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On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras
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作者 ZHU Hua ZHAO Jian-bin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第2期274-292,共19页
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-L... 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. 展开更多
关键词 DERIVATION Boolean element lattice implication algebra(LIA) 2-dimension linguistic lattice implication algebra(2DL-LIA) 2-dimension fuzzy linguistic information
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Lattice Implication Algebrasand MV-algebras
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作者 郭天榜 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第3期17-23, ,共7页
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 discuss... 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. 展开更多
关键词 lattice implication algebras MV algebras lattice order groups categorical equivalence
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On Certain Filters in Lattice Implication Algebras 被引量:3
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作者 刘军 徐扬 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第4期106-110, ,共5页
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 ti... 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. 展开更多
关键词 lattice implication algebra fliter I-feature filter involutory filter I. C. C
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Finite Simple Lattice Implication Algebras 被引量:1
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作者 ZHU Yi-quan 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期423-429,共7页
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... 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. 展开更多
关键词 lattice implication algebra SIMPLICITY PERIODICITY
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Prime Space of Lattice Implication Algebras
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作者 宋振明 郭天榜 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第4期46-50, ,共5页
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 di... 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. 展开更多
关键词 lattice implication algebra prime implication filter topological space prime space CATEGORY
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Linguistic Truth Values Lattice Implication Algebras
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作者 潘小东 徐扬 《Journal of Donghua University(English Edition)》 EI CAS 2006年第6期101-104,109,共5页
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... 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. 展开更多
关键词 linguistic truth value linguistic variable computing with words lattice implication algebra Subalgebra.
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On the Product and Factorization of Lattice Implication Algebras
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作者 秦克云 宋振明 徐扬 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第4期53-57,共5页
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 p... 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. 展开更多
关键词 lattice implication algebra lattice implication product algebra FACTORIZATION
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Subalgebra and LI-Ideal of Lattice Implication Algebras
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作者 吴明慧 徐扬 刘煦 《Journal of Southwest Jiaotong University(English Edition)》 2010年第3期250-253,共4页
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 im... 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. 展开更多
关键词 lattice implication subalgebra lattice H implication algebra Lukasiewicz implication algebra LI-ideal
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Implicative and Fuzzy Implicative Ideals of Lattice Implication Algebras 被引量:11
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作者 赵光峰 徐扬 宋振明 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第4期104-110,共7页
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... 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. 展开更多
关键词 lattice implication algebra fuzzy LI _ideal fuzzy filter implicative ideal fuzzy implicative ideal
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Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras
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作者 刘熠 刘军 +1 位作者 陈树伟 徐扬 《Journal of Shanghai Jiaotong university(Science)》 EI 2012年第2期166-170,共5页
The modal lattice implication algebra(i.e.,M-lattice implication algebra) is introduced and its properties are investigated.The modal lattice-valued propositional logical system is introduced by considering the M-latt... The modal lattice implication algebra(i.e.,M-lattice implication algebra) is introduced and its properties are investigated.The modal lattice-valued propositional logical system is introduced by considering the M-lattice implication algebra as the valuation field,and the syntax and semantic of the logical system are discussed,respectively. 展开更多
关键词 modal lattice implication algebras lattice-valued modal logic SEMANTIC SYNTAX
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The Logical Properties of Filters of Lattice Implication Algebra 被引量:3
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作者 王伟 徐扬 宋振明 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第3期8-13,共6页
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. S... 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. 展开更多
关键词 lattice implication algebra FILTER TRANSITIVITY
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LI-ideal Spaces of Lattice Implication Algebra 被引量:3
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作者 CHEN Shu-wei JIANG Bao-qing YANG Xiao-wei 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第4期504-511,共8页
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.
关键词 lattice implication algebra LI-ideal topological space topological properties
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Logical Properties of Lattice Filter of Lattice Implication Algebra 被引量:4
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作者 赖家俊 徐扬 宋振明 《Journal of Southwest Jiaotong University(English Edition)》 2007年第4期353-356,共4页
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... 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. 展开更多
关键词 Partially ordered set lattice lattice Filters lattice implication algebra FILTERS
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L-fuzzy Lattice Implication Algebra
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作者 SONG Qing-loug LI Chun-rui ZHAO Guang-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第2期246-251,共6页
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 latt... 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. 展开更多
关键词 L-Fuzzy lattice implication algebra
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Closure Operators of Lattice-valued Propositional Logic LP(X)
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作者 WANG Xue-fang ZHENG Feng-bin XU Yang 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第3期301-308,共8页
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 investi... 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. 展开更多
关键词 lattice-valued logic lattice implication algebras closure operators COMPACTNESS
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Syntactic Extension of Lattice-valued Propositional Logic LP(X)
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作者 ZHENG Feng-bin LI Qing-yu +1 位作者 WANG Xue-fang XU Yang 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第2期301-308,共8页
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.
关键词 lattice-valued logic lattice implication algebra (α β)-consequence (α β)-theorem formal proof
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Some Properties of α-Subsets
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作者 龙希庆 徐扬 顾秀梅 《Journal of Donghua University(English Edition)》 EI CAS 2006年第6期141-143,152,共4页
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... 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. 展开更多
关键词 lattice implication algebras lattice H implication algebras α - subsets annihilators.
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Ideal Resolution Principle for Lattice-Valued First-Order Logic Based on Lattice Implication Algebra 被引量:1
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作者 许伟涛 徐扬 《Journal of Shanghai Jiaotong university(Science)》 EI 2012年第2期178-181,共4页
As a continuate work,ideal-based resolution principle for lattice-valued first-order logic system LF(X) is proposed,which is an extension of α-resolution principle in lattice-valued logic system based on lattice impl... As a continuate work,ideal-based resolution principle for lattice-valued first-order logic system LF(X) is proposed,which is an extension of α-resolution principle in lattice-valued logic system based on lattice implication algebra.In this principle,the resolution level is an ideal of lattice implication algebra,instead of an element in truth-value field.Moreover,the soundness theorem is given.In the light of lifting lemma,the completeness theorem is established.This can provide a new tool for automated reasoning. 展开更多
关键词 automated reasoning lattice-valued logic lattice implication algebra generalized clause
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Some Properties of Fuzzy Filter and Its Category
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作者 郭天榜 程伟 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第3期18-22, ,共5页
This paper is devoted to the study of some properties of fuzzy filters in lattice implication algebras. The structure theorem of fuzzy filters and the category of the sets of fuzzy filters were established with some b... This paper is devoted to the study of some properties of fuzzy filters in lattice implication algebras. The structure theorem of fuzzy filters and the category of the sets of fuzzy filters were established with some basic properties of it were discussed. 展开更多
关键词 lattice implication algebra FILTER fuzzy filter
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On Some Properties of L Type Intuitionistic Fuzzy Family
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作者 岳树松 王建平 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第2期65-69,共5页
Intuitionistic fuzzy set is an extended form of Zadeh's fuzzy set. In this paper, the concept of L type intuitionistic fuzzy family based on lattice implication algebras was proposed and some of its properties we... Intuitionistic fuzzy set is an extended form of Zadeh's fuzzy set. In this paper, the concept of L type intuitionistic fuzzy family based on lattice implication algebras was proposed and some of its properties were discussed. 展开更多
关键词 lattice implication algebra L type intuitionistic fuzzy set L type intuitionistic fuzzy family
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