An Algorithm for Solving Fully Fuzzy Rough Integer Transportation problems

Abstract

A suggested algorithm, for solving fully fuzzy rough integer transportation problems (FFRITPs), is introduced in order to find an optimal solution and optimal values cost where the supply and demand are balanced. In real-life situations, the parameters of a transportation problems model may not be defined precisely, because of the current market globalization and some other uncontrollable factors. By study a special cases when all parameters and decision variables in the constraints and the objective function are trapezoidal fuzzy rough number (TrFRN). The methodology of the solution depends on dividing this problem into six crisp problems, and then assemble the solutions to find the optimal solution for the original problem. Furthermore, the proposed algorithm enable us to search for the optimal solution in the largest range of possible solutions. The split and separation method can be served as an important tool for the decision makers when they are handling various types of logistic problems having trapezoidal fuzzy rough variable and parameters. [ In addition, the motivation behind this study is to enable the decision makers to make the right decision considering the proposed solutions, while dealing with the uncertain and imprecise data] Finally, the effectiveness of the proposed procedure is illustrated through numerical example.