T-norms and t-conorms on a family of lattices

被引：4
|
作者：
Bejines, C. [1 ]
机构：
[1] Czech Tech Univ, Fac Elect Engn, Dept Cybernet, Prague, Czech Republic
来源：
FUZZY SETS AND SYSTEMS | 2022年 / 439卷
关键词：
T-norm; t-Conorm; Lattice; Archimedean; Divisible; 1-Lipschitz; TRIANGULAR NORMS; BOUNDED LATTICES; ORDINAL SUMS; UNINORMS;
D O I：
10.1016/j.fss.2021.05.008
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
This paper provides a complete classification of all t-norms on a family of lattices in terms of t-norms on discrete chains. Moreover, the cardinal of some classes on discrete chains is computed. Therefore, the number of t-norms on the family of lattices is obtained. Also, new results involving Archimedean and divisible t-norms are presented. Finally, we bring out dual results for t-conorms. (c) 2021 Elsevier B.V. All rights reserved.
引用
收藏
页码：55 / 74
页数：20
相关论文
共 50 条
  • [11] SOME METHODS TO OBTAIN T-NORMS AND T-CONORMS ON BOUNDED LATTICES
    Cayli, Gul Deniz
    KYBERNETIKA, 2019, 55 (02) : 273 - 294
  • [12] Some construction approaches for t-norms and t-conorms on bounded lattices
    Asici, Emel
    Mesiar, Radko
    AEQUATIONES MATHEMATICAE, 2022, 96 (05) : 955 - 979
  • [13] Some construction approaches for t-norms and t-conorms on bounded lattices
    Emel Aşıcı
    Radko Mesiar
    Aequationes mathematicae, 2022, 96 : 955 - 979
  • [14] Alternative approaches to obtain t-norms and t-conorms on bounded lattices
    Asici, E.
    Mesiar, R.
    IRANIAN JOURNAL OF FUZZY SYSTEMS, 2020, 17 (04): : 121 - 138
  • [15] Some methods to construct t-norms and t-conorms on bounded lattices
    Asici, Emel
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2021, 40 (06) : 10877 - 10892
  • [16] Andness Directedness for t-Norms and t-Conorms
    Torra, Vicenc
    MATHEMATICS, 2022, 10 (09)
  • [17] Vague and fuzzy t-norms and t-conorms
    Boixader, D.
    Recasens, J.
    FUZZY SETS AND SYSTEMS, 2022, 433 : 156 - 175
  • [18] Generalizing Leximin to t-norms and t-conorms
    Yager, RR
    Walker, CL
    Walker, EA
    NAFIPS 2004: ANNUAL MEETING OF THE NORTH AMERICAN FUZZY INFORMATION PROCESSING SOCIETY, VOLS 1AND 2: FUZZY SETS IN THE HEART OF THE CANADIAN ROCKIES, 2004, : 343 - 345
  • [19] Reducing t-norms and augmenting t-conorms
    Detyniecki, M
    Yager, RR
    Bouchon-Meunier, B
    INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 2002, 31 (03) : 265 - 276
  • [20] On the distributivity between t-norms and t-conorms
    Bertoluzza, C
    Doldi, V
    FUZZY SETS AND SYSTEMS, 2004, 142 (01) : 85 - 104
12345