Abstract
A 1-cut of a fuzzy relation (sometimes called a core) does not contain all the information that is represented by the fuzzy relation. Particularly, a fuzzy order ≼ on a universe X equipped with an fuzzy equality ≈ is not uniquely determined by its 1-cut 1≼={〈x,y〉 | (x≼y)=1} . That is, there are in general several fuzzy orders with a common 1-cut. We show that, if the fuzzy order obeys in addition the lattice structure (which many natural examples of fuzzy orders do), it is uniquely determined by its 1-cut. Moreover, we discuss consequences of this result for the so-called fuzzy concept lattices and formal concept analysis.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
