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The purpose of this study is to construct the multi-attribute group decision making (MAGDM) approach with linguistic Pythagorean fuzzy information (LPFI) based on generalized linguistic Pythagorean fuzzy aggregation operators (GLPFA). To begin with, we define the generalized indeterminacy degree-preference distance of linguistic Pythagorean fuzzy numbers (LPFNs), on the basis of it, we build a new approach for ranking the alternatives after analysing the existed comparison rule. In addition, we introduce the new version of t-norms (TNs) and t-conorms (TCs) named linguistic Pythagorean t-norms (LPTNs) and linguistic Pythagorean t-conorms (LPTCs), which can be used to handle the LPFI; some special cases for LPTNs and LPTCs are obtained and they can deal with Pythagorean fuzzy information (PFI). Thirdly, we introduce the generalized linguistic Pythagorean fuzzy average aggregation operator (GLPFAA) based on LPTN and LPTC along with their properties are also investigated, whilst, some special cases of GLPAA are obtained when LPTN and LPTC take some special TNs and TCs. Finally, a MAGDM approach based on some LPTNs and LPTCs is constructed to deal with some MAGDM problems with unknown attributes’weights and experts’ weights, before building the MAGDM approach, we define new cross-entropy to fix the experts’s weights and use the maximizing deviation to calculate the attributes’ weights based on the proposed indeterminacy degree-preference distance. Consequently, an illustrative example is provided in order to show the effectiveness and advantages of the proposed method and some comparisons are also carried out.

Multiattribute Group Decision-Making Approach With Linguistic Pythagorean Fuzzy Information