Abstract
In this work, by Zadeh’s extension principle, we extend representable uninorms and their fuzzy implications (coimplications) to type-2 fuzzy sets. Emphatically, we investigate in which algebras of fuzzy truth values the extended operations are type-2 uninorms and type-2 fuzzy implications (coimplications), respectively.
Highlights
Type-2 fuzzy sets, which were introduced by Zadeh [1] in 1975, are an extension of the ordinary fuzzy sets since truth values of the latter are precise on the unit interval [0, 1], while the former are equipped with fuzzy truth value mappings from [0, 1] to itself
Let A ⊆ F, JU,N be a (U,N)-coimplication derived from a conjunctive representable uninorm U
By Zadeh’s extension principle, we extended uninorms and fuzzy implications to type-2 fuzzy sets and defined type-2 uninorms and fuzzy implications
Summary
Type-2 fuzzy sets, which were introduced by Zadeh [1] in 1975, are an extension of the ordinary (type-1) fuzzy sets since truth values of the latter are precise on the unit interval [0, 1], while the former are equipped with fuzzy truth value mappings from [0, 1] to itself. [40] introduced the concept of type-2 uninorm, and extended uninorms, which belong to Umin and Umax classes, to type-2 fuzzy sets and discussed under which conditions they are type-2 uninorms. In this work, we will extend representable uninorms and fuzzy implications (coimplications) derived from them to type-2 fuzzy sets. The paper discusses in which algebra of fuzzy truth values they are classified in, i.e., type-2 uninorms and fuzzy implications (coimplications), respectively. (RU)-implications (coimplications) derived from representable uninorms, and study in which algebras of fuzzy truth values they are type-2 fuzzy implications (coimplications), and discuss their properties on type-2 fuzzy sets
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
