Distance measure based on geometric compression of Pythagorean fuzzy sets

Abstract

Pythagorean fuzzy sets (PFS) as a generation of Fuzzy sets has the greater representation space in handling uncertain information, which is applied to many fields. Distance between PFS which can measure the difference or discrepancy grade. Obviously, the distance between (1,0) and (0,1) is different from that between (0,0) and (0,1). However, some distance measure methods violate this result. To address above problem, the paper proposes a new distance measure based on geometric compression. In FPS, the sum of squares of membership, non-membership and hesitant is 1. In new method, membership, non-membership and hesitant information are regarded as x, y, z-axis to establish a space rectangular coordinate system. Based on the unit circle, the membership, non-membership and hesitant information are compressed to get the deformable ellipsoid. For hesitant information, it can be regarded to contain membership and non-membership information from the view of Dempster-Shafer evidence theory. What’s more, new distance measure not only satisfies the axiomatic definition of distance measure but also has nonlinear characteristics. In addition, the advantages of new method are indicated by comparing with other distance measure methods. Finally, the paper apply new method in the Multiattribute decision making problem, which provides a promising solution for addressing decision-making problems.