Applications of quantitative methods, which had been explicit attention during previous period (the last two centuries) is the method of application sales man or traveling salesman method. According to this interest by the actual need for a lot of the production sectors and companies that distribute their products, whether locally made or the imported for customers or other industry sectors where most of the productive sectors and companies distributed always aspired to (increase profits, imports, the production quantity, quantity of exports. etc. ...) this is the part of the other hand, want to behave during the process of distribution routes that achieve the best or the least or most appropriate.
The research aims to build a mathematical model to the Traveling salesman problem Fuzzy multi-objective describes the problem of transportation of flour from one of Mills General Company for the manufacture of grain to some Baghdad areas and solving model using the mathematical methods applied to solve the model to access the desired goal in determining the best path that achieves the shortest path and The least cost and fastest way to transport flour from the mill to the distribution areas to be selected on the basis of representation of the problem is achieved by all the terms of mathematical model proposed in Method a Traveling salesman problem (TSP) fuzzy multi-objective and through the use of two methods to solve of fuzzy multi-objective linear programming (FMOLP) and Intuitionists fuzzy optimization(IFO) in solving the problem of Traveling salesman problem(TSP) multi- objective under the fuzzy environment , For the purpose of determining the best method to solve the used to solve problem of the research has been selected to solve the two methods to compare their results with the path being followed by the actual transporters currently, as well as comparative optimal solutions for normal data(non-pure),With the adoption of the proposed method in determining the values of function pointers fuzzy used in solution the model and these indicators are an indicator of the level of acceptance in allowing or what is termed tolerances level of acceptance as well as aspiration levels and level of rejection tolerances.
