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

页数：21

共 50 条

[31] A new way to extend t-norms, t-conorms and negations
Palmeira, Eduardo
Bedregal, Benjamin
Mesiar, Radko
Fernandez, Javier
FUZZY SETS AND SYSTEMS, 2014, 240 : 1 - 21
[32] On the use of generalized mean with T-norms and T-conorms
Saastamoinen, K
2004 IEEE CONFERENCE ON CYBERNETICS AND INTELLIGENT SYSTEMS, VOLS 1 AND 2, 2004, : 569 - 573
[33] Uni-norms: A unification of t-norms and t-conorms
Yager, RR
Rybalov, A
1996 BIENNIAL CONFERENCE OF THE NORTH AMERICAN FUZZY INFORMATION PROCESSING SOCIETY - NAFIPS, 1996, : 50 - 54
[34] On the representation of intuitionistic fuzzy t-norms and t-conorms
Deschrijver, G
Cornelis, C
Kerre, EE
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2004, 12 (01) : 45 - 61
[35] Generic view on continuous t-norms and t-conorms
Perfilieva, I
COMPUTATIONAL INTELLIGENCE, THEORY AND APPLICATIONS, 2005, : 377 - 382
[36] Migrativity of Uninorms over T-norms and T-conorms
Mas, M.
Monserrat, M.
Ruiz-Aguilera, D.
Torrens, J.
AGGREGATION FUNCTIONS IN THEORY AND IN PRACTISE, 2013, 228 : 155 - 166
[37] T-norms and t-conorms continuous around diagonals
Mesiarova-Zemankova, Andrea
FUZZY SETS AND SYSTEMS, 2016, 299 : 105 - 112
[38] Multi-valued t-norms and t-conorms
Kehagias, A
Serafimidis, K
PROCEEDINGS OF THE 7TH JOINT CONFERENCE ON INFORMATION SCIENCES, 2003, : 241 - 244
[39] Choosing t-norms and t-conorms for fuzzy controllers
Ahmad, Khurshid
Mesiarova-Zemankova, Andrea
FOURTH INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS AND KNOWLEDGE DISCOVERY, VOL 2, PROCEEDINGS, 2007, : 641 - +
[40] A New Kind of Triangular Integrals Based on T-norms and T-conorms
Liu, Wan-li
Song, Xiao-qiu
Liu, Jin-bo
Zhang, Qiu-zhao
FUZZY INFORMATION AND ENGINEERING, 2012, 4 (01) : 13 - 27

← 1 2 3 4 5 →