Abstract
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.
Highlights
The theories and methods of multi-attribute decision making (MADM) are widely used in different fields such as economy, management and engineering
An important application field is fuzzy decision making, intuitionistic fuzzy set (IFS) has been successfully applied in some multi-attribute decision making (MADM), the sum of membership degree (MD) and non-membership degree (NMD) may be greater than 1 in some special real decision problems, this situation could not be described by IFS
MADM With LI Information based on Dempster-Shafer evidence theory; Zhang et al [57] established the outranking method for MCDM with LIFNs. (4) Linguistic Pythagorean fuzzy sets(LPFSs): rencently, Garg [40] introduced the concept of LPFSs based on Linguistic intuitionistic fuzzy sets (LIFS), some aggregation operators are defined and multi-attribute group decision making (MAGDM) approach with linguistic Pythagorean fuzzy information (LPFI) is built based on the proposed aggregation operators
Summary
The theories and methods of multi-attribute decision making (MADM) are widely used in different fields such as economy, management and engineering. Since PFS’s appearance, theory of PFS and its applications have been studied in depth, for example some information measures [3]–[5], improved score function [6]–[9], new operational laws [10], [11], aggregation operators [12]–[16] and many decision-making approaches [17], [18]. These studies are limited to deal with some uncertain information in quantitative environments.
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