A note on "Transportation problem under interval-valued intuitionistic fuzzy environment".

Bharti and Singh (International Journal of Fuzzy Systems 20 (2018), 1511-1522) proposed a method for solving a special type of interval-valued intuitionistic fuzzy transportation problems (IVIF-TPs) (transportation problems (TPs) in which the quantity of the product to be supplied is represented as a real number, whereas, all the other parameters are represented as interval-valued triangular intuitionistic fuzzy numbers (IVTIFNs)). In this note, an interval-valued intuitionistic fuzzy transportation problem (IVIF-TP) is solved by Bharti and Singh's method and shown that more than one IVTIFNs, representing the optimal interval-valued intuitionistic fuzzy (IVIF) transportation cost is obtained, which is mathematically incorrect as the obtained distinct IVTIFNs has different physical meanings. Also, it is pointed out that to resolve this flaw of Bharti and Singh's method may be considered as a challenging open research problem.