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On the problem of characterizing derivatives for the fuzzy-valued functions. II: Almost everywhere differentiability and strong Henstock integral. (English) Zbl 1095.26019
Summary: The concept of strong fuzzy Henstock integrability for fuzzy-valued functions is presented; a necessary and sufficient condition of almost everywhere differentiability for the fuzzy-valued functions is given by means of this concept. See also Part I [{\it Z. Gong, C. Wu} and {\it B. Li}, Fuzzy Sets Syst. 127, No. 3, 315--322 (2002; Zbl 0995.26018)].

26E50Fuzzy real analysis
28E10Fuzzy measure theory
26A39Special integrals of functions of one real variable
Full Text: DOI
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[3] Gong, Z.: The differentiability of primitives for the fuzzy-valued functions. Fuzzy systems math. 17, No. 2, 12-17 (2003)
[4] Gong, Z.; Wu, C.: On the problem of characterizing derivatives for the fuzzy-valued functions. Fuzzy sets and systems 127, 315-322 (2002) · Zbl 0995.26018
[5] Kaleva, O.: Fuzzy differential equations. Fuzzy sets and systems 24, 301-317 (1987) · Zbl 0646.34019
[6] Lee, P.: Lanzhou lecture on Henstock integration. (1989) · Zbl 0699.26004
[7] Puri, M. L.; Ralesu, D. A.: Differentials for fuzzy functions. J. math. Anal. appl. 91, 552-558 (1983) · Zbl 0528.54009
[8] Wu, C.; Gong, Z.: On Henstock integrals of fuzzy-valued functions (I). Fuzzy sets and systems 120, 523-532 (2001) · Zbl 0984.28010