Mehar ranking method for comparing connection numbers and its application in decision making

Kumar and Garg (Applied Intelligence, 2017, https://doi.org/10.1007/s10489-017-1067-0) pointed out the limitations of some existing methods for solving intuitionistic fuzzy multi-attribute decision-making (MADM) problems. Also, to overcome the limitations, Kumar and Garg proposed a connection number (CN) based method for solving intuitionistic fuzzy MADM problems. In this paper, it is shown that the ranking method, used in Step 5 of Kumar and Garg's method for comparing connection numbers (CNs), fails to compare two distinct CNs. Hence, Kumar and Garg's method fails to rank the alternatives of intuitionistic fuzzy MADM problems. Furthermore, to overcome the limitation of Kumar and Garg's method, a new ranking method (named as Mehar ranking method) is proposed for comparing CNs.