A Novel Two-Stage Multi-Criteria Decision-Making Method Based on Interval-Valued Pythagorean Fuzzy Aggregation Operators with Self-Confidence Levels

Abstract

Due to insufficient information in multi-criteria decision-making (MCDM) problems, the decision values given by experts are often fuzzy and uncertain. As an extension of Pythagorean fuzzy set (PFS), interval-valued Pythagorean fuzzy (IPF) set is a more effective and powerful tool to handle fuzzy information in decision problems. But, there are two key issues that needed to be solved: weights of experts in the IPF environment and IPF aggregation operators. For these issues, a two-stage MCDM method is constructed in the IPF environment. In the first stage, a novel method for determining the weights of experts is proposed by introducing IPF set (IPFS) into social networks. To do that, the concepts of trust function (TF) and trust score (TS) in the IPF environment are defined to obtain the objective weights of experts. Meanwhile, the subjective weights of experts are obtained from the number of experts. Afterward, the objective weight and subjective weight of each expert are combined to derive the weight of each expert. In the second stage, a novel weighted sum model (WSM) with novel IPF aggregation operators is constructed to rank alternatives. Considering the psychological behavior of experts, that is, self-confidence level, four IPF aggregation operators with self-confidence levels are defined, namely, the self-confidence interval-valued Pythagorean fuzzy weighted averaging (SC-IPFWA) and ordered weighted averaging (SC-IPFOWA) operator, the self-confidence interval-valued Pythagorean fuzzy weighted geometric (SC-IPFWG) and ordered weighted geometric (SC-IPFOWG) operator. Finally, a numerical case is used to verify the effectiveness of the proposed two-stage MCDM method.