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

作者：Wu, Xinxing^*; Chen, Guanrong; Wang, Lidong^*

来源：Fuzzy Sets and Systems, 2022, 441: 241-261.

DOI：10.1016/j.fss.2021.10.001

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

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 Hernandez 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.

• 单位
  西南石油大学; 吉林大学