On union and intersection of type-2 fuzzy sets not expressible by the sup-t-norm extension principle

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)241-261
Journal / PublicationFuzzy Sets and Systems
Online published7 Oct 2021
Publication statusPublished - 5 Aug 2022


This paper constructs a conjunction and a disjunction operator for type-2 fuzzy sets that cannot be expressed by the sup-t-norm extension principle applied to conjunction and disjunction of type-1 fuzzy sets by means of t-norms and t-conorms on the unit interval. This result answers affirmatively an open problem posed by Hernández et al. in 2015. The duality between the set-theoretic operators for type-2 fuzzy sets is obtained from the duality of set-theoretic operations on type-1 fuzzy sets.

Research Area(s)

  • Normal and convex function, t-Conorm, t-Norm, Type-2 fuzzy set