A New Distance Measure Based on Pythagorean Hesitant Fuzzy Sets and Its Application to Multi-Criteria Decision Making

The Pythagorean fuzzy set is characterized by five parameters, namely membership degree, non-membership degree, indeterminacy degree, strength of commitment about membership, and direction of commitment. And distance measure is an important index in Pythagorean Hesitant fuzzy (PHF) environment when solving the multicriteria decision-making problem. However, the existing distance measure considers the difference between the member ship degrees, the non-membership degrees, and the degrees of indeterminacy, but ignores the influence of the difference between the directions of PHF sets (PHFSs). The existing distance measure method may lead to unreasonable results sometimes. Inspired by above, the five parameters of PFS are extended to Pythagorean Hesitant Fuzzy set (PHFS) fully in this paper, generating new distance measures of PHFS and introducing some properties and theorems firstly. Then, the proposed method is applied in MCDM with PHF information by considering the distance between the positive ideal solution and each alternative. Finally, to validate the effectiveness of the proposed method, a pragmatic experiment is introduced for comparisons with existing methods.