Multiattribute decision making using probability density functions and transformed decision matrices in interval-valued intuitionistic fuzzy environments

Abstract

In this paper, we propose a new method for multiattribute decision making (MADM) using probability density functions and the transformed decision matrix (TDMx) of the decision matrix (DMx) offered by the decision maker (DM) in interval-valued intuitionistic fuzzy (IVIF) environments. First, it gets the TDMx of the DMx given by the DM. Then, it computes the average value of the interval-valued intuitionistic fuzzy values (IVIFVs) appearing at each column of the TDMx. Then, it calculates the variance of each IVIFV in the TDMx. Then, it computes the standard deviation (SD) of the IVIFVs appearing at each column of the TDMx. Then, based on the obtained TDMx, the obtained average value of the IVIFVs appearing at each column of the TDMx, and the obtained SD of the IVIFVs appearing at each column of the TDMx, it gets the z-score DMx. Then, each attribute’s IVIF weight is transformed into a crisp weight between zero and one. Finally, each alternative’s weighted score is calculated using the z-score DMx and each attribute’s transformed crisp weight. The larger the weighted score of an alternative, the better the preference order (PO) of the alternative. It can overcome the shortcomings of the existing MADM methods.