Assignment problem (AP) is an entrenched tool for solving engineering and management problems. &e Hungarian method is always used to fathom the AP in crisp cases. &is paper presents an algorithm of finding the optimum solution of the fuzzy AP by using the modified Hungarian method. &is method is utilized to get a minimum assignment cost in the fuzzy environment for a fuzzy AP. Firstly, we use the fuzzy numbers without any transformation. Secondly, the fuzzy AP is transformed into an interval AP based on the α-cut methodology. &en, the interval arithmetic operations and the order relations are applied to get the optimal solution by utilizing the modified Hungarian method. &e proposed algorithm requires less efforts and time to reach optimality, compared to the existing methods. Numerical examples are given to ensure the efficiency and the validity of the proposed algorithm. A study on the reuse of many valuable buildings is presented after using different government and service buildings in a manner that does not fit with its original function and heritage value. We offer a solution based on the scientific and realistic basis for requalification according to the variables and requirements of the social, cultural, and economic environments in the environment surrounding the valuable buildings.