Study on similarity measure for overlapped and non-overlapped data

The analysis on similarity measure considering fuzzy sets (FSs) for the case of non-overlapped data is done in this work. Similarity measure on overlapped case was not adequate due to inconsistencies for non-overlapped data in terms of similarity calculation. Hence, another similarity was proposed and this is proven by neighbor data information. With artificial data, the rational calculation results are obtained. Additionally, similarity analysis on extension of FSs to intuitionistic fuzzy sets (IFSs) is carried out. IFSs contain uncertainty known as hesitance, which is contained in fuzzy membership function itself. In comparison of similarity measure to FSs and IFSs, the upper bound of IFSs similarity measure was also obtained.