A Matrix-based Distance of Pythagorean Fuzzy Set and its Application in Medical Diagnosis
Yuanpeng He, Lijian Li, Tianxiang Zhan
TL;DR
This paper tackles the problem of measuring differences between Pythagorean fuzzy sets (PFSs) in uncertainty-laden medical diagnosis contexts. It introduces a matrix-based distance, D_N, built on an extended score SP_A and a fixed transformation matrix, with Y, N, and H derived from paired PFS components; the metric is proved to satisfy symmetry, identity, boundedness, and the triangle inequality. The authors also provide a practical decision-making algorithm and demonstrate applications to COVID-19 recognition and symptom-diagnosis tasks, showing improved discrimination over traditional distances. The work offers a robust, interpretable distance for PFSs that better captures the interplay among membership, non-membership, and hesitation, with potential for future enhancement via a learnable transformation matrix. Overall, the method advances distance-based PFS analysis and supports more reliable medical-pattern recognition under uncertainty.
Abstract
The pythagorean fuzzy set (PFS) which is developed based on intuitionistic fuzzy set, is more efficient in elaborating and disposing uncertainties in indeterminate situations, which is a very reason of that PFS is applied in various kinds of fields. How to measure the distance between two pythagorean fuzzy sets is still an open issue. Mnay kinds of methods have been proposed to present the of the question in former reaserches. However, not all of existing methods can accurately manifest differences among pythagorean fuzzy sets and satisfy the property of similarity. And some other kinds of methods neglect the relationship among three variables of pythagorean fuzzy set. To addrees the proplem, a new method of measuring distance is proposed which meets the requirements of axiom of distance measurement and is able to indicate the degree of distinction of PFSs well. Then some numerical examples are offered to to verify that the method of measuring distances can avoid the situation that some counter? intuitive and irrational results are produced and is more effective, reasonable and advanced than other similar methods. Besides, the proposed method of measuring distances between PFSs is applied in a real environment of application which is the medical diagnosis and is compared with other previous methods to demonstrate its superiority and efficiency. And the feasibility of the proposed method in handling uncertainties in practice is also proved at the same time.