Multi-granulation Rough Sets and Uncertainty Measurement for Multi-source Fuzzy Information System

Abstract

Rough set theory is an effective mathematical tool to deal with uncertain information. With the arrival of the information age, we need to handle not only single-source data sets, but also multi-source data sets. In real life; most of the data we face are fuzzy multi-source data sets. However, the rough set model has not been found for multi-source fuzzy information systems. This paper aims to study how to use the rough set model in multi-source fuzzy environment. Firstly, we define a distance formula between two objects in an information table and further propose a tolerance relation through this formula. Secondly, the supporting characteristic function is proposed by the inclusion relation between tolerance classes and concept set X. And then, from the perspective of multi-granulation, each information source is regarded as a granularity. The optimistic, pessimistic, generalized multi-granulation rough set model and some important properties are discussed in multi-source fuzzy information systems. At the same time, the uncertainty measurement are considered for the different models. Finally, some experiments are carried out to interpret and evaluate the validity and significance of the approach.