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Intersection and union of type-2 fuzzy sets and connection to $$(\alpha_1, \alpha_2)$$-double cuts. (English) Zbl 1254.03108
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) and 17th annual LFA meeting, Aix-Les-Bains, France, July 18–22, 2011. Amsterdam: Atlantis Press (ISBN 9978-90-78677-00-0). Paper No. 151, 1052-1059 (2011).
Summary: It is known that the standard intersection and union of type-1 fuzzy sets (i.e., the intersection and union under the minimum t-norm and maximum tconorm) are the only cutworthy operations for type-1 fuzzy sets. The aim of this paper is to show that a similar property holds also for type-2 fuzzy sets, with respect to some special cutting. As was already demonstrated, the intersection and union of type-2 fuzzy sets are not preserved in $$\alpha$$-planes. Thus, we study another kind of cutting, so-called double cuts, and show that the intersection and union of type-2 fuzzy sets are preserved in these double cuts.
For the entire collection see [Zbl 1226.03005].

##### MSC:
 3e+72 Theory of fuzzy sets, etc.
##### Keywords:
type-2 fuzzy sets; double cut; $$\alpha$$-plane; intersection; union
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