Probabilistic dual hesitant fuzzy MAGDM method based on generalized extended power average operator and its application to online teaching platform supplier selection

Abstract

Probabilistic dual hesitation fuzzy set (PDHFS) is a new tool used to enhance fuzzy and imprecise information in a changing and complex decision-making environment. Compared with the existing fuzzy sets, PDHFS is more suitable for identifying uncertain evaluation data in complex and realistic decision-making situations. The extended power average (EPA) and generalized power average (GPA) operators provide more information for the information aggregation process, reflecting the mutual support among all aggregation values. To solve the evaluation problems related to decision analysis involving extremely complex information, especially in the case of extreme data in the consideration of decision problems. In this paper, the generalized extended power average (GEPA) operator is proposed in the PDHF environment. This research has the following four important contributions. First, we propose a probability splitting algorithm of normalizing PDHFE, and give some new basic operations, score function, distance measures and aggregation operators. Second, to better integrate the advantages of EPA and GPA operators, we developed the GEPA operator, weighted form (WGEPA) and ordered form (GEPOWA). Meanwhile, by adjusting the parameter in three types of operators, we can find that many existing operators are special forms of the three types of operators. Third, extended the three types of operators to the PDHF environment, the PDHFGEPA, PDHFWGEPA, PDHFGEPOWA operators and some special aggregation operators are obtained, and studied their valuable properties in detail. Finally, taking the application of PDHFWGEPA operator as an example, a new multi-attribute group decision-making (MAGDM) technique is developed and used to solve the problem of online teaching platform supplier selection (OTPSS). Through parameter sensitivity analysis, the flexibility and stability of MAGDM technique are illustrated, and compared with some existing decision-making methods, the effectiveness of MAGDM method is proved. In addition, this technique also provides some theoretical references for dealing with other complex MAGDM problems, and provides a new operator for the extension of GEPA operator in other fuzzy environments. The biggest advantage of several operators is that they can pay full attention to the special role of extreme data in decision-making.