Quantifiers induced by subjective expected value of sample information with Bernstein polynomials

Abstract

A kind of personalized quantifier, the so-called SEVSI-induced quantifier as an acronym for Subjective Expected Value of Sample Information, is developed in this paper by introducing Bernstein polynomials of higher degree. This allows us to provide a novel solution to improve the final representation of the quantifier that generally performed poorly in our previous work, thus enhancing the quality of global approximation of functions and improving the operability of this kind of quantifier for practical use. We show some properties of the developed quantifier. We also prove the consistency of the OWA aggregation under the guidance of this type of quantifier. Finally, we experimentally show that the developed quantifier outperforms the one with the piecewise linear interpolation in many aspects of geometrical characteristics and operability. Thus it could be considered as an effective analytical tool to help handle the complex cases involving people's personalities or behavior intentions that have to be considered in decision making under uncertainty.