A decomposition theorem for the fuzzy Henstock integral

Authors:
B. Bongiorno;L. Di Piazza;K. Musiał
Affiliations:
University of Palermo, Department of Mathematics, Via Archirafi 34, 90123 Palermo, Italy;University of Palermo, Department of Mathematics, Via Archirafi 34, 90123 Palermo, Italy;Wrocław University, Institute of Mathematics, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Venue:
Fuzzy Sets and Systems
Year:
2012

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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.