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Erschienen in:
Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms Kapitel lesen Erstes Kapitel lesen

2021 | OriginalPaper | Buchkapitel

20. Decomposition of Intersections with Fuzzy Sets of Operands

verfasst von : S. O. Mashchenko, D. O. Kapustian

Erschienen in: Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics

Verlag: Springer International Publishing

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Abstract

We investigate the operation of intersection of fuzzy sets with a fuzzy set of operands. This is a natural generalization of the corresponding operation which involves a crisp set of operands. The decomposition approach was used to study the intersections of fuzzy sets with a fuzzy set of operands. The result of this operation is a type-2 fuzzy set (T2FS). We prove several results which enable us to simplify constructing the type-2 membership function. It is shown that the resulting T2FS can be decomposed according to secondary membership grades into a finite collection of type-1 fuzzy sets. Each of these sets is the intersection of the original sets with a crisp set of operands. This crisp set is the corresponding \(\alpha \)-cut of the fuzzy set of operands. Illustrative examples are given.

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Metadaten
Titel
Decomposition of Intersections with Fuzzy Sets of Operands
verfasst von
S. O. Mashchenko
D. O. Kapustian
Copyright-Jahr
2021
Buch
Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics

Print ISBN: 978-3-030-50301-7

Electronic ISBN: 978-3-030-50302-4

Copyright-Jahr: 2021

DOI
https://doi.org/10.1007/978-3-030-50302-4_20