A Novel Linguistic Interval-Valued Pythagorean Fuzzy Multi-Attribute Group Decision-Making for Sustainable Building Materials Selection

The linguistic interval-valued Pythagorean fuzzy (LIVPF) sets, which absorb the advantages of linguistic terms set and interval-valued Pythagorean fuzzy sets, can efficiently describe decision makers’ evaluation information in multi-attribute group decision-making (MAGDM) problems. When investigating aggregation operators of linguistic interval-valued Pythagorean fuzzy (LIVPF) information, we have to consider two important issues, viz. the operational rules of LIVPF numbers and aggregation functions. The classical Archimedean t-norm and t-conorm (ATT) are a famous t-norm and t-conorm, which can produce some special cases. Recently, ATT has been widely applied in different fuzzy decision-making information. Hence, in this paper, for the first issue, we propose some novel operational rules of LIVPF numbers based on ATT. The new operational laws are flexible and can generate some useful operations. For the second issue, we choose a powerful function, i.e., the extended power average (EPA) operator as the aggregation function. The prominent advantages of EPA are that it not only considers the relationship among input arguments, but also dynamically changes the weights of input arguments by employing a parameter. Hence, our proposed novel aggregation operators for LIVPFNs are flexible and is suitable to handle MAGDM problems in actual life. Afterward, we further present a novel MAGDM method under LIVPF conditions. The main finding of our study is a new MAGDM method, which is more powerful and flexible than existing ones. Finally, we apply the method in a sustainable building materials selection to show its effectiveness. Additionally, comparison analysis is provided to demonstrate the advantages and superiorities of the proposed method.