Relational Representations of Strongly Algebraic Lattices

In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

Implicative and Fuzzy Implicative Ideals of Lattice Implication Algebras

In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.

The Logical Properties of Filters of Lattice Implication Algebra

In this paper, we discuss some propertie s of lattice implication algebra and difine the transitivity of implication in a set, we show the transitivity of implication and the substitution Theorem hold i n filters. So every filter of lattice implication algebra satisfies the Syllogis m and substitution Theorem of propositional logic.

Fuzzy MP-filters Lattice on a Given FI-algebra

In this paper, the properties of fuzzy MP-filters are discussed by using methods of Domain theory in FI-algebras. It is proved that all fuzzy MP-filters of a given FI-algebra form a distributive algebraic lattice, particularly form a frame.

LI-ideal Spaces of Lattice Implication Algebra

In this paper, a topological space based on LI-ideals of a lattice implication algebra is constructed, and its topological properties, such as separability, compactness and connectedness are discussed.

On Certain Filters in Lattice Implication Algebras

Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper, we introduce the concept of. I-feature filters and involutory filters in fat tice implication algebras, and discussed some propert ies of them. Finally, the characterization of filters of any lattice implication algebra which satisfies Increasing Chain Conditions (I. C. C) is given.

Logical Properties of Lattice Filter of Lattice Implication Algebra

Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras （LIAs）, i. e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system.

Finite Simple Lattice Implication Algebras

In this paper, some necessary and sufficient conditions that a finite lattice implication algebra is simple are established. Specially, it is proved that a finite lattice implication algebra L is simple if and only if （L, ≤） is a chain, if and only if there exists the unique dual atom in L. Also, it is given that a finite lattice implication algebra with order of a prime number is simple.

Closure Operators of Lattice-valued Propositional Logic LP(X)

In this paper, closure operators of lattice-valued propositional logic LP（X） are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP（X） is investigated. At the same time, a tool for checking compactness of LP（X） is given.

On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra are proposed,the relation between lattice implication product algebra and its factors and some properties of lattice implication product algebras are discussed.

Prime Space of Lattice Implication Algebras

In this paper,after discussing the prime implication filter of lattice implication algebra,we introduced the concept of prime space of lattice implication algebra,in which we analysised its topological property and discussed the relation between the category of topological space and the category of lattice implication algebras.

Lattice Implication Algebrasand MV-algebras

Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper,the relationship between lattice implication algebras and MV algebra was discussed,and then proved that both of the categorys of the two algebras are categorical equivalence. Finally,the infinitely distributivity in lattice implication algebras were proved.

Linguistic Truth Values Lattice Implication Algebras

In order to study uncertainty reasoning and automatic reasoning with linguistic terms, in this paper, the set of basic linguistic truth values and the set of modifiers are defined, according to common sense; partially orderings are defined on them. Based on it, a lattice implication algebra model L18 of linguistic terms is built; furthermore, its some basic properties are discussed.

L-fuzzy Lattice Implication Algebra

This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.

Syntactic Extension of Lattice-valued Propositional Logic LP(X)

We have given a semantic extension of lattice-valued propositional logic LP（X） in [6]. In this paper, we investigate its corresponding syntactic extension of LP（X） and give the relations between these two extensions.

Subalgebra and LI-Ideal of Lattice Implication Algebras

First, we reviewed the definitions of lattice implication algebras, lattice implication subalgebras, and LI-ideals, and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice implication subalgebra and U-ideal, and found the least lattice implication subalgebra. Finally, the relation between lattice implication subalgebra and LI-ideal is presented. It is proved that no LI-ideals are non-trivial lattice implication subalgebras.

STRONGLY ALGEBRAIC LATTICES AND CONDITIONS OF MINIMAL MAPPING PRESERVING INFS

The tabor gives some characterizations of strongly algebraic lattices, and proves that thecategory of strongly algebraic lattices is complete and cocomplete. Finally, this paper gives thecomplete conditions under which the minimal mapping β: L→2L on a completely distributivelattice L preserves finite infs and arbitrary infs.

CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS

Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B = P, here A o B = AB ＋ BA is the usual Jordan product. In this article, we show that if ,A = AlgAN is a Hilbert space nest Mgebra and M = B（H）, or A =M= B（X）, then, a linear mapδ： A→M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P∈ B（X） if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.

Some Properties of α-Subsets

In this paper, the concept of α-subsets is introduced in a lattice implication algebra and some properties are discussed. Then we prove that an α-subset is a lattice ideal of L. In the end, we discuss the properties of annihilator.