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

Xinxing Wu; Guanrong Chen; Lidong Wang

doi:10.1016/j.fss.2021.10.001

Author(s)

Xinxing Wu
Guanrong Chen
Lidong Wang

Related Research Unit(s)

Department of Electrical Engineering

Detail(s)

Original language	English
Pages (from-to)	241-261
Journal / Publication	Fuzzy Sets and Systems
Volume	441
Online published	7 Oct 2021
Publication status	Published - 5 Aug 2022

Link(s)

DOI	DOI https://doi.org/10.1016/j.fss.2021.10.001 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-85117854735&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(38ae6273-1ffd-4096-b86f-cc9be011aa3b).html

Abstract

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.