Abstract
Linguistic term sets combining with different types of fuzzy sets to settle decision making problems have been a hot area of decision making research. Linguistic Pythagorean fuzzy sets (LPFSs) and soft sets have strong ability to model uncertainty of decision-making. However, there are still few studies about LPFSs at present and these studies have some deficiencies. Aiming at these problems, we do the following things. Firstly, we give the definition of linguistic Pythagorean fuzzy soft sets (LPFSSs), redefine the entropy for LPFSs and introduce a novel linguistic Pythagorean fuzzy entropy which is more simple and valid. Then we give another way to represent linguistic Pythagorean fuzzy numbers (LPFNs) which can better reflect the characteristics of LPFSs. Based on that, we give the definition of distance measures for LPFSs and propose a series of distance measures for LPFNs and LPFSs. Finally, we improve the TOPSIS method with the proposed entropy and distance measure under LPFSSs environment and then apply the method in two cases. Compared with other methods, it's shown that our method has better distinguishability in evaluation results and can deal with group decision-making problems under LPFSSs environment.
Highlights
Multiple attribute decision making(MADM) is a common problem which occurs in almost every field [1]–[5]
We give the definition of distance measures for Linguistic Pythagorean fuzzy sets (LPFSs) and propose a series of distance measures for linguistic Pythagorean fuzzy numbers (LPFNs) and LPFSs
DIRECTIONS In this paper, we improve the TOPSIS method to better deal with the MADM and MAGDM problems under linguistic Pythagorean fuzzy sets environment
Summary
Multiple attribute decision making(MADM) is a common problem which occurs in almost every field [1]–[5]. The ability of Pythagorean fuzzy sets to model such uncertainty of decision-making is much stronger than IFSs. So PFSs theory. Q. Han et al.: TOPSIS Method Based on Novel Entropy and Distance Measure for Linguistic Pythagorean Fuzzy Sets is a more powerful tool for expressing uncertain information when making decisions [18]. Akram et al [21] proposed a Pythagorean fuzzy TOPSIS method to deal with group decision making problems. Traditional TOPSIS method usually applies distance measures to compare the information between two fuzzy sets and obtain the degree of difference. To enrich the study of LPFSs and overcome the above defects, we improve the TOPSIS method for LPFSs and LPFSSs based on novel entropy measure and distance measures considering the features of linguistic Pythagorean fuzzy sets. It’s shown that our method has better distinguishability in evaluation results and can deal with group decision-making problems under LPFSSs environment
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