On derivations of linguistic truth-valued lattice implication algebras

被引：10

作者：

Zhu, Hua ^{[1
,2
]}

Liu, Yi ^{[3
]}

Xu, Yang ^{[1
]}

机构：

[1] Southwest Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Sichuan, Peoples R China

[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

[3] Neijiang Normal Univ, Coll Math & Informat Sci, Neijiang 641000, Sichuan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS | 2018年 / 9卷 / 04期

关键词：

Derivation; Isotone derivation; Regular derivation; Linguistic truth-valued lattice implication algebra (L-LIA); Lattice implication algebra (LIA); NEAR-RINGS; IDEALS; FILTERS; SET;

D O I：

10.1007/s13042-016-0551-x

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Algebraic characters of linguistic truth-valued lattice implication algebras (L-LIAs) are focused in this paper. Concretely, the concept of derivation coming from analytic theory is introduced in L-LIAs, and then some properties of derivations are given in L-LIAs. Subsequently, some special derivations (such as isotone deri-vation, embedding derivation, isomorphism derivation and regular derivation) are discussed in L-LIAs along with the relations among them. The relations between derivations and lattice implication homomorphisms are also investigated in L-LIAs. At the end, the derivations of some algebraic substructures are described in L-LIAs.

引用

页码：611 / 620

页数：10

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