  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.
