Transportation problem with interval-valued intuitionistic fuzzy sets: impact of a new ranking

To address uncertainty and hesitation of a real-life problem, interval-valued intuitionistic fuzzy sets (IVIFSs) have received increasing interest among researchers and industrialists. In this paper, we present an advanced illustration of IVIFSs using physical distancing during COVID-19 to understand the deep concept of IVIFSs. Due to special feature of an IVIFSs, it finds a better decision of a real-life problem having uncertainty and hesitation. Here some important arithmetic operations between two IVIFSs are also stated. Ranking of IVIFSs is a valuable tool and it is not easy to rank due to its ill-defined membership and non-membership degrees, and same difficulties arise in a wide variety of real-life problems. To tackle these difficulties, we introduce a new ranking function of IVIFSs, and it follows well to the law of trichotomy. And for its superiority, we compare it with some existing ranking functions by taking a suitable example. Furthermore, its applicability are tested on the basis of an IVIFSs. Further, it is very interesting to note that some unpredicted factors such as road condition, diesel prices, traffic condition and weather condition affect to the cost of transportation, and therefore, decision makers encounter uncertainty and hesitation to estimate cost of transportation. To resolve such issues, we consider transportation problem with IVIFSs parameters, and for its solution, a simple computational method is developed and illustrated.