A New Definition of Intuitionistic Fuzzy Rough Set and Its Similarity Measure

The definitions of intuitionistic fuzzy rough sets can usually be divided into two kinds. According to one kind, each intuitionistic fuzzy rough set is constructed by a couple of intuitionistic fuzzy sets. According to the other, each intuitionistic fuzzy rough set is constructed by a couple of fuzzy rough sets. In this paper, another kind definition is proposed that each intuitionistic fuzzy rough set is constructed by a couple of rough fuzzy sets. Then, "upper rough degree" and "lower rough degree" are introduced to characterize the relation between components in each intuitionistic fuzzy rough value. And then their meanings in three kinds intuitionistic fuzzy rough sets are illustrated respectively. Besides, a strong similarity measure between intuitionistic fuzzy rough sets is proposed. At last, an application is done to show the feasibility of the proposed measure function.