Abstract: The assignment problem is a great topic and frequently used in engineering and management sciences. In this problem, indicates the cost of assigning the ith person to a jth job. In this paper, ̃ denotes fuzzy assignment problem, Intuitionistic assignment problem, and Neutrosophic assignment problem by using Nonagonal fuzzy numbers, which are more logical and standardly in nature. Here, we proposed three different algorithms for finding optimal solution to the assignment problem. Finally, comparing all the results with an illustrative example.