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Controlled Fuzzy Evolution Equations

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Recent Advances in Intuitionistic Fuzzy Logic Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 372))

Abstract

This paper is concerned with controlled fuzzy nonlinear evolution equations of the form

$$\begin{aligned} u'(t) = A\,u(t) + f\Big ( t,u(t),u(\rho (t)) \Big )+B(t)c(t),\quad t\in [t_0,t_1] ; \quad u(t_0) = u_{0}. \end{aligned}$$

Where \(c(t)\in E^1\) is a control, A generate a fuzzy semigroup and \(B:[t_0,t_1]\longrightarrow \mathscr {L}(E^1)\). We use the fuzzy strongly continuous semigroups theory to prove the existence, uniqueness and some properties of mild solutions.

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Authors and Affiliations

  1. Sultan Moulay Slimane University, BP 523, Beni Mellal, Morocco

    Said Melliani, A. El Allaoui & L. S. Chadli

Authors
  1. Said Melliani
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  2. A. El Allaoui
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  3. L. S. Chadli
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Corresponding author

Correspondence to Said Melliani .

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Editors and Affiliations

  1. Department of Mathematics, Université Sultan Moulay Slimane, Beni Mellal, Morocco

    Said Melliani

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

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Melliani, S., El Allaoui, A., Chadli, L.S. (2019). Controlled Fuzzy Evolution Equations. In: Melliani, S., Castillo, O. (eds) Recent Advances in Intuitionistic Fuzzy Logic Systems. Studies in Fuzziness and Soft Computing, vol 372. Springer, Cham. https://doi.org/10.1007/978-3-030-02155-9_10

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