it is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. these conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.furthermore we introduce a new necessary and sucient condition for checkingstability of interv...

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{...

Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the linguistic information in the process of decision making. In this article, we investigate the group decision making problems in which all the linguistic information provided by the decision makers is expressed as interval type-2 fuzzy decision matrices where each of ...

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{...

In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...