Interval Pairwise Comparison Matrices have been widely used to account for uncertain statements concerning the preferences of decision makers. Several approaches have been proposed in the literature, such as multiplicative and fuzzy interval matrices. In this paper, we propose a general unified approach to Interval Pairwise Comparison Matrices, based on Abelian linearly ordered groups. In this ...

the linear system of equations ax = b where a = [aij ] in cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. in this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as drazin inverse andpseudo-inverse are investigated.

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp M matrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effe...

In this paper, we present Gauss-Sidel and successive over relaxation (SOR) iterative methods for finding the approximate solution system of fuzzy Sylvester equations (SFSE), AX + XB = C, where A and B are two m*m crisp matrices, C is an m*m fuzzy matrix and X is an m*m unknown matrix. Finally, the proposed iterative methods are illustrated by solving one example.

Today is a world of uncertainty with its associated problems, which can be well handled by soft set theory. In this paper, we extend sanchez`s approach for medical diagnosis using the representation of an interval valued fuzzy soft matrices. we introduce the definition of union and intersection of Interval valued fuzzy soft matrices with examples.Finally, we extend our approach in application o...

In this paper we present equivalent characterizations of k-Kernel symmetric Matrices. Necessary and sufficient conditions are determined for amatrix to be k-Kernel Symmetric.We give some basic results of kernel symmetric matrices. It is shown that k-symmetric implies k-Kernel symmetric but the converse need not be true. We derive some basic properties of k-Kernel symmetric fuzzy matrices. We ob...

Crisp comparison matrices produce crisp weight estimates. It is logical for an interval or fuzzy comparison matrix to give an interval or fuzzy weight estimate. In this paper, an eigenvector method (EM) is proposed to generate interval or fuzzy weight estimate from an interval or fuzzy comparison matrix, which differs from Csutora and Buckley’s LambdaMax method in several aspects. First, the pr...

Disinfection by-products (DBPs) are formed when disinfectants such as chlorine, chloramine, and ozone react with organic matter in water. Chlorine being the most common disinfectant used in the drinking water industry worldwide, significant attention has been focused on chlorinated DBPs. A new indexing method using fuzzy synthetic evaluation is proposed to determine the health risk associated w...