Abstract
Abstract The notion of IFI–ideal is introduced in lattice implication algebras. Firstly, the equivalent conditions of IF–ideals and IFI–ideals are given in lattice implication algebras. Then the proposition of IFI–ideal is investigated in lattice implication algebras. Next, the relations between IFI–ideal and IF–ideal, between IFI–ideal and IFI–filter, between IFI–ideal and fuzzy impilcative ideals, between IFI–ideal and implicative ideals are discussed in lattice implication algebras. Moreover, the extension theorem of IFI–ideals is obtained, and Ψ(L) which is composed of all IFI–ideals constitutes a closure system. Finally, we prove that ∀α ∈ [0;1], A = (µ0,α ; ) is an IFI–ideal of lattice implication algebra L if and only if L is a lattice H implication algebra.
Highlights
There are some certain information and uncertain information in the real world
It is natural to investigate similar type of generalizations of the existing fuzzy subsystems with other algebraic structure. With this objective in view, we introduce the notion of the intuitionistic fuzzy implicative ideal(briefly, IFI−ideal) in lattice implication algebras
The intuitionistic fuzzy set has become a considerable formal tool to deal with fuzzy information in the real world
Summary
There are some certain information and uncertain information in the real world. As we know, we can use classical logic to deal with certain information and some non-classical logic to deal with fuzzy information and uncertain information, for example lattice logic, fuzzy logic, etc. In 4, Jun introduced the notion of LI− ideals in lattice implication algebras and investigated some of its properties. In 2006, Zhu proposed the concept of the primary ideals in lattice implication algebras and investigated the related properties[18]. In 10, Pei applied the intuitionistic fuzzy set to lattice implication algebras, and introduced the notion of the intuitionistic fuzzy filter in lattice implication algebras. In 2009, Xu defined the notion of the intuitionistic fuzzy implicative filter in lattice implication algebras and investigated its related properties[12]. Zhu proposed the notion of the intuitionistic fuzzy ideal (briefly, IF−ideal) in lattice implication algebras, which was the dual algebraic structure of the intuitionistic fuzzy filter 21. With this objective in view, we introduce the notion of the intuitionistic fuzzy implicative ideal(briefly, IFI−ideal) in lattice implication algebras. It will be important to provide theoretical foundation to design intelligent information processing systems
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
