布尔代数的(λ,μ)模糊子代数

在布尔代数中引入了(λ,μ)-模糊子代数的概念,讨论了布尔代数的(λ,μ)模糊子代数的性质.证明了布尔代数的两个(λ,μ)-模糊子代数交与直积也是(λ,μ)-模糊子代数.     

布尔代数的双极值模糊子代数

在布尔代数中引入了双极值模糊子代数的概念,讨论了布尔代数的双极值模糊子代数的性质.证明了布尔代数的两个双极值模糊子代数交与直积也是双极值模糊子代数.     

模糊软布尔代数

将模糊软集与布尔代数相结合,定义了模糊软布尔代数、模糊软布尔子代数、模糊理想软布尔代数、模糊软布尔代数的模糊软同态的概念,并研究了它们的性质.     

关于T-S模的超直觉模糊群及其同态

本文研究了关于T-S模的直觉模糊正规子群、超直觉模糊群、超直觉模糊正规子群和直觉模糊商群,利用T模、S模的定义及性质,在两个经典群同态的意义下,获得了关于超直觉模糊群的同态与同构等若干结果.     

直觉模糊子环及其同构

利用既约集合套讨论了直觉模糊子环和直觉模糊理想的一些性质,并在两个经典环同态与同构意义下,定义了直觉模糊商环,商直觉模糊子环,以及直觉模糊子环的直和,并讨论了其相关性质.     

格蕴涵代数中的直觉模糊理想

给出格蕴涵代数中直觉模糊理想的定义,并研究了其性质。然后讨论了直觉模糊理想与模糊理想和LI-理想之间的关系。证明了直觉模糊理想与直觉模糊滤子的对偶关系。最后,得到了直觉模糊理想的全体集合Ψ(L)构成L-闭包系统。     

N(2,2,0)代数的T-模糊子代数和T-模糊理想

为了深入研究N(2,2,0)代数的代数结构,在N(2,2,0)代数中引入了T模糊子代数和T模糊理想的概念,进一步讨论了它们的性质.分别给出了N(2,2,0)代数的模糊子代数和模糊理想与子代数和理想的关系.证明了N(2,2,0)代数的两个T模糊子代数的模交也是T模糊子代数,而N(2,2,0)代数的两个T模糊理想的模交也是T模糊理想.     

格的生成直觉模糊理想

首先探讨了由一个直觉模糊子集生成格的直觉模糊理想的问题,给出了生成直觉模糊理想的刻画;其次研究了在经典格同态意义下,直觉模糊理想的像以及逆像,得到了格同态与生成直觉模糊理想的关系.     

半群的带有限度(α,β)的直觉模糊双理想

给出了半群中带有限度(α,β)的直觉模糊双理想的概念,研究了半群中带有限度(α,β)的直觉模糊双理想的若干性质和刻画。     

(λ,μ)直觉模糊子环(理想)

在直觉模糊集理论的基础上,首先引入了(λ,μ)直觉模糊子环和(λ,μ)直觉模糊理想的概念,讨论了它们的相关性质;其次在环同态的意义下,研究了(λ,μ)直觉模糊子环和(λ,μ)直觉模糊理想的同态像及其逆像.     

布尔代数的Fuzzy子代数和Fuzzy理想

引入了布尔代数的Fuzzy子代数、Fuzzy理想和Fuzzy商布尔代数的概念,给出了布尔代数的Fuzzy集是Fuzzy子代数(Fuzzy理想)的充要条件,讨论了布尔代数的Fuzzy子代数(Fuzzy理想)在布尔代数同态下的像和逆像,得到了布尔代数的Fuzzy子代数的同态基本定理。     

布尔代数上的Fuzzy同余关系

引入了布尔代数上的Fuzzy同余关系的概念，讨论了布尔代数上的Fuzzy同余关系与布尔代数的Fuzzy理想之间的关系，给出了商布尔代数的同构定理。     

Single-Valued Neutrosophic Lie Algebras

A single-valued neutrosophic (SVN) set is a powerful general formal framework that generalizes the concept of fuzzy set and intuitionistic fuzzy set. In SVN set, indeterminacy is quantified explicitly, and truth membership, indeterminacy membership, and falsity membership are independent. In this paper, we apply the notion of SVN sets to Lie algebras. We develop the concepts of SVN Lie subalgebras and SVN Lie ideals. We describe some interesting results of SVN Lie ideals.     

The Rough Intuitionistic Fuzzy Ideals of Intuitionistic Fuzzy Subrings in a Commutative Ring

The aim of this paper is to give some definitions of rough intuitionistic fuzzy ideal, rough intuitionistic fuzzy radical, rough prime (primary) intuitionistic fuzzy ideal and rough semiprime intuitionistic fuzzy ideal of an intuitionistic fuzzy subring, and also to give some properties of such ideals. Moreover, we give their nature under homomorphism.     

Intuitionistic fuzzy sublattices and ideals

We study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals of a lattice. Some characterization and properties of these intuitionistic fuzzy sublattices and ideals are established. Also we introduce the sum and product of two intuitionistic fuzzy ideals and prove that the sum and product of two Intuitionistic fuzzy ideals of a distributive lattice is again an intuitionistic fuzzy ideal. Moreover, we study the properties of intuitionistic fuzzy ideals under lattice homomorphism.     

BOOLEAN ALGEBRAS IN AST

In this paper we investigate Boolean algebras and their subalgebras in Alternative Set Theory (AST). We show that any two countable atomless Boolean algebras are isomorphic and we give an example of such a Boolean algebra. One other main result is, that there is an infinite Boolean algebra freely generated by a set. At the end of the paper we show that the sentence “There is no non-trivial free group which is a set” is consistent with AST.     

格蕴涵代数的直觉模糊LI-理想

本文深入研究了格蕴涵代数的直觉模糊\textit{LI}-理想理论.给出了直觉模糊\textit{LI}-理想的若干新的性质和等价刻画. 建立了由一个直觉模糊集生成的直觉模糊\textit{LI}-理想的表示定理.证明了一个格蕴涵代数的全体之集模糊\textit{LI}-理想之集在直觉模糊包含序下构成一个完备的分配格.     

Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets

Two basic inference models of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). The Triple I method is a very important method to solve the problems of FMP and FMT. The aim of this paper is to extend the Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets. In the paper, we first investigate the algebra operators' properties on the lattice structure of intuitionistic fuzzy information and provide the unified form of residual implications which indicates the relationship between intuitionistic fuzzy implications and fuzzy implications. Then we present the intuitionistic fuzzy reasoning version of the Triple I principles based on the models of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) and give the Triple I method of intuitionistic fuzzy reasoning for residual implications. Moreover, we discuss the reductivity of the Triple I methods for IFMP and IFMT. Finally, we propose α-Triple I method of intuitionistic fuzzy reasoning.     

Fuzzy dot ideals and fuzzy dot H-ideals of BCH-algebras

The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated. The relations among fuzzy ideal, fuzzy H-ideal, fuzzy dot ideal and fuzzy dot H-ideals in BCH- algebras are discussed, several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals （fuzzy dot H-ideals） are studied. The relations between a fuzzy dot ideal （fuzzy dot H-ideal） in BCH-algebras and a fuzzy dot ideal （fuzzy dot H-ideal） in the product algebra of BCH-algebras are given.