As the generalization of intuitionistic fuzzy set, Pythagorean fuzzy set was introduced. It is a pair of membership and non-membership grade where the sum of the squares of membership and non-membership grade should be less than or equal to 1. Pythagorean fuzzy set get more attention to deal with uncertainity. In this paper we apply Pythagorean fuzzy set in ideal theory of hypersemigroups. We introduce Pythagorean fuzzy left(right) hyperideals in hypersemigroups. We define t−level cut of Pythagorean fuzzy hyperideal is in hypersemigroup. Also we introduce Pythagorean fuzzy interior hyperideals in hypersemigroups and explain it with detailed example. Some theorems and results are also studied. Relation between Pythagorean fuzzy right(left) hyperideal, Pythagorean fuzzy subsemihypergroup and Pythagorean fuzzy interior hyperideal is given.Publisher's Versio
