In this paper, we develop a novel multiple attribute decision making (MADM) method using the improved intuitionistic fuzzy weighted geometric (IIFWG) operator of intuitionistic fuzzy values (IFVs) proposed in this paper. First, we develop the IIFWG operator of IFVs to conquer the weak points of the existing operators of IFVs, where they have the drawbacks that their aggregated values are indeterminate in some situations. Based on the proposed IIFWG operator of IFVs, we present a MADM method to overcome the weak points of the existing MADM methods, which have the shortcomings that they obtain unreasonable ranking orders (ROs) of alternatives or they cannot discriminate the ROs of alternatives in some circumstances.

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.

In this paper, we propose a new multiple attribute decision making (MADM) method based on the nonlinear programming (NLP) methodology, the TOPSIS method and interval-valued intuitionistic fuzzy values (IVIFVs). The evaluating values of the alternatives with respect to attributes and the attributes' weights are represented by IVIFVs. The NLP methodology is applied to get the optimal attributes' weights. The proposed MADM method can overcome the drawbacks of the existing MADM methods to deal with MADM problems using IVIFVs. (C) 2019 Elsevier Inc. All rights reserved.

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.