Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations

摘要

In this paper, we initially present and compile the tools and theories that are necessary for a Rough Set analysis of a general type of fuzzy data. From this study, we have developed two original contributions that can enhance the application of Fuzzy Rough Sets techniques to data that may be affected by several sources of uncertainty in its measurement process. For this type of analysis, we have first considered the construction of homogeneous granules in which reflexivity, symmetry and a certain transitivity property are satisfied. This has encouraged us to study the application of T-similarity relations in this framework and to examine the available theorems that permit us to aggregate this type of relations. As a part of this study, we have also developed a new theorem that allows us to use the dual of the generalized means as an aggregation operator in the Fuzzy Rough Sets context. Another theoretical development that tries to respond to a practical problem is the concept of β-precision aggregation. We use this new notion to export Ziarko's Variable Precision Rough Set model to the analysis of fuzzy data, a generalization that becomes a necessity for the Fuzzy Rough Sets analysis of large databases. The utility of this approach is demonstrated with an application example in the Vehicle database donated by the Turing Institute.