Convergence of powers of reciprocal fuzzy matrices
Information Sciences: an International Journal
Convergence, eigen fuzzy sets and stability analysis of relational matrices
Fuzzy Sets and Systems
Convergence of the power sequence of a nearly monotone increasing fuzzy matrix
Fuzzy Sets and Systems
On the oscillating power sequence of a fuzzy matrix
Fuzzy Sets and Systems
A note on the power sequence of a fuzzy matrix
Fuzzy Sets and Systems
On the convergence of a fuzzy matrix in the sense of triangular norms
Fuzzy Sets and Systems
Note on "Convergence of powers of a fuzzy matrix"
Fuzzy Sets and Systems
Convergence of max-arithmetic mean powers of a fuzzy matrix
Fuzzy Sets and Systems
Szpilrajn's theorem on fuzzy orderings
Fuzzy Sets and Systems
Canonical form of a transitive fuzzy matrix
Fuzzy Sets and Systems
Convergence of powers of a fuzzy transitive matrix
Fuzzy Sets and Systems
Transitivity of generalized fuzzy matrices
Fuzzy Sets and Systems
Sufficient conditions for the stability of linear Takagi-Sugeno free fuzzy systems
IEEE Transactions on Fuzzy Systems
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Fuzzy matrices have been proposed to represent fuzzy relations on finite universes. Since Thomason's paper in 1977 showing that the max-min powers of a 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 include max-min/max-product/max-Archimedean t-norm/max-t-norm/max-arithmetic mean operations, respectively. In this paper, we consider the max-generalized mean powers of a fuzzy matrix which is an extension of the max-arithmetic mean operation. We show that the powers of such fuzzy matrices are always convergent. As an application, we consider fuzzy Markov chains with the max-generalized mean operations for the fuzzy transition matrix. Our results imply that these fuzzy Markov chains are always ergodic and robust with respect to small perturbations of the transition matrices.