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 Recent Issues Online First Volume 1, Issue 1

### The Strong and Weak Solutions of Fuzzy Optimal Control Problem with State Conditions at the Final Time

Pages: 45 – 67

#### Authors

Altyeb Mohammed Mustafa, Zengtai Gong, Mawia Osman

#### Abstract

In this paper, with and without restrictions imposed on the fuzzy objective functional, we define two different types of fuzzy Hamiltonian function used together with the concepts of parameterizing the fuzzy valued function and its differentiation and integration by the left and right-hand functions of its $$\alpha$$-level set and fuzzy variational approaches to prove the necessary conditions for fuzzy optimal control problem with state conditions at the final time. In addition, we introduce the concepts of strong and weak solutions to our problem to guarantee that the optimal solutions are fuzzy functions. Three examples are given to illustrate our main results.

Full Text (PDF format)

Received: 18 February 2020; Accepted: 14 March 2020.