A three-phase method for Pythagorean fuzzy multi-attribute group decision making and application to haze management

Pythagorean fuzzy set (PFS), as a new extension of intuitionistic fuzzy set (IFS), has recently been utilized to describe uncertain information in decision making. This paper aims to develop a three-phase method for addressing multi-attribute group decision making (MAGDM) with Pythagorean fuzzy numbers (PFNs) and apply to haze management. Firstly, the normalized projection of PFNs is defined. Then the entropy and Riemann closeness degree of PFNs are proposed. Based on the normalized projection of PFNs, an extended TOPSIS method is presented to determine the DMs’ weights. A collective decision matrix is obtained by aggregating individual matrices with the DMs’ weights. Subsequently, the deviation of score from entropy and the deviation of accuracy from entropy are defined, respectively. Then a multi-objective parametric comprehensive deviation programming model is constructed to derive the attribute weights. A weighted collective matrix is obtained by the derived attribute weights. The positive ideal solution (PIS) and negative ideal solution (NIS) are determined according to the weighted collective matrix. By calculating the Riemann closeness degrees of alternatives to PIS and NIS, the ranking values of alternatives are computed to generate the ranking order of alternatives. Finally, a haze management example is elaborated to illustrate the feasibility of the proposed method. To illustrate the stability and practicality of the proposed method, the sensitivity analysis, validity test and comparative analysis are conducted.