Personalized quantifier by Bernstein polynomials combined with interpolation spline

A new form of personalized quantifier is developed in this paper, with which to investigate and formalize people's personalities or behavior intentions that have to be considered in increasingly complex situations. As we show in the article, the developed quantifier is realized by generalized Bernstein polynomials combined with interpolation spline, and finally expressed as a sequence of piecewise nonlinear polynomials with an adjustable degree. It is characterized by many excellent properties exemplified by such terms as sufficient smoothness, shape‐preserving interpolation, and a high rate of convergence. In particular, the consistency of the ordered weighted averaging (OWA) aggregation under the guidance of the developed quantifier is addressed and proved. This actually provides a sound theoretical basis for practical use. We also experimentally show that the developed quantifier significantly outperforms, in all respects of geometrical characteristics, the other ones presented in previous work, whether from a viewpoint of global approximation of functions or local one. As such, the developed quantifier could be considered as an effective analytical tool for decision making under uncertainty in which different personality traits have to be taken into account.