## On integration of fuzzy mappings.(English)Zbl 0671.28009

Summary: We introduce the concept of an integral of a fuzzy mapping. This generalizes the integral introduced by Matłoka and also extends Riemann-Stieltjes integral over a closed interval to fuzzy mappings.

### MSC:

 2.8e+11 Fuzzy measure theory 3e+72 Theory of fuzzy sets, etc.
Full Text:

### References:

 [1] Aumann, R.J., Integrals of set valued functions, J. math. anal. appl., 12, 1-12, (1965) · Zbl 0163.06301 [2] Debreu, G., Integration of correspondences, (), 351-372 · Zbl 0211.52803 [3] Debreu, G.; Schmeidler, D., The Radon-Nikodym derivation of a correspondence, (), 41-56 [4] Dubois, D.; Prade, H., Towards fuzzy differential calculus, part 1: integration of fuzzy mappings, Fuzzy sets and systems, 8, 1-17, (1982) · Zbl 0493.28002 [5] Dubois, D.; Prade, H., Towards fuzzy differential calculus, part 2: integration on fuzzy intervals, Fuzzy sets and systems, 8, 105-116, (1982) · Zbl 0493.28003 [6] Suarez Garcia, F.; Gil Alvarez, P., Two families of fuzzy integrals, Fuzzy sets and system, 18, 67-81, (1986) · Zbl 0595.28011 [7] Hildenbrandt, W., Existence of equilibria for economies with production and a measure space of consumers, Econometrica, 38, 608-623, (1970) · Zbl 0208.23203 [8] Kaleva, O., A differential and integral calculus for fuzzy mappings and fuzzy differential equations, Report 48 of Tampere university of technology, (1984), Tampere [9] Klement, E.P., Some relations between integration on fuzzy sets and fuzzy measures, () · Zbl 0491.28005 [10] M. Matłoka, Integration of fuzzy mappings, Private communication. · Zbl 0788.28012 [11] Ralescu, D.A., Integration on fuzzy sets, (1979), Indian University Bloomington, IN [12] Renming, Song, On the (N) fuzzy interval, Fuzzy math., 3, 91-106, (1985) · Zbl 0641.28014 [13] Rudin, W., Principles of mathematical analysis, (1976), McGraw-Hill New York · Zbl 0148.02903 [14] Ru-huai, Zhao, The (N) fuzzy integral, J. math. res. and exposition, 1, 37-44, (1981) [15] Schmeidler, D., Fatou’s lemma in several dimensions, (), 1-5 · Zbl 0187.31403 [16] Sugeno, M., Theory of fuzzy integrals and its applications, () · Zbl 0316.60005 [17] Zi-Xiao, Wang, Fuzzy measures and measures of fuzziness, J. math. anal. appl., 104, 589-601, (1984) · Zbl 0597.28011 [18] Yager, R.R., A note on probabilities of fuzzy events, Inform. sci., 18, 113-129, (1979) · Zbl 0438.60006 [19] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
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.