Set-valued mapping and Rough Probability

TL;DR

This paper explores the concept of rough probability within stochastic approximation spaces, utilizing set-valued mappings to derive results on rough expectation and variance, advancing the theoretical framework of rough set theory.

Contribution

It introduces a novel approach to rough probability using set-valued mappings in stochastic spaces, extending the theoretical understanding of rough expectation and variance.

Findings

Derived formulas for rough expectation and variance

Extended rough probability theory using set-valued mappings

Provided new insights into stochastic approximation spaces

Abstract

In 1982, the theory of rough sets proposed by Pawlak and in 2013, Luay concerned a rough probability by using the notion of Topology. In this paper, we study the rough probability in the stochastic approximation spaces by using set-valued mapping and obtain results on rough expectation, and rough variance.