Clifford's order obtained from uninorms on bounded lattices

Gupta, Vikash Kumar and Jayaram, Balasubramaniam (2022) Clifford's order obtained from uninorms on bounded lattices. Fuzzy Sets and Systems. pp. 1-18. ISSN 0165-0114

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Abstract

Inspired by the work of Clifford on obtaining order from semigroups, many works have proposed different ways of obtaining orders from associative fuzzy logic operations. However, unlike Clifford's relation, these were dependent on the subdomain of its arguments. Recently, it was shown that a property termed Quasi-Projectivity (QP) is necessary to obtain an order from Clifford's relation. Further, for the underlying domain [0,1] it was shown that while all t-norms, t-conorms and nullnorms satisfy (QP), giving rise to posets, not all classes of uninorms satisfy (QP). Several constructions of uninorms U exist on bounded lattices, which unlike [0,1] may neither be total nor complete. In this work, we investigate the satisfaction of (QP) for these constructions. This study merits attention since it offers an alternate perspective - that a uninorm U on a lattice L can be seen as a t-norm on the obtained U-poset. © 2022 Elsevier B.V.

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IITH Creators:

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

Item Type:

Article

Additional Information:

We would like to thank the AE and the reviewers for their insightful comments, which helped in both simplifying many results and considerably enhancing the readability of the submission. The work described in this article was supported by University Grants Commission (UGC), New Delhi, India (Ref. No. 20/12/2015(ii)EU-V). The second author would like to gratefully acknowledge the partial support of SERB under the project MTR/2020/000506.

Uncontrolled Keywords:

Bounded lattices; F-posets; Ordered sets; T-norms; Uninorms

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

. LibTrainee 2021

Date Deposited:

15 Sep 2022 14:32

Last Modified:

15 Sep 2022 14:32