all elements in the fuzzy matrix have values in the closed interval [0,1]
This study shows that the repeated compositions of a sequence of n fuzzy matrices oscillate among n fuzzy matrices, each with a period n, once the number of compositions exceeds a certain threshold
This study considers the case of the composition between a square fuzzy matrix C and a repeated sequence of n fuzzy matrices A0, A1, . . . , An−1, as defined below: (
Summary
Fuzzy relations describe vague relationships among elements. the composition of fuzzy relations provides a way to infer new fuzzy relations. Thomason [6] first proved that the sequence of consecutive powers of a fuzzy matrix with a max-min composition either converges to an idempotent matrix or oscillates with a finite period. Pang and Guu [10] later showed that the limiting behavior of the consecutive powers of a max-product fuzzy matrix relates to the notion of an asymptotic period. Lur et al [13] showed that the powers of a fuzzy matrix with respect to the max-weighted power mean composition are always convergent. This study investigates the limiting behavior of repeated compositions of a sequence of fuzzy matrices with respect to the max-weighted power mean composition. This study considers the case of the composition between a square fuzzy matrix C and a repeated sequence of n fuzzy matrices A0 , A1 , . This study shows that G(C, A0 , A1 , . . . , An−1 , k) and F( A0 , A1 , . . . , An−1 , k) exhibit the same limiting behavior as k approaches infinity
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
