Embedding problem of fuzzy number space. II. (English) Zbl 0771.46045
Summary: Using a concrete structure into which we embed the fuzzy number space \(E^ 1\), several necessary and sufficient conditions of fuzzy set valued functions are given by means of abstract function theory. [For part I see ibid. 44, No. 1, 33-38 (1991; Zbl 0757.46066)].
MSC:
| 46S40 | Fuzzy functional analysis |
| 26E50 | Fuzzy real analysis |
| 47S40 | Fuzzy operator theory |
| 47H04 | Set-valued operators |
Keywords:
embedding problem; fuzzy number space; fuzzy set valued functions; abstract function theoryCitations:
Zbl 0757.46066References:
| [1] | Bergström, H., Weak Convergence of Measures (1982), Academic Press: Academic Press New York · Zbl 0538.28003 |
| [2] | Castaing, C.; Valadier, M., Convex Analysis and Measurable Multifunction (1977), Springer-Verlag: Springer-Verlag Berlin · Zbl 0346.46038 |
| [3] | Goetschel, R.; Voxman, W., Elementary fuzzy calculus, Fuzzy Sets and Systems, 18, 31-43 (1986) · Zbl 0626.26014 |
| [4] | Hille, E.; Phillips, R. S., Functional analysis and semi-groups, (American Mathematical Society Colloquium, Vol. 31 (1957)) · Zbl 0078.10004 |
| [5] | Kaleva, O., Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301-317 (1987) · Zbl 0646.34019 |
| [6] | Kaleva, O., The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35, 389-396 (1990) · Zbl 0696.34005 |
| [7] | Klambauer, G., Mathematical Analysis (1975), Marcel Dekker: Marcel Dekker New York · Zbl 0317.26001 |
| [8] | Tiefu, Liu, On linear operators from \(D\)[0,1] to a Banach space \(E\), J. Math., 8, 106-112 (1988) · Zbl 0712.47030 |
| [9] | Matłoka, M., On fuzzy integrals, (Albrycht, J.; Wisnieski, H., Proceedings of Second Polish Symposium on Interval and Fuzzy Mathematics (1987), Politechnika Poznansk: Politechnika Poznansk Poznan), 163-170 · Zbl 0642.26015 |
| [10] | Nguyen, H. T., A note on the extension principle for fuzzy sets, J. Math. Anal. Appl., 64, 369-380 (1978) · Zbl 0377.04004 |
| [11] | Puri, M. L.; Ralescu, D. A., Differential for fuzzy functions, J. Math. Anal. Appl., 91, 552-558 (1983) · Zbl 0528.54009 |
| [12] | Puri, M. L.; Ralescu, D. A., Fuzzy random variables, J. Math. Anal. Appl., 114, 409-422 (1986) · Zbl 0592.60004 |
| [13] | Riesz, F.; Nagy, B. S.Z., Leçons d’Analyse Fonctionnelle (1955), Akademiai Kiado: Akademiai Kiado Budapest · Zbl 0064.35404 |
| [14] | Wilianski, A., Modern Methods in Topological Vector Spaces (1978), McGraw-Hill: McGraw-Hill New York · Zbl 0395.46001 |
| [15] | Congxin, Wu; Ming, Ma, An embedding operator for fuzzy number space \(E^1\) and its applications for fuzzy integrals, (Third Congress of IFSA. Third Congress of IFSA, Seattle (1989)) · Zbl 0734.28020 |
| [16] | Congxin, Wu; Ming, Ma, On embedding problem of fuzzy number space; Part I, Fuzzy Sets and Systems, 44, 33-38 (1991) · Zbl 0757.46066 |
| [17] | Congxin, Wu; Linsheng, Zhao; Tiefu, Liu, Bounded Variation Functions — Their Generalizations and Applications (1988), Hei-longjiang Scientific Publishing House: Hei-longjiang Scientific Publishing House Harbin |
| [18] | Gohman, E. K., Integral Stibtbesu i ego Prilozheniya (1958), Moscow |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
