Three-Stage Multi-Attribute Group Decision-Making Method Based on Interval-Valued Spherical Fuzzy Density Operator

The information aggregation operator in a fuzzy environment effectively reduces information errors and enhances the accuracy of decision-making. In this paper, considering the preference of decision makers (DMs) for dense distribution of evaluation information, we introduce density intermediate operators and propose interval-valued spherical fuzzy density intermediate operators, which include the interval-valued spherical fuzzy density weighted arithmetic average (IVSFDWAA) operator and the interval-valued spherical fuzzy density weighted geometric average (IVSFDWGA) operator, to achieve effective aggregation of information and study their related properties. In addition, the distance measure and entropy theory in the interval-valued spherical fuzzy environment are extended, and the weight of attributes is determined by comprehensive fuzzy information entropy. On this basis, a three-stage multi-attribute group decision-making method combining TOPSIS is proposed. Finally, an example is provided to illustrate the effectiveness of the proposed method, and its sensitivity and comparative analysis are carried out.