Solving Fuzzy Fractional Assignment Problem using Genetic Approach

• Published in: International journal of mathematical, engineering and management sciences Vol. 7; no. 4; pp. 589 - 602
• Main Authors: Buvaneshwari, T. K., Anuradha, D.
• Format: Journal Article
• Language: English
• Published: Dehradun International Journal of Mathematical, Engineering and Management Sciences 01.08.2022; Ram Arti Publishers
• Subjects: Assignment problem; efficient solutions; fractional assignment problem; fuzzy linear membership function; Fuzzy sets; Genetic algorithms; genetic approach; Mutation; optimal compromise solution; Random variables
• ISSN: 2455-7749; 2455-7749
• DOI: 10.33889/IJMEMS.2022.7.4.038

This manuscript highlights solving the fractional assignment problems (FAP) with parameters as triangular fuzzy numbers. The following is an explanation of the key contribution of the planned study. FAP is an AP with the ratio of objective functions. Of these objective functions, one objective function is minimization whereas the other function is maximization. Now, the fuzzy FAP is changed into a deterministic problem using the α-cut of fuzzy linear membership function on each parameter and then solved using a genetic algorithm (GA) procedure. The procedure so obtained is solved to obtain the set of efficient/non-efficient solutions and the optimal compromise solution. A numerical example is illustrated to explore the efficiency of our proposed genetic approach. A comparative study has been done between the proposed approach and the genetic algorithm tool (Matlab). This approach assists the decision-makers (DM) in selecting a preferred solution based on their economic level.