Multiattribute decision making based on probability density functions and the variances and standard deviations of largest ranges of evaluating interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method based on probability density functions (PDFs) and the variances and standard deviations of the largest ranges of evaluating interval-valued intuitionistic fuzzy values (IVIFVs). First, the proposed MADM method gets the largest range of each evaluating IVIFV in the decision matrix and calculates the average value of the largest ranges of each attribute. Then, it gets the PDF of the largest range of each evaluating IVIFV in the decision matrix, calculates the variance of each largest range and calculates the standard deviation of the largest ranges of each attribute. Then, it constructs the z-score decision matrix and gets the transformed weight of the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute. Finally, it calculates the weighted score of each alternative based on the obtained z-score decision matrix and the transformed weight of the IVIF weight of each attribute. The larger the value of the weighted score, the better the preference order (PO) of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods. (C) 2019 Elsevier Inc. All rights reserved.