A Mathematical Extension Of Rough Set-Based Issues Toward Uncertain Information Analysis

Rough set theory was originally proposed for analyzing data gathered in data tables, often referred to as information systems. The lower and upper approximations introduced within this theory are known as the very useful concepts. The theory as a whole now becomes a recognized foundation for granular computing. This paper investigates the rough set-based issues for analyzing table data with uncertainty. In reality, tables with non-deterministic information are focused on instead of tables with deterministic information, and several mathematical properties are examined. Especially, decision rule generation from tables with non-deterministic information is highlighted. This investigation is also applied to tables with uncertain numerical data. As a result, a new mathematical framework for analyzing tables with uncertain information is formalized.