Solution of Fuzzy Maximal Flow Problems of Vehicles in Province of Diwaniyah Using the Ranking Function for Fuzzy Linear Programming Model

Abstract

The traffic jams taking place in the cities of the Republic of Iraq in general and the province of Diwaniyah especially, causes return to the large numbers of the modern vehicles that have been imported in the last ten years and the lack of omission for old vehicles in the province, resulting in the accumulation of a large number of vehicles that exceed the capacity of the city's streets, all these reasons combined led to traffic congestion clear at the time of the beginning of work in the morning, So researchers chose local area network of the main roads of the province of Diwaniyah, which is considered the most important in terms of traffic congestion, it was identified fuzzy numbers for vehicles flowing at the time of the beginning of work in the morning for paths of this network as the trapezoidal fuzzy numbers. The objective of this study is to find the fuzzy optimal solution of fuzzy max flow problems for number of vehicles which flowing at the beginning of work per day by using mathematical and quantitative methods as a method of fuzzy max flow problems to clarify the fuzzy numbers for vehicles flowing at the beginning of work in the morning for all paths of this network also a method of fuzzy linear programming was used for building the fuzzy linear programming model of fuzzy max flow problems, finally Ranking function and arithmetic operations were used for defuzzification the building model.