Abstract
The algebra of truth values of type-2 fuzzy sets is not a lattice, but some of its subalgebras may be lattices. In this paper, we give a necessary and sufficient condition under which subalgebras of the truth value algebra of type-2 fuzzy sets form lattices. Further, we prove that if a certain subalgebra is a lattice, then it is isomorphic to an appropriate subalgebra whose all elements are convex functions with the same height. Based on these results, if a certain subalgebra is a lattice, the equivalent characterizations of the partial order in it are given.
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.
