Abstract
Admissible orders have brought the structure of chains in the framework of interval-valued fuzzy sets. However, a deeper study of functions monotone with respect to admissible orders is still missing in the literature. In this work, we consider the construction of negations and strong negations on intervals with respect to admissible orders, in particular, for the Xu and Yager and lexicographical orders, as well as for those based on $K_\alpha$ operators. We introduce and discuss an approach to the construction of strong negations on intervals with respect to $K_{\alpha,\beta }$ orders based on an arbitrary couple of strong negations defined over the standard real interval $[0,1]$ . The introduced strong negations have a deep impact on all fields exploiting fuzzy methods dealing with intervals, allowing to introduce complements, dual aggregations, implications, entropies, etc.
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.
