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Solving Fuzzy Assignment Problem using Ranking of Generalized Trapezoidal Fuzzy Numbers

Affiliations

  • Department of Mathematics, Jeppiaar Engineering College, Chennai - 600119, India
  • Department of Mathematics, A. M. Jain College, Chennai - 600114, India

Abstract


Background/Objectives: The fuzzy optimal solution is totally based on ranking or comparing fuzzy numbers. Ranking fuzzy numbers play an vital role in decision making problems, data analysis and socio economics systems. The aim is to optimize the total cost of assigning all the jobs to the available persons. Ranking fuzzy number offers an powerful tool for handling fuzzy assignment problems. Methods/Statistical analysis: In this paper we used Hungarian method for solving fuzzy assignment problems using generalized trapezoidal fuzzy numbers. By using the ranking procedure we convert the fuzzy assignment problem to a crisp value assignment problem which then can be solved using Hungarian Method to find the fuzzy optimal solution. We presented the method which is not only simple in calculation but also gives better approximation and satisfactory results which is illustrated through the numerical examples. Findings: We propose a new ranking method which discriminates the fuzzy numbers where as few of the existing method fails to discriminates the fuzzy numbers. This method ranks all types of fuzzy numbers i.e. normal and generalized fuzzy numbers. Both triangular and trapezoidal fuzzy numbers). It is evident from the numerical examples that the proposed ranking measure for a fuzzy assignment problem is easy to compute and cost effective and gives much more optimal value. Applications/Improvements: The proposed ranking procedure can be applied in various decision making problems. This ranking method could also be used to solve other types of problems like game theory, project schedules, transportation problems.

Keywords

Fuzzy Assignment Problem, Ranking Function, Trapezoidal Fuzzy Numbers.

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References


  • Zadeh LA. Fuzzy sets. Information and Control. 1965; 8:338-53.
  • Bortolan G, Degani R. A review of some methods for ranking fuzzy subsets. Fuzzy Set and Systems. 1985; 15:1-19.
  • Chen SJ, Hwang CL. Fuzzy multiple attribute decision making. Berlin: Springer; 1992.
  • Jain R. Decision making in the presence of fuzzy variables. IEEE Transactions on Systems. Man and Cybernetics. 1976; 6:698-703.
  • Lee LW, Chen SM. Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations. Experts Systems with Applications. 2008; 34:2763-71.
  • Phani Bushan Rao P, Ravishankar N. Ranking fuzzy numbers with a distance method using circumcenter of centroids and an Index of Modality. Advances in Fuzzy System. 2011; 10:1155-61.
  • Valvis E. A new linear ordering of fuzzy numbers on subsets of F(R). Fuzzy Optimization and Decision Making. 2009; 8:141-63.
  • Wang YJ, Lee HS. The revised method of ranking fuzzy numbers with an area between the centroid and original points. Computer and Mathematics with Applications. 2008; 55:2033-42.
  • Nirmala G, Anju R. Cost Minimization assignment problem using fuzzy quantifier. International Journal of Computer Science and Information Technologies. 2014; 5:7948-50.
  • Yager RR. A procedure for ordering fuzzy subsets of the unit interval. Information Sciences. 1981; 24:143-61.

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