Assignment problem (AP) is an entrenched tool for solving engineering and management problems. The Hungarian method is always used to fathom the AP in crisp cases. This paper presents an algorithm of finding the optimum solution of the fuzzy AP by using the modified Hungarian method. This 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 -cut methodology. Then, the interval arithmetic operations and the order relations are applied to get the optimal solution by utilizing the modified Hungarian method. The 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.

中文翻译：

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使用匈牙利方法中的区间运算解决模糊分配问题及其在埃及有价房屋修复中的应用

分配问题（AP）是解决工程和管理问题的根深蒂固的工具。在脆弱的情况下，始终使用匈牙利方法来找出AP。本文提出了一种使用改进的匈牙利方法寻找模糊AP最优解的算法。该方法用于在模糊环境中获得模糊AP的最小分配成本。首先，我们使用模糊数而不进行任何变换。其次，基于-将模糊AP转换为区间AP削减方法。然后，利用改进的匈牙利方法，应用区间算术运算和阶数关系来获得最佳解。与现有方法相比，所提出的算法需要更少的精力和时间来达到最优。数值例子说明了所提算法的有效性和有效性。在使用不同的政府和服务性建筑物后，提出了许多有价值的建筑物的再利用研究，但这些方法不符合其原始功能和遗产价值。我们根据珍贵建筑物周围环境中的社会，文化和经济环境的变量和要求，在科学和现实的基础上提供重新认证的解决方案。