Interval-Valued Pythagorean Fuzzy Extended Bonferroni Mean For Dealing With Heterogenous Relationship Among Attributes

Owing to the information insufficiency, it might be difficult for decision makers to precisely evaluate their assessments in real decision-making. As a new extension of the Pythagorean fuzzy sets, the interval-valued Pythagorean fuzzy sets (IVPFSs) can availably provide enough input space for decision makers to evaluate their assessments with interval numbers. By extending the Bonferroni mean to model the heterogeneous interrelationship among attributes, the extended Bonferroni mean (EBM) was examined. Considering the partition structure of relationship among the attributes, we introduce the EBM into the interval-valued Pythagorean fuzzy environment and develop two new aggregation operators, namely, interval-valued Pythagorean fuzzy extended Bonferroni mean and weighted interval-valued Pythagorean fuzzy extended Bonferroni mean (WIVPFEBM) operators. Meanwhile, some of their special cases and properties are also deeply discussed. Subsequently, by employing the WIVPFEBM operator, we propose an approach for multiple attribute decision making with IVPFSs. Finally, a practical illustration of the E-commerce project selection problem is investigated by our proposed method, which successfully demonstrates the applicability of our results.