A New Method for MAGDM Based on Improved TOPSIS and a Novel Pythagorean Fuzzy Soft Entropy

Abstract

A decision-making environment is full of uncertainty and complexity. Existing tools include fuzzy sets, soft sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets (PFSs) and so on. Compared with intuitionistic fuzzy sets (IFSs), PFSs proposed by Yager have advantages in handling vagueness in the real world and possess good symmetry. The entropy measure is the most widespread form of uncertainty measure. In this paper, we improve the technique for order preference by similarity to an ideal solution (TOPSIS) method to better deal with multiple-attribute group decision making (MAGDM) problems based on Pythagorean fuzzy soft sets (PFSSs). To better determine the weights of attributes, we firstly define a novel Pythagorean fuzzy soft entropy which is more reasonable and valid. Meanwhile the entropy has good symmetry. Entropy for PFSSs which is used to determine the subjective weights of attributes is also defined. Then we introduce a measure to calculate integrated weights by combining objective weights and subjective weights. Based on the integrated weights, the TOPSIS method is generalized and improved to solve the MAGDM problem. A distance measure taking into account the characteristics of Pythagorean fuzzy numbers (PFNs) is used to calculate distance between alternatives and ideal solutions. Finally, the proposed MAGDM method is applied in the case of selecting a missile position. Compared with other methods, it is shown that the proposed method can rank alternatives more reasonably and have higher distinguishability.

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

“…Definition 11 [18], [37]: Let U be an initial universe set and E be a set of parameters. Let PF U indicate the collection of the whole Pythagorean fuzzy(PF) subsets of U .…”

“…Xue and Xu [38] proposed Pythagorean fuzzy entropy(PFE) and Interval-valued PFE (IVPFE). Han [18] defined a novel PFE, based on which, the Pythagorean fuzzy soft entropy is proposed. Lin [29] first proposed the entropy measure of LPFSs in 2019.…”

“…We have proposed a TOPSIS method based on the novel linguistic Pythagorean fuzzy entropy and distance measure to deal with multiple attributes group decision making. In this example(Adapted from [18]), the method will be Table 5.…”

“…Step 2: Calculate linguistic Pythagorean fuzzy entropy H (A, c j ) by utilizing Equation (18). Step 3: The three experts give their subjective weights vector λ = {0.24, 0.17, 0.18, 0.23, 0.18}.…”

“…The ability of Pythagorean fuzzy sets to model such uncertainty of decision-making is much stronger than IFSs. So PFSs theory is a more powerful tool for expressing uncertain information when making decisions [18].…”