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Issue:A method for solving unbalanced intuitionistic fuzzy transportation problems

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Title of paper: A method for solving unbalanced intuitionistic fuzzy transportation problems
Author(s):
P. Senthil Kumar
PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli-620 020, Tamil Nadu, India
senthilsoft_5760@yahoo.com , senthilsoft1985@gmail.com
R. Jahir Hussain
PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli-620 020, Tamil Nadu, India
hssn_jhr@yahoo.com
Published in: "Notes on IFS", Volume 21, 2015, Number 3, pages 54—65
Download:  PDF (227  Kb, File info)
Abstract: In conventional transportation problem (TP), supplies, demands and costs are always certain. This paper develops an approach to solve the unbalanced transportation problem where as all the parameters are not in deterministic numbers but imprecise ones. Here, all the parameters of the TP are considered to the triangular intuitionistic fuzzy numbers (TIFNs). The existing ranking procedure of Varghese and Kuriakose is used to transform the unbalanced intuitionistic fuzzy transportation problem (UIFTP) into a crisp one so that the conventional method may be applied to solve the TP. The occupied cells of unbalanced crisp TP that we obtained are as same as the occupied cells of UIFTP.

On the basis of this idea the solution procedure is differs from unbalanced crisp TP to UIFTP in allocation step only. Therefore, the new method and new multiplication operation on triangular intuitionistic fuzzy number (TIFN) is proposed to find the optimal solution in terms of TIFN. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful.

Keywords: Intuitionistic fuzzy set, Triangular intuitionistic fuzzy number, Unbalanced intuitionistic fuzzy transportation problem, PSK method, Optimal solution.
AMS Classification: 03E72, 03F55, 90B06.
References:
  1. Antony, R. J. P., Savarimuthu, S. J., & Pathinathan, T. (2014) Method for solving the transportation problem using triangular intuitionistic fuzzy number. International Journal of Computing Algorithm, 3, 590–605.
  2. Atanassov, K. (1983) Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).
  3. Atanassov, K. (1995) Issue:Ideas for intuitionistic fuzzy equations, inequalities and optimization, Notes on Intuitionistic Fuzzy Sets, 1(1), 17–24.
  4. Burillo, P., Bustince, H., & Mohedano, V. (1994) Issue:Some definitions of intuitionistic fuzzy number-first properties. Proceedings of the 1 st workshop on fuzzy based expert system, pages, Sofia, Bulgaria, September 1994, 53–55.
  5. Dinager, D. S., & Palanivel, K. (2009) The Transportation problem in fuzzy environment, Int. Journal of Algorithm, Computing and Mathematics, 2, 65–71.
  6. Dinagar, D. S., & Thiripurasundari K (2014) A navel method for solving fuzzy transportation problem involving intuitionistic trapezoidal fuzzy numbers. International Journal of Current Research, 6, 7038–7041.
  7. Gani, A. N., & Abbas, S. (2012) Mixed constraint intuitionistic fuzzy transportation problem. Proceedings in International Conference on Mathematical Modeling and Applied Soft Computing (MMASC-2012), Coimbatore Institute of Technology, 1, 832–843.
  8. Hussain, R. J., & Kumar, P. S. (2012a) Algorithmic approach for solving intuitionistic fuzzy transportation problem. Applied Mathematical Sciences, 6, 3981–3989.
  9. Hussain, R. J., & Kumar, P. S. (2012b) The transportation problem with the aid of triangular intuitionistic fuzzy numbers. Proceedings in International Conference on Mathematical Modeling and Applied Soft Computing (MMASC-2012), Coimbatore Institute of Technology, 1, 819–825.
  10. Hussain, R. J., & Kumar, P. S. (2013) An optimal more-for-less solution of mixed constraints intuitionistic fuzzy transportation problems. Int. J. Contemp. Math. Sciences, 8, 565–576.
  11. Kumar, P. S., & Hussain, R. J. (2014) A systematic approach for solving mixed intuitionistic fuzzy transportation problems. International Journal of Pure and Applied Mathematics, 92, 181–190.
  12. Mohideen, S. I., & Kumar, P. S. (2010) A comparative study on transportation problem in fuzzy environment. International Journal of Mathematics Research, 2, 151–158.
  13. Pandian, P., & Natarajan, G. (2010) A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Applied Mathematics Sciences, 4, 79–90.
  14. Taha, H. A. (2008) Operations Research: An Introduction. 8th edition, Pearson Education India.
  15. Varghese, A., & Kuriakose, S. (2012) Issue:Centroid of an intuitionistic fuzzy number. Notes on Intuitionistic Fuzzy Sets, 18(1), 19–24.
  16. Zadeh, L. A. (1965) Fuzzy sets. Information and Control, 8, 338–353. 65
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