Wu, Congxin; Gong, Zengtai On Henstock integrals of interval-valued functions and fuzzy-valued functions. (English) Zbl 0973.26009 Fuzzy Sets Syst. 115, No. 3, 377-391 (2000). Henstock integrals of interval-valued functions and fuzzy-valued functions are defined and discussed. Several necessary and sufficient conditions of integrability are given by means of the Henstock-Pettis integral theory. Reviewer: Tuan Seng Chew (Singapore) Cited in 23 Documents MSC: 26A39 Denjoy and Perron integrals, other special integrals 26E50 Fuzzy real analysis Keywords:Henstock integral; fuzzy numbers; interval-valued functions; fuzzy-valued functions; Henstock-Pettis integral PDF BibTeX XML Cite \textit{C. Wu} and \textit{Z. Gong}, Fuzzy Sets Syst. 115, No. 3, 377--391 (2000; Zbl 0973.26009) Full Text: DOI OpenURL References: [1] J. Diestel, J.J. Uhl Jr, Vector Measures, vol. 15, American Mathematical Society, Providence, RI, 1977. [2] Goetschel, R.; Voxman, W., Elementary fuzzy calculus, Fuzzy sets and systems, 18, 31-43, (1986) · Zbl 0626.26014 [3] Henstock, R., Theory of integration, (1963), Butterworth London · Zbl 0154.05001 [4] Kaleva, O., Fuzzy differential equations, Fuzzy sets and systems, 24, 301-317, (1987) · Zbl 0646.34019 [5] Pengyee, Lee, Lanzhou lectures on Henstock integration, (1989), World Scientific Singapore · Zbl 0699.26004 [6] Lee Pengyee, Generalized convergence theorems for Denjoy-Perron integral, in: P.S. Bullen et al. (Eds.), New Integrals, Lecture Notes in Math. vol. 1419, Springer, Berlin, 1990, pp. 97-109. [7] Luo Chengzhong, Wang Demu, Extension of the integral of interval-valued function and the integral of fuzzy-valued function, Fuzzy Math. 3 (1983) 45- (in chinese). · Zbl 0546.28005 [8] Ming, Ma, Embedding problem of fuzzy number spaces: part 4, Fuzzy sets and systems, 58, 185-193, (1993) · Zbl 0789.46069 [9] M. Matloka, On fuzzy integral, Proc. Polish Symp., Interval and Fuzzy Math. ’86, Poznan, 1986, pp. 163-170. · Zbl 0626.26012 [10] Nanda, S., On integration of fuzzy mapping, Fuzzy sets and systems, 32, 95-101, (1989) · Zbl 0671.28009 [11] Rudin, W., Functional analysis, (1973), McGraw-Hill New York · Zbl 0253.46001 [12] Wilansky, A., Modern methods in topological vector space, (1978), McGraw-Hill New York · Zbl 0395.46001 [13] Congxin, Wu; Ming, Ma, Embedding problem of fuzzy number spaces: part I, Fuzzy sets and systems, 44, 33-38, (1991) · Zbl 0757.46066 [14] Congxin, Wu; Ming, Ma, Embedding problem of fuzzy number spaces: part II, Fuzzy sets and systems, 45, 189-202, (1992) · Zbl 0771.46045 [15] Congxin, Wu; Xiaobo, Yao; Cao, S.S., The vector-valued integrals of Henstock and Denjoy, Sains malaysiana, 24, 4, 13-22, (1995) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.