Using Interval Operations in the Hungarian Method to Solve the Fuzzy Assignment Problem and Its Application in the Rehabilitation Problem of Valuable Buildings in Egypt

Abstract

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 α-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.

A supply risk perspective integrated sustainable supplier selection model in the intuitionistic fuzzy environment

“…They considered the decision-making process for reducing a set of all suppliers to a smaller set of eligible suppliers. Elsisy et al ( 2020 ) presented a new algorithm for finding the optimum solution of the fuzzy assignment problem applying the Hungarian method, and it showed high efficiency through the practice in reuse of valuable buildings in Egypt. Assisting the DM to dissect the situations of uncertain judgment, El Sayed et al ( 2022 ) proposed a new approach that can directly capture uncertainty aspects.…”

An Educative Approach to Booth Assignment for a School Carnival

“…The problem stated above forms a special case of the generalized assignment problem (GAP) [1,2,[4][5][6][7][8][9], which is concerned with combinatorial optimization [10,11]. One of the most challenging issues in combinatorial optimization is to effectively deal with the combinatorial explosion [10,11].…”

One’s Fixing Method for a Distinct Symmetric Fuzzy Assignment Model

“…(5, 6, 7, 7), (4,5,6,6) (0, 1, 2, 2), (−1, 0, 1, 1) (3,5,6,6), (2,4,5,5) (5,8,9,9), (4,7,8,8) (12,15,16,16), (11,14,15,15) (7,9,10,10), (6,8,9,9) (5, 7, 8, 8), (4,6,7,7) (1,5,6,6), (0, 4, 5, 5)…”

“…Ref. [5] established a modified Hungarian method-based algorithm for identifying the best fuzzy AP solution presented. For a fuzzy AP, this approach is used to determine the lowest assignment cost possible.…”