Total views : 92

A New Solution Approach to Solve Fuzzy Assignment Problems


  • Department of Mathematics, Faculty of Science and Humanities, SRM University, Kattankulathur, Chennai - 603203, Tamil Nadu, India


Objectives: To provide a method to solve a fuzzy assignment with out sacrificing its nature. Findings: Another technique is proposed to find the fuzzy optimal arrangement for assignment problems with triangular fuzzy numbers. We create fuzzy adaptation of Hungarian algorithm for the arrangement of fuzzy assignment problems without changing over them to established pro- portional. The proposed strategy is straightforward and to apply for discovering arrangement of fuzzy assignment problems happening, all things considered, circumstances. To outline the proposed technique cases are given and the got results.


Fuzzy Sets,Fuzzy Numbers, fuzzy Assignment Problem, Fuzzy Ranking, Fuzzy Arithmetic, Triangular Fuzzy Number

Full Text:

 |  (PDF views: 122)


  • Amphora R, Bhatia HL, Puri MC. Bi-criteria assignment problem. Opsearch. 1982; 19:8496.
  • Anzai Y. On integer fractional programming J. Operation.Res. Soc. Japan. 1974; 17:4966.
  • Balinski ML, Gomory RE. A primal method for the assignment and transportation problems. Management Sci. 1964; 10:578593.
  • Bellman RE, Zadeh LA. Decision making in a fuzzy environment.Management Sci. 1970; 17(4):141164. Crossref
  • Chanas S, Kuchta D. A concept of the optimal solution of the transportation problem with fuzzy cost. Fuzzy Sets and Systems. 1996; 82:299305. Crossref
  • Chanas S, Kolodziejczyk W, Machai A. A Fuzzy approach to the transportation problem. Fuzzy Sets and Systems. 1984; 13: 211–21. Crossref
  • Chanas S, Kuchta D. Fuzzy integer transportation problem.Fuzzy Sets and Systems. 1998; 98:291–8. Crossref
  • Chen MS. On a fuzzy assignment problem. Tamkang Journal of Mathematics. 1985; 22:407–11.
  • Chi-Jen L, Ue-pyng W. A labeling algorithm for the fuzzy assignment problem. Fuzzy Sets and Systems. 2004; 142:373–9. Crossref
  • Dubois D, Prade H. Fuzzy Sets and Systems: Theory and Applications. New York: Academic Press; 1980. [11] Dubois D, Fortemps P. Computing improved optimal solutions to max-min flexible constraint satisfaction problems. European J. Operations Research. 1999; 118:95–126. Crossref
  • Ganesan K, Veeramani P. On Arithmetic Operations of Interval Numbers. International Journal of Uncertainty, Fuzziness and Knowledge - Based Systems. 2005; 13(6):619– 31. Crossref
  • Ganesan K, Veeramani P. Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers. Annals of Operations Research. 2006; 143:305–15. Crossref
  • Gillett BE. Introduction to Operations Research-A Computer - Oriented Algorithm Approach. New York: McGraw-Hill; 1976. PMCid:PMC1687636
  • Haken H, Schanz M, Starke J. Treatment of combinatorial optimization problems using selection equations with costterms. Part Two-dimensional assignment problems Physica D. 1999; 134:227–41. Crossref
  • Long-Sheng H, Li-Pu Z. Solution method for Fuzzy Assignment problem with Restriction of Qualification.Proceedings of the Sixth International Conference on Intelligent Systems De- sign and Applications, ISDA06, 2006.
  • Kalaiarasi K, Sindhu S, Arunadevi M. Optimization of fuzzy assignment model with triangular fuzzy numbers using Ro- bust Ranking technique. International Journal of Innovative Science, Engg. Technology. 2014; 1:10–5.
  • Kaucher E. Interval analysis in extended interval space IR.Comput. Suppl. 1980; 2:3349. Crossref
  • Kuhn HW. The Hungarian method for the assignment problem Naval Res. Logistic. Quart. 1956; 2:8397.
  • Kumar A, Gupta A. Methods for solving fuzzy assignment problems and fuzzy traveling salesman problems with different membership functions. Fuzzy Information and Engineering. 2011; 3:332–5. Crossref
  • Kumar A, Gupta A, Kaur A. Methods for solving fully fuzzy assignment problems using triangular fuzzy numbers. World Academy of Science, Engineering and Technology. 2009; 3:968–71.
  • Kumar A, Kaur J, Singh P. A new method for solving fully fuzzy linear programming problems. Appl. Math. Model. 2011; 35:817–23. Crossref
  • Li L, Lai KK. A fuzzy approach to the multi objective transportation problem. Comput. Oper. Res. 2000; 27:4357. Crossref
  • Malhotra R, Bhatia HL, Puri MC. Bi-criteria assignment problem. Opsearch. 1982; 19:8496.
  • Nirmala T, Datta D, Kushwaha HS, Ganesan K. Inverse Interval Matrix: A New Approach. Applied Mathematical Sciences. 2011; 5(13):607–24.
  • Ramesh G, Ganesan K. Interval Linear Programming with generalized interval arithmetic. International Journal of Scientific and Engineering Research. 2011; 2(11).
  • Sakawa M, Nishizaki I, Uemura Y. Interactive fuzzy programming for two level linear and linear fractional production and assignment problems: a case study. European J.Oper.Res. 2001; 135:142–57 Crossref
  • Sangeetha K, Begum HH, Pavithra M. Ranking of triangular fuzzy number method to solve an unbalancedassignment problem. Journal of Global Research in Mathematical Archives. 2015; 2(8):6–11.
  • Mukherjee S, Basu K. A More Realistic Assignment Problem with Fuzzy Costs and Fuzzy Restrictions. Advances in Fuzzy Mathematics. 2010; 5(3):395–404.
  • Oh ML, Eigeartaigh L. A fuzzy transportation algorithm.Fuzzy Sets and Systems. 1982; 8:235–43. Crossref
  • Wang X. Fuzzy optimal assignment problem. Fuzzy Math. 1987; 3:101108.
  • Werner B. Interactive multiple objective programming subject to flexible constraints. European J. Oper. Res. 1987; 31:342349. Crossref
  • Yager RR. A procedure for ordering fuzzy subsets of the unit interval. Information Sciences. 1981; 24:143–61. Crossref
  • Zadeh LA. Fuzzy sets. Information and control. 1965; 8:338–53. Crossref
  • Zimmermann HJ. Fuzzy set theory and its applications. 4th ed. Kluwer Academic publishers; 1998.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.