in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

and Applied Analysis 3 by Fujimoto 3 and Liu and Chen 4, 5 with the functional analysis approach. As for b , in case X is convex compact, and S is convex compact-valued with and without the upper hemicontinuous condition, it has also been studied by Liu and Zhang 6, 7 with the nonlinear analysis methods attributed to 8–10 , in particular, using the classical RogalskiCornet Theorem see 8, Theore...

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

The classes of P-, P 0-, R 0-, semimonotone, strictly semimonotone, column suucient, and nondegenerate matrices play important roles in studying solution properties of equations and complementarity problems and conver-gence/complexity analysis of methods for solving these problems. It is known that the problem of deciding whether a square matrix with integer/rational entries is a P-(or nondegen...