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Intuitionistic fuzzy transportation problem with various kinds of uncertainties in parameters and variables

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Abstract

In real-life decisions usually we have to suffer through different states of uncertainties. In this article, we formulate a transportation problem in which costs, supplies and demands all are different types of real, fuzzy or intuitionistic fuzzy numbers that is the data has different types of uncertainties. We propose a ranking procedure for intuitionistic fuzzy numbers. Using the proposed ranking function intuitionistic fuzzy methods are proposed to find starting basic feasible solution in terms of trapezoidal intuitionistic fuzzy numbers. Intuitionistic fuzzy modified distribution method is proposed to find optimal solution. We illustrate the methodology by numerical examples.

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References

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MathSciNet  MATH  Google Scholar 

  • Bellman R, Zadeh LA (1970) Decision making in fuzzy environment. Manag Sci 17(B):141–164

    Article  MathSciNet  MATH  Google Scholar 

  • Dempe S, Starostina T (2006) Optimal toll charges in a fuzzy flow problem. In: Proceedings of the international conference, 9th fuzzy days in Dortmund, Germany, 18–20 Sept

  • Dinager DS, Palanivel K (2009) The transportation problem in fuzzy environment. Int J Algorithm Comput Math 12(3):93–106

    Google Scholar 

  • Ismail MS, Kumar SP (2010) A comparative study on transportation problem in fuzzy environment. Int J Math Res 2(1):151–158

    Google Scholar 

  • Kumar M, Yadav SP, Kumar S (2011) A new approach for analyzing the fuzzy system reliability using intuitionistic fuzzy number. Int J Ind Syst Eng 8:135–156

    Google Scholar 

  • Liou TS, Wang MJJ (1992) Ranking fuzzy numbers with integral value. Fuzzy Sets Syst 50:247–255

    Article  MathSciNet  MATH  Google Scholar 

  • Nagoorgani A, Razak KA (2006) Two stage fuzzy transportation problem. J Phys Sci 10:63–69

    Google Scholar 

  • 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

    MATH  Google Scholar 

  • Singh SK, Yadav SP (2014a) Efficient approach for solving type-1 intuitionistic fuzzy transportation problem. Int J Syst Assur Eng Manag. doi:10.1007/s13198-014-0274-x

    Google Scholar 

  • Singh SK, Yadav SP (2014b) A new approach for solving intuitionistic fuzzy transportation problem of type-2. Ann Oper Res. doi:10.1007/s10479-014-1724-1

    MathSciNet  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Comput 8:338–353

    MathSciNet  MATH  Google Scholar 

  • Zangiabadi M, Maleki HR (2013) Fuzzy goal programming technique to solve multi-objective transportation problems with some non-linear membership functions. Iran J Fuzzy Syst 10(1):61–74

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

The first author gratefully acknowledges the financial support given by the Ministry of Human Resource and Development (MHRD), Govt. of India, India.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Sujeet Kumar Singh & Shiv Prasad Yadav

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  1. Sujeet Kumar Singh
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  2. Shiv Prasad Yadav
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Correspondence to Sujeet Kumar Singh.

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Singh, S.K., Yadav, S.P. Intuitionistic fuzzy transportation problem with various kinds of uncertainties in parameters and variables. Int J Syst Assur Eng Manag 7, 262–272 (2016). https://doi.org/10.1007/s13198-016-0456-9

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  • DOI: https://doi.org/10.1007/s13198-016-0456-9

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