Let α be a p×q interval matrix with p≥q and the endpoints of all its entries in Q. We prove that, if contains rank-r real r∈{2,q−2,q−1,q}, then it rational matrix.

The research on supplier selection is abundant and the works usually only consider the critical success factors in the buyer–supplier relationship. However, the negative aspects of the buyer–supplier relationship must also be considered simultaneously. In this paper we propose a comprehensive model for ranking an arbitrary number of suppliers, selecting a number of them and allocating a quota o...

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...

We establish a characterization of almost P-matrices via sign non-reversal property. In this we are inspired by the analogous results for N-matrices. Next, interval hull two m×n matrices A=(aij) and B=(bij), denoted I(A,B), is collection all C∈Rn×n such that each cij convex combination aij bij. Using property, identify finite subset I(A,B) determines if in N-matrices/almost P-matrices. This pro...

This paper proposes a two-stage fuzzy logarithmic preference programming with multi-criteria decisionmaking, in order to derive the priorities of comparison matrices in the analytic hierarchy pprocess (AHP) and the analytic network process (ANP). The Fuzzy Preference Programming (FPP) proposed by Mikhailov and Singh [L. Mikhailov, M.G. Singh, Fuzzy assessment of priorities with application to c...

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 ...

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness 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 interval...