# A Matrix-based Distance of Pythagorean Fuzzy Set and its Application in Medical Diagnosis

arXiv: https://arxiv.org/abs/2102.01538 · HTML: https://mlsanity.com/paper/2102.01538/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 40 references that are in the map.
- First posted on arXiv 31 Jan 2021.

## Builds on (most cited first, 1 of 1)

- [A total uncertainty measure for D numbers based on belief intervals](https://mlsanity.com/paper/1801.00702/) (2017)

## Built on by (most cited first, 6 of 6)

- [An Adaptive Framework for Multi-View Clustering Leveraging Conditional Entropy Optimization](https://mlsanity.com/paper/2412.17647/) (2024)
- [Complementarity-driven Representation Learning for Multi-modal Knowledge Graph Completion](https://mlsanity.com/paper/2507.20620/) (2025)
- [Residual Feature-Reutilization Inception Network for Image Classification](https://mlsanity.com/paper/2412.19433/) (2024)
- [Mutual Evidential Deep Learning for Medical Image Segmentation](https://mlsanity.com/paper/2505.12418/) (2025)
- [Co-Evidential Fusion with Information Volume for Medical Image Segmentation](https://mlsanity.com/paper/2506.02492/) (2025)
- [Adaptive Fuzzy Time Series Forecasting via Partially Asymmetric Convolution and Sub-Sliding Window Fusion](https://mlsanity.com/paper/2507.20641/) (2025)

## Abstract (arXiv)

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.