NDLI: On complete fuzzy preorders and their characterizations

Content Provider	Springer Nature Link
Author	Montes, Ignacio Díaz, Susana Montes, Susana
Copyright Year	2010
Abstract	In the context of crisp or classical relations, one may find several alternative characterizations of the concept of a total preorder. In this contribution, we first discuss the way of translating those characterizations to the framework of fuzzy relations. Those new properties depend on t-norms. We focus on two important families of t-norms, namely those that do not admit zero divisors and those that are rotation invariant. For these families, we study whether or not the properties shown for fuzzy relations lead to characterizations of complete fuzzy preorders. Special attention is paid to the minimum operator, which shows the best behaviour in preserving most of the characterizations known for crisp relations.
Starting Page	1999
Ending Page	2011
Page Count	13
File Format	PDF
ISSN	14327643
Journal	Soft Computing
Volume Number	15
Issue Number	10
e-ISSN	14337479
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-06-27
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Preorder Completeness t-Norm without zero divisor Rotation invariant t-norm Computational Intelligence Mathematical Logic and Foundations Artificial Intelligence (incl. Robotics) Control, Robotics, Mechatronics
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Software Geometry and Topology

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On complete fuzzy preorders and their characterizations