Generalised approximate equalities based on rough fuzzy sets & rough measures of fuzzy sets

In an attempt to incorporate user knowledge in order to decide about the equality of sets, the concepts of approximate equalities using rough sets were introduced. These notions have been generalised in several ways and very recently [1] extended four types of approximate equalities using rough fuzzy sets instead of only rough sets. To be precise, a concept of leveled approximate equality was introduced and properties were studied. In this paper we extend this work with case studies to illustrate the applications of the concepts and compare them respectively. We also introduce and discuss the rough measures of basic sets, fuzzy sets and interpret four types of approximate equalities in terms of the accuracy measure as well as rough measures. The analysis had provided a clear distinguish notion in terms of the measures.