Transportation Problem in Neutrosophic Environment

Abstract

The transportation problem (TP) is popular in operation research due to its versatile applications in real life. Uncertainty exists in most of the real-life problems, which cause it laborious to find the cost (supply/demand) exactly. The fuzzy set is the well-known field for handling the uncertainty but has some limitations. For that reason, in this chapter introduces another set of values called neutrosophic set. It is a generalization of crisp sets, fuzzy set, and intuitionistic fuzzy set, which is handle the uncertain, unpredictable, and insufficient information in real-life problem. Here consider some neutrosophic sets of values for supply, demand, and cell cost. In this chapter, extension of linear programming principle, extension of north west principle, extension of Vogel's approximation method (VAM) principle, and extended principle of MODI method are used for solving the TP with neutrosophic environment called neutrosophic transportation problem (NTP), and these methods are compared using neutrosophic sets of value as well as a combination of neutrosophic and crisp value for analyzing the every real-life uncertain situation.