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The pythagorean fuzzy set (PFS) which is developed based on intuitionisticfuzzy set, is more efficient in elaborating and disposing uncertainties inindeterminate situations, which is a very reason of that PFS is applied invarious kinds of fields. How to measure the distance between two pythagoreanfuzzy sets is still an open issue. Mnay kinds of methods have been proposed topresent the of the question in former reaserches. However, not all of existingmethods can accurately manifest differences among pythagorean fuzzy sets andsatisfy the property of similarity. And some other kinds of methods neglect therelationship among three variables of pythagorean fuzzy set. To addrees theproplem, a new method of measuring distance is proposed which meets therequirements of axiom of distance measurement and is able to indicate thedegree of distinction of PFSs well. Then some numerical examples are offered toto verify that the method of measuring distances can avoid the situation thatsome counter? intuitive and irrational results are produced and is moreeffective, reasonable and advanced than other similar methods. Besides, theproposed method of measuring distances between PFSs is applied in a realenvironment of application which is the medical diagnosis and is compared withother previous methods to demonstrate its superiority and efficiency. And thefeasibility of the proposed method in handling uncertainties in practice isalso proved at the same time.

A new distance measure of Pythagorean fuzzy sets based on matrix and and its application in medical diagnosis