Linguistic Pythagorean fuzzy numbers (LPFNs) are better tools for dealing with imprecision and vagueness. This article develops a new multiattribute group decision-making approach with LPFNs. The attribute values are LPFNs, and the information about the attribute weight is incomplete. Extended the notion of the traditional grey relational analysis (GRA) method, a new extension of the GRA method based on LPFN details is introduced. We develop a new distance measure and entropy measure for LPFNs. Moreover, a decision-making approach is proposed based on the traditional. GRA method and steps for solving LPFMAGDM problems with incompletely known weight information are given. The degree of grey relation between positive (PIS) and negative-ideal solutions (NIS) are determined. A relative relational degree is considered by calculating the degree of grey relation to the LPF-PIS and the LPF-NIS, respectively. Finally, an illustrative example is also given to show the application and effectiveness and compare the developed approach with existing methods.
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Khan et al. (2022) studied this question.