A non-commutative generalization of quasi-MV algebras

被引：0
|
作者：
Liu, Jianming [1 ]
Chen, Wenjuan [1 ]
机构：
[1] Univ Jinan, Sch Math Sci, 336 Nan Xinzhuang Rd, Jinan 250022, Shandong, Peoples R China
来源：
2016 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE) | 2016年
基金：
中国国家自然科学基金;
关键词：
pseudo-quasi-MV algebras; normal ideals; ideal congruences; pseudo-quasi-Wa[!text type='js']js[!/text]berg algebras; categorical equivalence;
D O I：
暂无
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, we introduce and investigate a noncommutative generalization of quasi-MV algebras, called pseudoquasi-MV algebras (pseudo-qMV algebras for short). And then we characterize the bijective relation between ideal congruences and normal ideals of a pseudo-qMV algebra. Finally, we prove that pseudo-qMV algebras are categorically equivalent to pseudoquasi-Wajsberg algebras which are the non-commutative generalization of quasi-Wajsberg algebras.
引用
收藏
页码：122 / 126
页数：5
相关论文
共 50 条
  • [1] Quasi-MV* algebras: a generalization of MV*-algebras
    Yingying Jiang
    Wenjuan Chen
    Soft Computing, 2022, 26 : 6999 - 7015
  • [2] Quasi-MV* algebras: a generalization of MV*-algebras
    Jiang, Yingying
    Chen, Wenjuan
    SOFT COMPUTING, 2022, 26 (15) : 6999 - 7015
  • [3] A non-commutative generalization of MV-algebras
    Jiří Rachůnek
    Czechoslovak Mathematical Journal, 2002, 52 : 255 - 273
  • [4] A non-commutative generalization of MV-algebras
    Rachunek, J
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2002, 52 (02) : 255 - 273
  • [5] ON SOME PROPERTIES OF QUASI-MV ALGEBRAS AND √′ QUASI-MV ALGEBRAS. PART IV
    Jipsen, Peter
    Ledda, Antonio
    Paoli, Francesco
    REPORTS ON MATHEMATICAL LOGIC, 2013, 48 : 3 - 36
  • [6] ON SOME PROPERTIES OF QUASI-MV ALGEBRAS AND √′QUASI-MV ALGEBRAS. PART III
    Kowalski, Tomasz
    Paoli, Francesco
    REPORTS ON MATHEMATICAL LOGIC, 2010, 45 : 161 - 199
  • [7] On some properties of quasi-MV algebras and √′ quasi-MV algebras.: Part II
    Bou, Felix
    Paoli, Francesco
    Ledda, Antonio
    Freytes, Hector
    SOFT COMPUTING, 2008, 12 (04) : 341 - 352
  • [8] The Logic of Quasi-MV Algebras
    Bou, Felix
    Paoli, Francesco
    Ledda, Antonio
    Spinks, Matthew
    Giuntini, Roberto
    JOURNAL OF LOGIC AND COMPUTATION, 2010, 20 (02) : 619 - 643
  • [9] MV-algebras with operators (the commutative and the non-commutative case)
    Flondor, P
    Leustean, I
    DISCRETE MATHEMATICS, 2004, 274 (1-3) : 41 - 76
  • [10] Logics from √′ Quasi-MV Algebras
    Paoli, Francesco
    Ledda, Antonio
    Spinks, Matthew
    Freytes, Hector
    Giuntini, Roberto
    INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2011, 50 (12) : 3882 - 3902
12345