Fuzzy logic in smart traffic management systems for cities or urban areas seems to be a really challenging subject to explore. But one such chapter here, integration of fuzzy logic within traffic control management systems certainly broadens its horizons. Increased rapid urban population growth has defined traffic congestion as a severe bottleneck for city planning and management. There exists overwhelming and increasing pressure on civil infrastructure and construction firms to prosper upon issues concerning the mobility within urban enclosed areas. This often leads to severe delayed cumulative negative implications both economically and psychologically within city populations. This paper bases itself with addressing difficulties of computer adjusting traffic signals or city traffic control management systems during or per each minute in zones of wide alternating flux while taking fuzzy logic principles into consideration. It attempts to find a solution to smart city system challenges like high traffic congestion, increasing air pollution by inefficient vehicle use and fast changing city environment. Severe underestimation of fuzziness that exists within human perception causes significant lapse, misconception, and wastage of time to design real adjustment techniques. Fuzzy logic based systems implement bespoke membership functions and inference rules to test, refine and investigate in real-time condition and scenario the dependence of traffic data, vehicle density, traffic speed, and other random external parameters. When fuzzy logic and modern internet connected computers and sensors are fused together smart traffic systems can significantly aid in automation of traffic control signals to allow or deny vehicles access to roads, increase these vehicles priority along with emergency vehicles during time periods of heavy congestion while keeping road safety. The aim of this paper is realization of fuzzy logic based traffic control management framework for minimizing the delay in traffic congestion whilst maximizing the value of truly constructive time. This paper also illustrates the value of fuzzy logic in addressing the shortcomings of conventional traffic management systems with predefined signal changing schedule and manual supervision. Furthermore, this study highlights the possible impediments to fuzzy logic systems such as data uncertainty, computational complexity, and scalability problems This paper presents urban traffic control fuzzy logic cases and simulations while forecasting AI and machine learning's future impact on modern traffic control system development.