Dialectics of Counting and Measures of Rough Theories

TL;DR

This paper introduces new rough natural number systems to enhance measures in Rough Set theory and reduces dependence on prior axiomatic frameworks, providing improved results and representations.

Contribution

It presents novel rough natural number systems that improve measures in Rough Set theory and minimizes reliance on previous axiomatic assumptions.

Findings

Enhanced measures of rough sets and multiple knowledge models.

Reduced dependence on axiomatic granule theory.

New results on number representation and measures.

Abstract

New concepts of rough natural number systems, recently introduced by the present author, are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and measures of mutual consistency of multiple models of knowledge. In this research paper, the explicit dependence on the axiomatic theory of granules of \cite{AM99} is reduced and more results on the measures and representation of the numbers are proved.