Revision of pattern recognition problems

Abstract

The purpose of this paper is threefold. First, we show that the first similarity measure of Zhang and Fu (2006) can solve the pattern recognition problem such that the challenge of Yusoff et al. (2011) is questionable. Second, we provide an analytical proof that inclusion relations for the extended membership and non-membership functions are preserved. Third, we provide a counter example to illustrate that the extended hesitancy was not preserved for the inclusion relation. Our findings will be contributed to future researchers for developing new similarity measures.