The Fuzzy Lattice of Ideals and Filters of an Almost Distributive Fuzzy Lattice

In this paper, the concept of fuzzy lattice is discussed. It is proved that a fuzzy poset (IA(L),B) and (FA(L),B) forms a fuzzy lattice, where IA(L) and FA(L) are the set containing all ideals, and the set containing all filters of an Almost Distributive Fuzzy Lattice(ADFL) respectively. In addition we proved that, a fuzzy poset (PIA(L),B) and (PFA(L),B) forms fuzzy distributive lattice, where PIA and PFA(L) denotes the set containing all principal ideals and the set containing all principal filters of an ADFL. Finally, it is proved that for any ideal I and filter F of an ADFL, IiA = {(i]A : i in I} and FfA = {[f)A : f in F} are ideals of a fuzzy distributive lattice (PIA(L),B) and (PFA(L),B) respectively, and FiA = {(f]A : f in F} and IfA = {[i)A : i in I} are filters of a distributive fuzzy lattice (PIA(L),B) and (PFA(L),B) respectively

Heyting Almost Distributive fuzzy Lattices

In this paper, we introduce the concept of Heyting almost distributive fuzzy lattices (HADFL) using the concepts of Heyting almost distributive lattices (HADL), almost distributive fuzzy lattices, fuzzy partial order relation and fuzzy Heyting algebra. Using the properties of fuzzy Heyting algebra, we also give a necessary and sufficient condition for an HADFL to be fuzzy Heyting algebra (FHA)

Birkhoff center of Almost Distributive Fuzzy Lattice

The concept of Birkhoff center B_A(R) of an Almost distributive fuzzy lattice (R,A) with maximal element is introduced. We also prove that BA(R) is relatively complemented ADFL and product of ADFL is a gain ADFL

L-Fuzzy Filters of a Poset

Many generalizations of ideals and filters of a lattice to an arbitrary poset have been studied by different scholars. The authors of this paper introduced several generalizations of L-fuzzy ideal of a lattice to an arbitrary poset in [1]. In this paper, we introduce several L-fuzzy filters of a poset which generalize the L-fuzzy filter of a lattice and give several characterizations of them

Implicative Almost Distributive Lattice

In this paper, we introduce the concept of Implicative Almost Distributive Lattices (IADLs) as a generalization of implicative algebra in the class of Almost Distributive Lattices. We discuss some properties of IADL and derive some equivalent conditions in IADLs. We also discuss some characterizations of IADL to become an implicative algebra

Transitive and Absorbent Filters of Implicative Almost Distributive Lattices

In this paper, we introduce the concept of transitive and absorbent filters of implicative almost distributive lattices and studied their properties. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. A set of equivalent conditions is obtained for a filter to become an absorbent filter

Fuzzy Amicable sets of an Almost Distributive Fuzzy Lattice

In this paper, we introduce the concept of Fuzzy Amicable sets, we prove some properties of Fuzzy Amicable set, too. We also prove that two Fuzzy compatible elements of an Almost distributive Fuzzy Lattice (ADFL) are equal if and only if their corresponding unique Fuzzy amicable elements are equal. We define the homomorphism of two Almost Distributive Fuzzy lattices (ADFL) and finally we observe that any two Fuzzy amicable set in an Almost Distributive Fuzzy Lattice (ADFL) are isomorphic

On Homomorphism and Cartesian Products of Intuitionistic Fuzzy PMS-subalgebra of a PMS-algebra

In this paper, we introduce the notion of intuitionistic fuzzy PMS-subalgebras under homomorphism and Cartesian product and investigate several properties. We study the homomorphic image and inverse image of the intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, which are also intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, and find some other interesting results. Furthermore, we also prove that the Cartesian product of intuitionistic fuzzy PMS-subalgebras is again an intuitionistic fuzzy PMS-subalgebra and characterize it in terms of its level sets. Finally, we consider the strongest intuitionistic fuzzy PMS-relations on an intuitionistic fuzzy set in a PMS-algebra and demonstrate that an intuitionistic fuzzy PMS-relation on an intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra if and only if the corresponding intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra of a PMS-algebra