“…IFS has been found to be more useful to deal with vagueness and uncertainty than fuzzy set. Over the last decades, many researchers have investigated the IFS theory and applied it to various fields, including decision making [7,10,23,25,26,35,37,44,49,50,[56][57][58][59]61], logic programming [6], medical diagnosis [14,51,55], pattern recognition [29,31,34,36,39,41,52,54,64], robotic systems [24], and fuzzy topology [1,12,33,38,46,47], etc. Atanassov and Gargov [5] further generalized IFS in the spirit of ordinary interval-valued fuzzy sets and defined the notion of interval-valued intuitionistic fuzzy set (IVIFS).…”