Abstract
In today’s real world problems such as in corporate or in industrial, the experts and the decision makers have to suffer with uncertainty as well as with hesitation usually, due to the complexity of the situations. The main reasons behind these complexities are lack of good communications with all involved persons, error in data’s, understanding of markets, unawareness of customers etc. So, In this paper, we consider a transportation problem having uncertainty and hesitation in supply and demand. We formulate the problem and utilize triangular intuitionistic fuzzy numbers (TIFNs) to deal with uncertainty and hesitation. We propose intuitionistic fuzzy methods to find starting basic feasible solution in terms of TIFNs. Intuitionistic fuzzy modified distribution method has been proposed to find optimal solution. The shortcomings of the existing methods have been pointed out. The proposed method is illustrated by numerical examples.
Similar content being viewed by others
References
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Bector CR, Chandra S (2002) On duality in linear programming under fuzzy environment. Fuzzy Sets Syst 125:317–325
Bellman R, Zadeh LA (1970) Decision making in fuzzy environment. Manag Sci 17(B):141–164
Dinager DS, Palanivel K (2009) The transportation problem in fuzzy environment. Int J Algorithm Comput Math 12(3):93–106
Ebrahimipur V, Qurayshi SF, Shabani A, Shoja BM (2011) Reliability optimization of multi-state weighted k-out-of-n systems by fuzzy mathematical programming and genetic algorithm. Int J Syst Assur Eng Manag 2(4):312–318
Ganesan K, Veeramani P (2006) Fuzzy linear programs with trapezoidal fuzzy numbers. Ann Oper Res 143:305–315
Hussain RJ, Kumar PS (2012) Algorithmic approach for solving intuitionistic fuzzy transportation problem. Appl Math Sci 6(80):3981–3989
Kapur PK, Pham H, Gupta A, Jha PC (2011) Optimal release policy under fuzzy environment. Int J Syst Assur Eng Manag 2(1):48–58
Kaur A, Kumar A (2012) A new approach for solving fuzzy transportation problem using generalized trapezoidal fuzzy number. Appl Soft Comput 12:1201–1213
Kheirfam B, Verdegay JL (2013) The dual simplex method and sensitivity analysis for fuzzy linear programming with symmetric trapezoidal numbers. Fuzzy Optim Decis Mak 12:171–189
Mohideen IS, Kumar PS (2010) A comparative study on transportation problem in fuzzy environment. Int J Math Res 2(1):151–158
Nagoorgani A, Abbas S (2013) A new method for solving intuitionistic fuzzy transportation problem. Appl Math Sci 7(28):1357–1365
Nagoorgani A, Ponnalagu K (2012) A new approach on solving intuitionistic fuzzy linear programming problem. Appl Math Sci 6(70):3467–3474
Nagoorgani A, Razak KA (2006) Two stage fuzzy transportation problem. J Phys Sci 10:63–69
Pandian P, Natarajan G (2010) A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problem. Appl Math Sci 4(2):79–90
Zadeh LA (1965) Fuzzy sets. Inf Comput 8:338–353
Zimmerman HJ (1996) Fuzzy set theory and its applications. Allied Publisher Limited, New Delhi Second Revised Edition
Acknowledgments
The authors gratefully acknowledge the critical comments given by the learned reviewer which helped us to improve the manuscript. The first author gratefully acknowledges the financial support given by the Ministry of Human Resource and Development (MHRD), Govt. of India, India.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Singh, S.K., Yadav, S.P. Efficient approach for solving type-1 intuitionistic fuzzy transportation problem. Int J Syst Assur Eng Manag 6, 259–267 (2015). https://doi.org/10.1007/s13198-014-0274-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13198-014-0274-x