Lattice implication ordered semigroups

被引：21
作者：
Pan, Xiaodong [1 ,2 ]
Xu, Yang [2 ]
机构：
[1] SW Jiaotong Univ, Dept Math, Chengdu 610031, Peoples R China
[2] SW Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Peoples R China
来源：
INFORMATION SCIENCES | 2008年 / 178卷 / 02期
基金：
高等学校博士学科点专项科研基金; 中国国家自然科学基金;
关键词：
lattice ordered semigroup; implication semigroup; lattice implication algebra; filter; sl ideal;
D O I：
10.1016/j.ins.2007.08.017
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
From the viewpoint of semantics, lattice implication algebras provide a basis to establish lattice-valued logic with truth value in a relatively general lattice. In this paper, we first introduce two notions of lattice implication n-ordered semigroup, and lattice implication p-ordered semigroup, which induced by lattice implication algebras. Secondly, we study some of their basic properties and prove that a lattice implication n-ordered semigroup is a residuated semigroup, and a lattice implication p-ordered semigroup is an arithmetic lattice ordered semigroup. We also define the homomorphism mapping between lattice implication n-ordered semigroups. Finally, we discuss some properties of filters and sl ideals in lattice implication n-ordered semigroups and lattice implication p-ordered semigroups. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：403 / 413
页数：11
相关论文
共 50 条
  • [41] On the Characteristic of Proper Lattice Implication Algebras
    徐扬
    秦克云
    数学季刊, 1994, (04) : 14 - 17
  • [42] L-fuzzy Lattice Implication Algebra
    SONG Qing-long
    数学季刊, 2006, (02) : 246 - 251
  • [43] IFI-ideals of lattice implication algebras
    Zhu, Hua
    Zhao, Jianbin
    Xu, Yang
    INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 2013, 6 (06) : 1002 - 1011
  • [44] (∈,∈ ∨q) -Fuzzy Filters of Lattice Implication Algebras
    Peng Jiayin
    APPLIED INFORMATICS AND COMMUNICATION, PT 4, 2011, 227 : 397 - 404
  • [45] IFI-ideals of lattice implication algebras
    Hua Zhu
    Jianbin Zhao
    Yang Xu
    International Journal of Computational Intelligence Systems, 2013, 6 : 1002 - 1011
  • [46] On f-derivations of lattice implication algebras
    Yon, Yong Ho
    Kim, Kyung Ho
    ARS COMBINATORIA, 2013, 110 : 205 - 215
  • [47] (∈,∈vq)-fuzzy filters of lattice implication algebras
    Peng Jiayin
    2010 THE 3RD INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE AND INDUSTRIAL APPLICATION (PACIIA2010), VOL IV, 2010, : 220 - 223
  • [48] A more general form of interval valued fuzzy filters in ordered semigroups
    Muhammad Sajjad Ali Khan
    Saleem Abdullah
    Kostaq Hila
    Afrika Matematika, 2021, 32 : 1435 - 1455
  • [49] Amore general form of interval valued fuzzy filters in ordered semigroups
    Khan, Muhammad Sajjad Ali
    Abdullah, Saleem
    Hila, Kostaq
    AFRIKA MATEMATIKA, 2021, 32 (7-8) : 1435 - 1455
  • [50] More General Forms of Interval Valued Fuzzy Filters of Ordered Semigroups
    Davvaz, Bijan
    Khan, Asghar
    Sarmin, Nor Haniza
    Khan, Hidayatullah
    INTERNATIONAL JOURNAL OF FUZZY SYSTEMS, 2013, 15 (02) : 110 - 126
12345