New constructions of t-norms and t-conorms on bounded lattices and trellises

被引：0
|
作者：
Zhao, Yifan [1 ]
Liu, Hua-Wen [1 ]
机构：
[1] Shandong Univ, Sch Math, Jinan, Peoples R China
来源：
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS | 2025年
基金：
中国国家自然科学基金;
关键词：
t-norms; t-conorms; bounded lattices; bounded trellises; TRIANGULAR NORMS; ORDINAL SUMS; BIODIVERSITY; TRANSITIVITY; OPERATORS; PROMOTES;
D O I：
10.1080/03081079.2025.2457559
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, we propose a rather effective method to construct t-norms using weak interior operators on appropriate bounded lattices, which covers several construction methods in the literature. We also present a generic construction method for t-norms on bounded trellises with the help of quasi-interior operators. In particular, we give the necessary and sufficient condition for this kind of construction and discuss how to relax the condition. Finally, the dual results for construction of t-conorms via weak (quasi-)closure operators on bounded lattices (trellises) are presented.
引用
收藏
页数：21
相关论文
共 50 条
  • [41] Associative operators based on t-norms and t-conorms
    Mas, M
    Mesiar, R
    Monserrat, M
    Torrens, J
    INTELLIGENT SYSTEMS FOR INFORMATION PROCESSING: FROM REPRESENTATION TO APPLICATIONS, 2003, : 393 - 404
  • [42] Multi-valued t-norms and t-conorms
    Kehagias, A
    Serafimidis, K
    PROCEEDINGS OF THE 7TH JOINT CONFERENCE ON INFORMATION SCIENCES, 2003, : 84 - 87
  • [43] A family of multi-valued t-norms and t-conorms
    Kehagias, Athanasios
    Computational Intelligence Based on Lattice Theory, 2007, 67 : 341 - 360
  • [44] The weak dominance between t-norms and t-conorms revisited
    Liu, Qiao-Yun
    Qin, Feng
    FUZZY SETS AND SYSTEMS, 2024, 487
  • [45] Usage of the T-norms and T-conorms in Medical Data Classification
    Saastamoinen, Kalle
    BEC 2008: 2008 INTERNATIONAL BIENNIAL BALTIC ELECTRONICS CONFERENCE, PROCEEDINGS, 2008, : 183 - 186
  • [46] Strict Archimedean t-norms and t-conorms as universal approximators
    Nguyen, HT
    Kreinovich, V
    Wojciechowski, P
    INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 1998, 18 (3-4) : 239 - 249
  • [47] Migrative uninorms and nullnorms over t-norms and t-conorms
    Mas, M.
    Monserrat, M.
    Ruiz-Aguilera, D.
    Torrens, J.
    FUZZY SETS AND SYSTEMS, 2015, 261 : 20 - 32
  • [48] The construction of fuzzy-valued t-norms and t-conorms
    Kehagias, Athanasios
    COMPUTATIONAL INTELLIGENCE BASED ON LATTICE THEORY, 2007, 67 : 361 - 370
  • [49] On the distributivity for the ordinal sums of implications over t-norms and t-conorms
    Zhao, Bin
    Lu, Jing
    INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2023, 152 : 284 - 296
  • [50] An addendum to "Migrative uninorms and nullnorms over t-norms and t-conorms"
    Zong, Wenwen
    Su, Yong
    Liu, Hua-Wen
    FUZZY SETS AND SYSTEMS, 2016, 299 : 146 - 150
12345