We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.
Bongiorno, B., Di Piazza, L., Musial, K. (2012). A Decomposition Theorem for the Fuzzy Henstock Integral. FUZZY SETS AND SYSTEMS, 200, 36-47 [10.1016/j.fss.2011.12.006].
A Decomposition Theorem for the Fuzzy Henstock Integral
BONGIORNO, Benedetto;DI PIAZZA, Luisa;
2012-01-01
Abstract
We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.
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