Discussion for extended similarity measures

Abstract

In this paper, we show that the first similarity measure of Zhang and Fu (2006) can solve the pattern recognition problem that was proposed by Yusoff et al. (2011) to challenge Zhang and Fu (2006). We also provide an analytical prove to verify that the inclusion relations are preserved for the extended membership function and non-membership functions. At last, we provide a counter example to illustrate that the extended hesitancy does not preserve the inclusion relation. Our findings will provide future researchers to develop new similarity measures.

Subject Classification:

• 03C13

Keywords:

• Pattern recognition
• Intuitionistic fuzzy sets (IFSs)
• Similarity measures