On constructing the largest and smallest uninorms on bounded lattices

Xie, A; Li, S

On constructing the largest and smallest uninorms on bounded lattices

Xie, A Li, S

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Publisher:: ELSEVIER
Publication Type:: Journal Article
Citation:: Fuzzy Sets and Systems, 2020, 386, pp. 95-104
Issue Date:: 2020-05-01

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Field	Value	Language
dc.contributor.author	Xie, A
dc.contributor.author	Li, S https://orcid.org/0000-0002-3332-2546
dc.date.accessioned	2020-05-05T22:43:25Z
dc.date.available	2020-05-05T22:43:25Z
dc.date.issued	2020-05-01
dc.identifier.citation	Fuzzy Sets and Systems, 2020, 386, pp. 95-104
dc.identifier.issn	0165-0114
dc.identifier.issn	1872-6801
dc.identifier.uri	http://hdl.handle.net/10453/140497
dc.description.abstract	© 2019 Elsevier B.V. Uninorms on the unit interval are a common extension of triangular norms (t-norms) and triangular conorms (t-conorms). As important aggregation operators, uninorms play a very important role in fuzzy logic and expert systems. Recently, several researchers have studied constructions of uninorms on more general bounded lattices. In particular, Çaylı (2019) gave two methods for constructing uninorms on a bounded lattice L with e∈L∖{0,1}, which is based on a t-norm Te on [0,e] and a t-conorms Se on [e,1] that satisfy strict boundary conditions. In this paper, we propose two new methods for constructing uninorms on bounded lattices. Our constructed uninorms are indeed the largest and the smallest among all uninorms on L that have the same restrictions Te and Se on [0,e] and, respectively, [e,1]. Moreover, our constructions does not require the boundary condition, and thus completely solved an open problem raised by Çaylı.
dc.language	English
dc.publisher	ELSEVIER
dc.relation.ispartof	Fuzzy Sets and Systems
dc.relation.isbasedon	10.1016/j.fss.2019.04.020
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0101 Pure Mathematics, 0801 Artificial Intelligence and Image Processing
dc.subject.classification	Artificial Intelligence & Image Processing
dc.title	On constructing the largest and smallest uninorms on bounded lattices
dc.type	Journal Article
utslib.citation.volume	386
utslib.for	0101 Pure Mathematics
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0101 Pure Mathematics
utslib.for	0801 Artificial Intelligence and Image Processing
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	open_access	*
dc.date.updated	2020-05-05T22:43:23Z
pubs.publication-status	Published
pubs.volume	386
utslib.start-page	95

Abstract:

© 2019 Elsevier B.V. Uninorms on the unit interval are a common extension of triangular norms (t-norms) and triangular conorms (t-conorms). As important aggregation operators, uninorms play a very important role in fuzzy logic and expert systems. Recently, several researchers have studied constructions of uninorms on more general bounded lattices. In particular, Çaylı (2019) gave two methods for constructing uninorms on a bounded lattice L with e∈L∖{0,1}, which is based on a t-norm Te on [0,e] and a t-conorms Se on [e,1] that satisfy strict boundary conditions. In this paper, we propose two new methods for constructing uninorms on bounded lattices. Our constructed uninorms are indeed the largest and the smallest among all uninorms on L that have the same restrictions Te and Se on [0,e] and, respectively, [e,1]. Moreover, our constructions does not require the boundary condition, and thus completely solved an open problem raised by Çaylı.

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http://hdl.handle.net/10453/140497