The concept of intuitionistic fuzzy set was introduced by Atanassov [1, 2] and intuitionistic fuzzy modal operators were defined in 1999 by Atanassov [3]. In following years, new intuitionistic fuzzy modal operators were defined and their properties were examined by several authors [4, 20, 5, 9, 8, 10, 11].

The theory of hyperstructures was introduced by Marty in 1934 [23]. Marty defined the notion of a hypergroup and then many researchers studied on this new field of modern algebra and developed it. Davvaz defined the concept of fuzzy -ideal of an -ring which is a generalization of the concept of fuzzy ideal [13]. The notion of intuitionistic fuzzy -ideal of an -ring were introduced by Davvaz and Dudek in 2006 [16].

In this paper, we apply the concept of an intuitionistic fuzzy modal operator to intuitionistic fuzzy -ideal of an -ring.

intuitionistic fuzzy modal operator, intuitionistic fuzzy -ideal of an -ring, fuzzy -ideal of an -ring.