Vol.4, No 16, 2004 pp. 1-10
UDC 517.9(045)
Invited Paper

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THE CONNECTION BETWEEN SET AND FUZZY DIFFERENTIAL EQUATIONS
V. Lakshmikantham
Dept. of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL. 32901, USA

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Abstract. The study of fuzzy differential equations (FDEs) forms a suitable setting for mathematical modeling of real world problems in which uncertainties or vagueness pervades. In recent years, the theory of FDEs has been investigated extensively in the original formulation as well as in an alternative framework, which leads to ordinary multivalued differential inclusions. It has recently been realized that initiating the study of set differential equations in a metric space has several advantages, in addition to providing a natural setting for considering FDEs. In this talk, we present some interesting results in this direction with the necessary background material.
Key words: Set differential equations, fuzzy differential equations

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VEZA IZMEDJU SKUPA I FAZI DIFERENCIJALNIH JEDNAČINA Proučavanje fazi diferencijalnih jednačina (FDE) formira odgovarajuće okruženje praktičnih problema koji su prožeti neizvesnošću i nejasnoćama. Proteklih godina, teorija FDE je opširno proučavana u originalnoj formulaciji kao i u alternativnom okviru, što vodi ka običnom ubrajanju diferencijalnih višestrukih vrednosti. Nedavno se došlo do zaključka da uvodjenje proučavanja skupa diferencijalnih jednačina u metričkom prostoru ima nekoliko prednosti uz stvaranje prirodnog okruženja za proučavanje FDE. U ovom radu se predstavljaju zanimljivi rezultati u ovom pravcu uz neophodan materijal.
Ključne reči: skup diferencijalnih jednačina, fazi diferencijalne jednačine.