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An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2

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Abstract

In the transportation problem, transportation cost depends on several uncontrollable factors such as fluctuation in the fuel price, weather condition, road condition, etc. In most cases, exact information is utilized, but in the real world applications these quantities are imprecise and unconfirmed. Most researchers studied transportation problem with fuzzy and intuitionistic fuzzy parameters. But, both fuzzy and intuitionistic fuzzy parameters utilize fixed membership and non-membership degrees which do not deal properly with the situation of uncertainty and hesitation. Thus, we are faced with another type of ambiguity that cannot be handled by using fuzzy or intuitionistic fuzzy set. In the current work, we have designed a transportation problem in which supplies and demands are crisp numbers and costs are interval valued intuitionistic fuzzy numbers. This type of problem is termed as interval valued intuitionistic fuzzy transportation problem of Type-2. Hence, to deal with ambiguity and uncertainty in transportation problem, an algorithm is developed to find out the optimal solution of interval valued intuitionistic fuzzy transportation problem of Type-2. Finally the proposed algorithm is illustrated with the help of a numerical example and the results are compared with the existing methods.

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References

  • Antony RJP, Savarimuthu SJ, Pathinathan T (2014) Method for solving the transportation problem using triangular intuitionistic fuzzy number. Int J Comput Algorithm 3(1), 590–605

    Google Scholar 

  • Anusha V, Sireesha V (2022) A new distance measure to rank type-2 intuitionistic fuzzy sets and its application to multi-criteria group decision making. Int J Fuzzy Syst Appl (IJFSA) 11(1):1–17

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • Atanassov KT, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349

    Article  MathSciNet  MATH  Google Scholar 

  • Bharati SK, Singh SR (2020) Interval-valued intuitionistic fuzzy linear programming problem. New Math Nat Comput 16(01), 53–71

    Article  Google Scholar 

  • Bharati SK (2021) Transportation problem with interval-valued intuitionistic fuzzy sets: impact of a new ranking. Prog Artif Intell 10(2), 129–145

    Article  Google Scholar 

  • Bharati SK, Singh SR (2018) Transportation problem under interval-valued intuitionistic fuzzy environment. Int J Fuzzy Syst 20(5), 1511–1522

    Article  Google Scholar 

  • Ebrahimnejad A, Verdegay JL (2018) A new approach for solving fully intuitionistic fuzzy transportation problems. Fuzzy Optim Decis Making 17(4), 447–474

    Article  MathSciNet  MATH  Google Scholar 

  • Gani AN, Abbas S (2013) A new method for solving intuitionistic fuzzy transportation problem. Appl Math Sci 7(28), 1357–1365

    Google Scholar 

  • Garg H, Singh S (2020) Algorithm for solving group decision-making problems based on the similarity measures under type 2 intuitionistic fuzzy sets environment. Soft Comput 24(10), 7361–7381

    Article  MATH  Google Scholar 

  • Gupta S, Garg H, Chaudhary S (2020) Parameter estimation and optimization of multi-objective capacitated stochastic transportation problem for gamma distribution. Complex Intell Syst 6(3), 651–667

    Article  Google Scholar 

  • Josephine FS, Francina Nishandhi ASI (2020) a dynamic method for solving intuitionistic fuzzy transportation problem. Eur J Mol Clin Med 7(11):2020

  • Kumar PS (2020) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int J Syst Assur Eng Manag 11(1), 189–222

    Article  Google Scholar 

  • Kumar PS (2020) Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem. Int J Oper Res 37(3), 418–451

    Article  MathSciNet  Google Scholar 

  • Mahmoodirad A, Allahviranloo T, Niroomand S (2019) DA new effective solution method for fully intuitionistic fuzzy transportation problem. Soft Comput 23(12), 4521–4530

    Article  MATH  Google Scholar 

  • Mishra A, Kumar A (2020) JMD method for transforming an unbalanced fully intuitionistic fuzzy transportation problem into a balanced fully intuitionistic fuzzy transportation problem. Soft Comput 24(20), 15639–15654

    Article  MATH  Google Scholar 

  • Mitchell HB (2004) Ranking-intuitionistic fuzzy numbers. Int J Uncertain Fuzziness Knowl -Based Syst 12(03), 377–386

    Article  MathSciNet  MATH  Google Scholar 

  • Mukherjee S, Basu K (2012) Solution of a class of intuitionistic fuzzy assignment problem by using similarity measures. Knowl-Based Syst 27:170–179

    Article  Google Scholar 

  • Nayagam VLG, Sivaraman G (2011) Ranking of interval-valued intuitionistic fuzzy sets. Appl Soft Comput 11(4), 3368–3372

    Article  Google Scholar 

  • Pandian P (2014) Realistic method for solving fully intuitionistic fuzzy transportation problems. Appl Math Sci 8(113), 5633–5639

    Google Scholar 

  • Parvathi R, Malathi C (2012) Intuitionistic fuzzy linear optimization. Notes Intuit Fuzzy Sets 18(1), 48–56

    MATH  Google Scholar 

  • Pratihar J, Kumar R, Edalatpanah SA, Dey A (2021) Modified Vogel’s approximation method for transportation problem under uncertain environment. Complex Intell Syst 7(1), 29–40

    Article  Google Scholar 

  • Şahin R (2016) Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets. Soft Comput 20(7), 2557–2563

    Article  MATH  Google Scholar 

  • Singh S, Garg H (2017) Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process. Appl Intell 46(4), 788–799

    Article  Google Scholar 

  • Singh SK, Yadav SP (2016) A new approach for solving intuitionistic fuzzy transportation problem of type-2. Ann Oper Res 243(1), 349–363

    Article  MathSciNet  MATH  Google Scholar 

  • Singh SK, Yadav SP (2015) Efficient approach for solving type-1 intuitionistic fuzzy transportation problem. Int J Syst Assur Eng Manag 6(3), 259–267

    Article  Google Scholar 

  • Sola HB, Fernandez J, Hagras H, Herrera F, Pagola M, Barrenechea E (2014) Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: Toward a wider view on their relationship. IEEE Trans Fuzzy Syst 23(5), 1876–1882

    Article  Google Scholar 

  • Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3), 505–518

    Article  MathSciNet  MATH  Google Scholar 

  • V. Traneva, S. Tranev, Intuitionistic fuzzy transportation problem by zero point method. In: 2020 15th Conference on Computer Science and Information Systems (FedCSIS). IEEE. (pp. 349-358) (2020)

  • Xue Y, Deng Y (2021) Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. Appl Intell 51(8), 6224–6233

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are thankful to The Council of Scientific and Industrial Research (CSIR), India, the Govt. of India, for financial support in persuing this research.

Funding

The author (Ashutosh Choudhary) is thankful to the Council of Scientific and Industrial Research (CSIR), India for financial support (Grant No. 09/143(0894)/2017-EMR-I) in the form of Senior Research Fellowship (SRF) to carry out the research work.

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

    Ashutosh Choudhary & Shiv Prasad Yadav

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  1. Ashutosh Choudhary
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  2. Shiv Prasad Yadav
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Correspondence to Ashutosh Choudhary.

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Choudhary, A., Yadav, S.P. An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2. Int J Syst Assur Eng Manag 13, 2992–3001 (2022). https://doi.org/10.1007/s13198-022-01771-6

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