In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group G, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided. Basic criteria for finding a nearest consistent pairwise comparisons matrix (extended to the class of group G) are proposed. A geometric interpretation of pairwis...

This paper will investigate the optimum portfolio for an investor, taking into account 5 criteria. The mean variance model of portfolio optimization that was introduced by Markowitz includes two objective functions; these two criteria, risk and return do not encompass all of the information about investment; information like annual dividends, S&P star ranking and return in later years which is ...

We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider an equivalent $FFLS$ by using an appropriate permutation to simplify fuzzy multiplications. T...

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In realworld applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the co...

We will show here that the principal eigenvector of a matrix is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison consistent or near consistent matrix. A positive reciprocal n by n consistent matrix W = (wij) satisfies the relation wik = wij wjk . If the principal eigenvector of W is w=(w1 , ... ,wn ) the entries of W may be written as wij = wi ...

In the analytic hierarchy process (AHP), the consistency of pairwise comparison is measured by the consistency index (CI) value of pairwise comparison matrices. The CI value is defined by the size and the principal eigenvalue of comparison matrix, and the larger the CI value is, the less consistent pairwise comparison is. In this paper, we propose the estimation method of consistency intervals,...