Some Methods for Prioritization of Alternatives of MADM Problems In Fuzzy Environment And Its Extensions

Abstract

Several methods have been proposed in the literature for prioritization of alternatives of MADM problems under fuzzy environment and its extensions. In this thesis, it is shown that (i) The methods to check the consistency of a triangular fuzzy pairwise comparison matrix, interval fuzzy pairwise comparison matrix, trapezoidal fuzzy pairwise comparison matrix and triangular neutrosophic pairwise comparison matrix, used in recently proposed methods for the prioritization of alternatives of MADM problems under triangular fuzzy environment, interval fuzzy environment, trapezoidal fuzzy environment and triangular neutrosophic fuzzy environment are not appropriate. Also, appropriate methods have been proposed to check the consistency of these pairwise comparison matrices. (ii) Prioritization of alternatives of MADM problems under interval-valued intuitionistic fuzzy environment have been discussed in the literature recently. But, it is observed that an inappropriate expression has been used to evaluate the attribute weights. A modified expression is proposed to evaluate the attribute weights. (iii) Considering interval-valued triangular fuzzy values, various alternatives of MADM problems have been ranked in the literature. However, it is found that the method used to obtain the normalized crisp relative weights from the intervalvalued triangular fuzzy weights is not correct. Also, a new method has been proposed to obtain the normalized crisp relative weights from the interval-valued triangular fuzzy weights. (iv) The limitation of the method given by Colak and Kaya [69] for prioritization of alternatives of MADM problems under interval type-2 fuzzy environment has been pointed out. (v) The flaws of a recently proposed method for obtaining the fuzzy maximal eigenvalue and the corresponding normalized fuzzy maximal eigenvector of a triangular fuzzy pairwise comparison matrix have been pointed out. Also, to resolve these flaws, a new method has been proposed for obtaining the fuzzy maximal eigenvalue and the corresponding normalized fuzzy maximal eigenvector of a triangular fuzzy pairwise comparison matrix.