Hesitant fuzzy set is extremely useful performance to express people's uncertainty. But there are delicate points in conventional hesitant fuzzy set, which articulated the membershipdegrees of an element to a given set only by some crisp numbers .Hesitant fuzzy set to Triangular Fuzzy Hesitant Fuzzy Set (THFS), in which the membership degreeof an element to a given set is expressed by several possible triangular fuzzy numbers. A new plan to determine the critical path in the project network using Triangular Hesitant Fuzzy set (THF).In this project network Each activity time is THFS.One of multicriteriadecision making Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used for the project network to identify the best path in the project.Finally a numerical exemplar is furnished to elucidate the critical path of the project network
