Generation of continuous T-norms through latticial operations

Jayaram, Balasubramaniam (2023) Generation of continuous T-norms through latticial operations. Fuzzy Sets and Systems, 462. p. 108398. ISSN 0165-0114

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Abstract

It is well known that the usual point-wise ordering over the set T of t-norms makes it a poset but not a lattice, i.e., the point-wise maximum or minimum of two t-norms need not always be a t-norm again. In this work, we propose, two binary operations [Formula presented] on the set TCA of continuous Archimedean t-norms and obtain, via these binary operations, a partial order relation ⊑, different from the usual point-wise order ≤, on the set TCA. As an interesting outcome of this structure, some stronger versions of some existing results dealing with the upper and lower bounds of two continuous Archimedean t-norms with respect to the point-wise order ≤ are also obtained. Finally, with the help of the operations [Formula presented] on the set TCA, two binary operations ⊕,⊗ on the set TC of continuous t-norms are proposed and showed that (TC,⊕,⊗) is a lattice. Thus we have both a way of generating continuous t-norms from continuous t-norms and also obtain an order on them.

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IITH Creators:

IITH Creators	ORCiD
Jayaram, Balasubramaniam	http://orcid.org/0000-0001-7370-3821

Item Type:

Article

Uncontrolled Keywords:

Additive generators; Continuous Archimedean t-norms; Distributive lattice; Lattice operations; Partial order; T-norms; Artificial intelligence; Additive generators; Archimedean t-norms; Binary operations; Continuous archimedean t-norm; Continuous t-norms; Distributive lattice; Lattice operations; Partial order; Point wise; T - Norm; Fuzzy logic

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

Mr Nigam Prasad Bisoyi

Date Deposited:

04 Jan 2024 14:01

Last Modified:

04 Jan 2024 14:01

URI:

http://raiithold.iith.ac.in/id/eprint/11766