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Integral transform of fuzzy numbers. (Chinese. English summary) Zbl 1264.44004

Summary: Integral transform and inverse integral transform of fuzzy numbers are defined by using the joint membership of two fuzzy numbers. It is proved that the fuzzy number obtained by integral transforming a fuzzy number has the same support and kernel as that of the original one. Moreover, a necessary and sufficient condition under that a given fuzzy number with bounded support will not changed after integral transforming and inverse integral transforming is given. Additionally, two applications illustrate the integral transform of of fuzzy numbers.

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
03E72 Theory of fuzzy sets, etc.
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