Case Of Intuitionistic Fuzzy Ideal (filter)

The lattice is one of the most basic objects of order algebra. Intuitionistic fuzzy sets and rough sets are powerful tools for dealing with uncertainty information. Cross-integration of the lattice algebra, fuzzy mathematics and information science, not on-ly enriches the theory of fuzzy mathematics, but also provides profound applications background for the lattice algebra. In order to simplify the complex algebraic structu-re, some structures and properties of the original algebra systems are portrayed by u-sing fuzzy algebraic research results. In this paper, the notion of intuitionistic fuzzy i-deals (filters) in lattices is introduced and some properties of them are investigated. The intuitionistic fuzzy ideal (filter) generated by an intuitionistic fuzzy set is discus-sed. Then using generated intuitionistic fuzzy ideals (filters), the algebraic structure of the set of intuitionistic fuzzy ideals (filters) of a lattice is obtained. Moreover, in the sense of the homomorphism between two crisp lattices, the image and the inverse i-mage of intuitionistic fuzzy ideals (filters) and generated intuitionistic fuzzy ideals (fi-lters) are studied, respectively. Also, the notions of the upper and lower approximati-ons of an intuitionistic fuzzy set are introduced and some related properties of them are given. And the corresponding relationships between the upper and lower approxi-mations of intuitionistic fuzzy ideals (filters) and the upper and lower approximations of their homomorphism images are obtained. Finally, the notion of intuitionistic fuzzy congruence relation on lattices is introduced and the intuitionistic fuzzy ideals (filters) of intuitionistic fuzzy quotient lattices are studied.