Kaleva, Osmo Fuzzy differential equations. (English) Zbl 0646.34019 Fuzzy Sets Syst. 24, 301-317 (1987). A differential and integral calculus for fuzzy-set-valued mappings was developed in recent papers of Dubois and Prade, and Puri and Ralescu. The purpose of this paper is to study differential equations for fuzzy-set- valued mappings of a real variable whose values are normal, convex, upper semi-continuous and compactly supported fuzzy sets in \(R^ n\). The differentiability and integrability properties of such functions are studied and an existence and uniqueness theorem for a solution to a fuzzy differential equation is given. Reviewer: B.Rodriguez-Salinas Cited in 12 ReviewsCited in 605 Documents MSC: 34A99 General theory for ordinary differential equations Keywords:fuzzy-set-valued mappings × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Aumann, R. J., Integrals of set-valued functions, J. Math. Anal. Appl., 12, 1-12 (1965) · Zbl 0163.06301 [2] Berge, C., Escapes Topologiques; Fonctions Multivoques (1959), Dunod: Dunod Paris · Zbl 0088.14703 [3] Bradley, M.; Datko, R., Some analytic and measure theoretic properties of set-valued mappings, SIAM J. Control Optim., 15, 625-635 (1977) · Zbl 0354.28001 [4] Castaing, C.; Valadier, M., Convex Analysis and Measurable Multifunctions (1977), Springer: Springer Berlin · Zbl 0346.46038 [5] Debreu, G., Integration of correspondences, (Proc. Fifth Berkeley Symp. Math. Statist. Probab., Vol. 2 (1967), Univ. California Press: Univ. California Press Berkeley, CA), 351-372, Part 1 · Zbl 0211.52803 [6] Dubois, D.; Prade, H., Towards fuzzy differential calculus — Part 1, Fuzzy Sets and Systems, 8, 1-17 (1982) · Zbl 0493.28002 [7] Dubois, D.; Prade, H., Towards fuzzy differential calculus — Part 2, Fuzzy Sets and Systems, 8, 105-116 (1982) · Zbl 0493.28003 [8] Dubois, D.; Prade, H., Towards fuzzy differential calculus — Part 3, Fuzzy Sets and Systems, 8, 225-234 (1982) · Zbl 0499.28009 [9] Hukuhara, M., Integration des applications measurables dont la valeur est un compact convexe, Funkcialaj. Ekvacioj., 10, 205-223 (1967) · Zbl 0161.24701 [10] Kaleva, O., On the convergence of fuzzy sets, Fuzzy Sets and Systems, 17, 53-65 (1985) · Zbl 0584.54004 [11] McShane, E. J., Stochastic differential equations, J. Multivariate Anal., 5, 121-177 (1975) · Zbl 0323.60059 [12] Negoita, C. V.; Ralescu, D. A., Applications of Fuzzy Sets to Systems Analysis (1975), Wiley: Wiley New York · Zbl 0326.94002 [13] Nguyen, H. T., A note on the extension principle for fuzzy sets, J. Math. Anal. Appl., 64, 369-380 (1978) · Zbl 0377.04004 [14] Puri, M. L.; Ralescu, D. A., Differentials for fuzzy functions, J. Math. Anal. Appl., 91, 552-558 (1983) · Zbl 0528.54009 [15] Puri, M. L.; Ralescu, D. A., Fuzzy random variables, J. Math. Anal. Appl., 114, 409-422 (1986) · Zbl 0592.60004 [16] Royden, H. L., Real Analysis (1968), Macmillan: Macmillan London · Zbl 0197.03501 [17] Rådström, H., An embedding theorem for spaces of convex sets, (Proc. Amer. Math. Soc., 3 (1952)), 165-169 · Zbl 0046.33304 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.