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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 [Z. Gong, C. Wu and B. Li, Fuzzy Sets Syst. 127, No. 3, 315–322 (2002; Zbl 0995.26018)].

MSC:

26E50 Fuzzy real analysis
28E10 Fuzzy measure theory
26A39 Denjoy and Perron integrals, other special integrals

Citations:

Zbl 0995.26018
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References:

[1] Diamond, P.; Kloeden, P. E., Metric Spaces of Fuzzy Sets: Theory Applications (1994), World Scientific: World Scientific Singapore
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[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), World Scientific: World Scientific Singapore, New Jersey, London, Hong Kong · 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
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