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

页码：55 / 74

页数：20

共 50 条

[1] On Generating of t-Norms and t-Conorms on Bounded Lattices
Cayli, Gul Deniz
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 2020, 28 (05) : 807 - 835
[2] On a new class of t-norms and t-conorms on bounded lattices
Cayli, Gul Deniz
FUZZY SETS AND SYSTEMS, 2018, 332 : 129 - 143
[3] The additive generators of t-norms and t-conorms on bounded lattices
Sun, Xiang-Rong
Liu, Hua-Wen
Fuzzy Sets and Systems, 2021, 408 : 13 - 25
[4] The additive generators of t-norms and t-conorms on bounded lattices
Sun, Xiang-Rong
Liu, Hua-Wen
FUZZY SETS AND SYSTEMS, 2021, 408 : 13 - 25
[5] Ordinal Sums of t-norms and t-conorms on Bounded Lattices
Dvorak, Antonin
Holcapek, Michal
NEW TRENDS IN AGGREGATION THEORY, 2019, 981 : 289 - 301
[6] New constructions of t-norms and t-conorms on bounded lattices
Shi, Jie Qiong
Zhao, Bin
AEQUATIONES MATHEMATICAE, 2024, 98 (06) : 1527 - 1564
[7] A family of multi-valued t-norms and t-conorms
Kehagias, Athanasios
Computational Intelligence Based on Lattice Theory, 2007, 67 : 341 - 360
[8] Characterizing Ordinal Sum for t-norms and t-conorms on Bounded Lattices
Cayli, Gull Deniz
ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1, 2018, 641 : 443 - 454
[9] New constructions of t-norms and t-conorms on bounded lattices and trellises
Zhao, Yifan
Liu, Hua-Wen
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 2025,
[10] Nullnorms on bounded lattices derived from t-norms and t-conorms
Cayli, Gul Deniz
INFORMATION SCIENCES, 2020, 512 : 1134 - 1154

← 1 2 3 4 5 →