PG & Research Department of Mathematics, Holy Cross College(Autonomous) Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu.
This paper focuses a multi-objective fractional transportation problem based on dual hesitant fuzzy numbers. The traditional fuzzy set deals with the single membership value to express vagueness of an element. It is not applicable to give several possible membership values at the same time. The hesitant fuzzy set provides the better way to overcome these uncertainties by giving the several possible membership degrees to single element. The mathematical model of dual hesitant multi objective fractional transportation problem is formulated. A new method is proposed to solve dual hesitant multi objective fractional transportation problem with non-linear discount cost. The aim of this proposed method to optimize the ratios of the objective functions with non-linear discount cost. A numerical example is shown to check the effectiveness of the proposed method.