TOPSIS Method Based on Novel Entropy and Distance Measure for Linguistic Pythagorean Fuzzy Sets With Their Application in Multiple Attribute Decision Making

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.

Keywords

• Linguistic Pythagorean fuzzy sets
• Soft sets
• distance measure
• entropy
• multiple attribute decision making