New constructions of t-norms and t-conorms on bounded lattices and trellises.
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| Title: | New constructions of t-norms and t-conorms on bounded lattices and trellises. |
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| Authors: | Zhao, Yifan1 (AUTHOR), Liu, Hua-Wen1 (AUTHOR) hw.liu@sdu.edu.cn |
| Source: | International Journal of General Systems. Jan2026, Vol. 55 Issue 1, p70-90. 21p. |
| Subjects: | Triangular norms, Lattice theory, Operator functions, Design, Banach lattices |
| Abstract: | 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | 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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 03081079 |
| DOI: | 10.1080/03081079.2025.2457559 |
