Fuzzy q-Bernstein polynomials

In this note, we give the definition of the fuzzy q-Bernstein polynomials and discuss their properties. We obtain the approximation rate of the fuzzy q-Bernstein polynomials and the fuzzy limit q-Bernstein operators. We show that the fuzzy q-Bernstein polynomials have the shape-preserving properties. We also obtain the convergence rate of the fuzzy q-Bernstein polynomials for fixed q ∈ (0, 1). The surprising fact is that we can transfer results of q-Bernstein polynomials in the case q ∈ (0, 1) into the fuzzy setting.

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