A Possibilistic Approach of the Max-Product Bernstein Kind Operators

By analogy with the probabilistic approach of the classical Bernstein polynomials, in this paper firstly we give the proof for the uniform convergence of the nonlinear max-product Bernstein operator by using the theory of possibility. This new approach, which interprets the max-product Bernstein operator as a possibilistic expectation of a particular fuzzy variable having a possibilistic Bernoulli distribution, does not only offer a good justification for the max-product Bernstein operator, but also allows to extend the method to other discrete max-product Bernstein type operators.