Bounded variation, absolute continuity and absolute integrability for fuzzy-number-valued functions

Authors:
Zengtai Gong;Congxin Wu
Affiliations:
Department of mathematics, Harbin Institute of Technology, Harbin, China;Department of mathematics, Harbin Institute of Technology, Harbin, China
Venue:
Fuzzy Sets and Systems
Year:
2002

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Abstract

In this paper, the concepts of bounded variation and absolute continuity for the fuzzy-number-valued functions are presented and discussed by means of the representation of the absolute value for fuzzy numbers. The relations among bounded variation, absolute continuity, Kaleva's integral and fuzzy Henstock integral are characterized. Especially, the representation of absolute continuous fuzzy valued functions is given by Henstock (Kaleva) integral of absolutely Henstock (Kaleva) integrable fuzzy-number-valued functions.