Abstract
This paper is a further extension for four papers, Zhang and Fu (2006, Pattern Recognition Letters 27, 1307-1317), Yusoff, Abdullah and Wahab (2011, International Journal of Computational and Mathematical Sciences 5 (2), 70-74), Lin (2014, International Journal of Information and Management Sciences 25, article in press) and Lin and Julian (Journal of Discrete Mathematical Sciences and Cryptography 2014, 17, article in press). The extended similarity measure is examined in detail to provide a new verification to prove the monotonic property is preserved.
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