Abstract
The notions of fuzzy ideals are introduced in coresiduated lattices. The characterizations of fuzzy ideals, fuzzy prime ideals, and fuzzy strong prime ideals in coresiduated lattices are investigated and the relations between ideals and fuzzy ideals are established. Moreover, the equivalence of fuzzy prime ideals and fuzzy strong prime ideals is proved in prelinear coresiduated lattices. Furthermore, the conditions under which a fuzzy prime ideal is derived from a fuzzy ideal are presented in prelinear coresiduated lattices.
Highlights
Residuated lattices provide an algebra frame for the algebraic semantics of formal fuzzy logics such as MV-algebras, BLalgebras, and R0-algebras [1,2,3,4,5,6]
It is a useful tool to characterize the intuitionistic fuzzy operators and plays a vital role in the theory basses of Triple I method of intuitionistic fuzzy reasoning
It is well known that ideal is an important part of algebra structure for various fuzzy logic semantics
Summary
Residuated lattices provide an algebra frame for the algebraic semantics of formal fuzzy logics such as MV-algebras, BLalgebras, and R0-algebras (or MTL-algebras) [1,2,3,4,5,6]. Ideal is interesting because it is closely related to congruence relation It plays a vital role in Chang’s Subdirect Representation Theorem of MV-algebras [3]. It was used to obtain the unified form of intuitionistic fuzzy difference operators and the Triple D method solutions of intuitionistic fuzzy reasoning problems in [14]. We intend to introduce the notions of fuzzy ideals in coresiduated lattices and develop the ideal theory of coresiduated lattices.
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