Distance measure based on geometric compression of Pythagorean fuzzy sets

Haoxin Gai; Xiaozhuan Gao

doi:10.1117/12.3032001

8 June 2024 Distance measure based on geometric compression of Pythagorean fuzzy sets

Haoxin Gai, Xiaozhuan Gao

Proceedings Volume 13171, Third International Conference on Algorithms, Microchips, and Network Applications (AMNA 2024); 1317114 (2024) https://doi.org/10.1117/12.3032001
Event: 3rd International Conference on Algorithms, Microchips and Network Applications (AMNA 2024), 2024, Jinan, China

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.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Haoxin Gai and Xiaozhuan Gao "Distance measure based on geometric compression of Pythagorean fuzzy sets", Proc. SPIE 13171, Third International Conference on Algorithms, Microchips, and Network Applications (AMNA 2024), 1317114 (8 June 2024); https://doi.org/10.1117/12.3032001

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