Optimal Solution of Fuzzy Assignment Problems Using Ranking Technique

Authors

  • Amit Kumar Nandan Research Scholar, Department of Mathematics, B. R. A. Bihar University, Muzaffarpur, Bihar, India Author
  • J. P. Tripathi Department of Mathematics, R.N. College, Hajipur, B. R. A. Bihar University, Muzaffarpur, Bihar, India Author
  • V. K. Tiwari Department of Commerce, Government Degree College Sukrauli, Kushinagar, U.P., India Author
  • R. K. Shukla Department of Mathematics, Government Degree College Sukrauli, Kushinagar, U.P., India Author

Keywords:

Fuzzy Assignment Problem, Triangular Fuzzy Function, Ranking Function, Fuzzy Numbers

Abstract

Operation Research has thoroughly studied the Assignment Problem, which is a type of Linear Programming Problem (LPP). It is an important problem in decision-making. In this paper, we are using the Fuzzy technique to simplify Assignment problems and these problems are known as Fuzzy Assignment Problems. In the Fuzzy Assignment Problem, we are using a triangular fuzzy function to optimize the costs. In this paper, we have discussed two formulas: One method is based on an odd number of fuzzy numbers, while the other is based on an even number of fuzzy numbers to find the optimal cost from the given problems by using the Ranking Technique.

Downloads

Download data is not yet available.

References

Zadeh, L.: Fuzzy set. Inf. Control 8, 338–353 (1965)

Pandian, P., Kavitha, K.: A new method for solving fuzzy assignment problems. Ann. Pure Appl. Math 1(1), 69–83 (2012)

Kadhirvel, K., Balamurugan, K.: Method for solving Hungarian assignment problems using the triangular and trapezoidal fuzzy number. Int. J. Eng. Res. Appl. (IJERA) 2(5), 399–403 (2012)

Berghman, L., Leus, R., Spieksma, F.: Optimal solutions for a dock assignment problem with trailer transportation. Ann. Oper. Res. 3–25 (2014)

Khandelwal, A.: A modified approach for assignment method. Int. J. Latest Res. Sci. Technol.

(2), 136–138 (2014)

Nirmala, G., Anju, G.: Cost minimization assignment problem using fuzzy quantifier. Int. J. Comput. Sci. Inf. Technol. 5(6), 7948–7950 (2014)

Anuradha, D.: On solving fuzzy solid assignment problems. Int. Res. J. Eng. Technol. (IRJET)

(5), 322–325 (2015)

Singh, J., Thakur, N.: A Novel method to solve assignment problem in fuzzy environment. Ind. Eng. Lett. 5(2), 31–35 (2015)

Frimpong, F., Owusu, A.: Allocation of classroom space using linear programming (A case study: Premier nurses training college, Kumasi). J. Econ. Sustain. Dev. 6(2), 12–19 (2015)

Ghadle, K., Pathade, P.: Optimal solution of balanced and unbalanced fuzzy transportation problem using hexagonal fuzzy number. Int. J. Math. Res. 5(2), 131–137 (2016)

Ghadle, K., Pathade, P.: An improvement to one’s BCM for balance and unbalanced transship- ment problem by using fuzzy numbers. Accepted Springer Book Series-Trends in Mathematics (2018)

Ghadle, K., Ingle, S.: Optimal solution of a mixed type fuzzy transportation problem. Int. J. Fuzzy Math. Arch. 15(1), 83–89 (2018)

Kumar, A. & Gupta, A. (2011), Methods for solving fuzzy assignment problems and fuzzy traveling salesman problems with different membership functions. Fuzzy Information and Engineering 3, 332-335

Kumar, A. & Gupta, A. (2012), Assignment and Travelling Salesman Problems with Coefficients as LR Fuzzy Parameters, Int. J. of App. Sci. and Engg. 10, 155-170

Kumar, A. & Gupta, A. & Kaur, A. (2009), Methods for solving fully fuzzy assignment problems using triangular fuzzy numbers, World Academy of Science, Engineering, and Technology 3, 968-971

Kumar, A. & Bhatia, N. (2011), A new method for solving fuzzy sensitivity analysis for fuzzy linear programming problems, Int. J. of App. Science and Engineering 9, 169-176.

Downloads

Published

15-03-2024

Issue

Section

Research Articles

How to Cite

Optimal Solution of Fuzzy Assignment Problems Using Ranking Technique. (2024). International Journal of Scientific Research in Science and Technology, 11(2), 975-983. https://ijsrst.com/index.php/home/article/view/IJSRST24112554

Similar Articles

1-10 of 20

You may also start an advanced similarity search for this article.