Abstract
This study presents a novel multi-attribute decision-making (MADM) model on the basis of Pythagorean fuzzy linguistic information measures. To do so, we first present a new concept of Pythagorean fuzzy linguistic sets to describe fuzziness and inconsistent information, in which the Pythagorean fuzzy linguistic values (PFLVs) are represented by the linguistic membership degree and linguistic non-membership degree. Then, we introduce two axiomatic definitions of information measures for PFLVs, including Pythagorean fuzzy linguistic entropy and the Pythagorean fuzzy linguistic similarity measure, to measure the uncertainty degree of PFLVs and the similarity degree between among PFLVs. In addition, based on the logarithmic function, we construct two new information measure formulas and verify that they satisfy the axiomatic conditions of the Pythagorean fuzzy linguistic entropy and similarity measure, respectively. We further explore the relationship between the Pythagorean fuzzy linguistic entropy and similarity measure. Finally, we present a novel Pythagorean fuzzy linguistic MADM model with the Pythagorean fuzzy linguistic entropy and similarity measure. A numerical example of selecting the most desirable sustainable blockchain product is given, and a comparison with the existing approach was performed to validate the reliability of the developed decision-making model.
Highlights
Multi-attribute decision-making (MADM) is an attractive and potentially useful approach in addressing complex decision situations
Considering the desirable characteristics of Pythagorean fuzzy sets (PFSs) and linguistic term sets (LTSs), we introduce here a new concept of Pythagorean fuzzy linguistic sets (PFLSs), in which the decision-making evaluation information is described with Pythagorean fuzzy linguistic values (PFLVs), and each PFLV is represented by the degrees of linguistic membership and linguistic non-membership
There are many decision-making methods in the existing literature [41,42], these methods cannot address situations in which the input decision-making information takes the form of PFLVs
Summary
Multi-attribute decision-making (MADM) is an attractive and potentially useful approach in addressing complex decision situations. Owing to the existing information measures for HFSs having drawbacks and limitations, Hu et al [32] designed several new effective and reliable distance, similarity, and entropy measures for HFSs. For MADM problems with interval-valued HFSs, Jin et al [33] introduced three axiomatic definitions of interval-valued hesitant fuzzy information measures, and established several formulas with a continuous ordered weighted averaging operator. Two axiomatic definitions of information measures for PFLVs are presented; With the help of logarithmic functions, two new information measure formulas were constructed; A novel Pythagorean fuzzy linguistic multi-attribute decision-making model was developed to derive reliable ranking of the alternatives. Conclusions and further research are presented in the last section
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