A Possibilistic Approach of the Max-Product Bernstein Kind Operators

作者：Gal Sorin G^*

来源：Results in Mathematics, 2014, 65(3-4): 453-462.

DOI：10.1007/s00025-013-0357-z

• Approximation by max-product Bernstein kind operator
• theory of possibility
• possibility distribution
• Chebyshev type inequality

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.

• 出版日期2014-6