Abstract
Gupta et al. (Complex and Intelligent Systems (2020) 6:651–667) proposed three mathematical models for three different types of multi-objective capacitated interval type-2 fuzzy stochastic transportation problems as well as proposed an approach to solve the proposed mathematical models. In this note, it is pointed out that out of these three mathematical models, the first two mathematical models are not appropriate. Also, the appropriate mathematical models corresponding to the first two mathematical models are proposed. Furthermore, it is pointed out that some mathematical incorrect assumptions are considered in the above-mentioned approach. Therefore, it is inappropriate to use this approach to solve the proposed mathematical models as well as the third existing mathematical model. To propose an appropriate approach for solving the proposed mathematical models as well as the third existing mathematical model is a challenging open research problem.
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References
Chen, S.M., Lee, L.W.: Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Syst Appl 37(1), 824–833 (2010)
Sinha, B., Das, A., Bera, U.K.: Profit maximization solid transportation problem with trapezoidal interval type-2 fuzzy numbers. Int. J. Appl. Comput. Math. 2(1), 41–56 (2016)
Gupta, S., Garg, H., Chaudhary, S.: Parameter estimation and optimization of multi-objective capacitated stochastic transportation problem for gamma distribution. Complex Intell. Syst. 6(3), 651–667 (2020)
Khalil, A.M., Hassan, N.: A note on “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets.” Appl. Math. Model. 41, 684–690 (2017)
Zimmermann, H.J.: Fuzzy set theory and its applications, 4th edn. Kluwer Academic Publisher, Dordrecht (2001)
Hu, J., Zhang, Y., Chen, X., Liu, Y.: Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number. Knowl.-Based Syst. 43, 21–29 (2013)
Bera, S., Giri, P.K., Jana, D.K., Basu, K., Maiti, M.: Fixed charge 4D-TP for a breakable item under hybrid random type-2 uncertain environments. Inf. Sci. 527, 128–158 (2020)
Jana, S.H., Jana, B.: Application of random triangular and Gaussian type-2 fuzzy variable to solve fixed charge multi-item four dimensional transportation problem. Appl. Soft. Comput. 96, 106589 (2020)
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The authors would like to thank the anonymous reviewers for their insightful comments and suggestions.
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Bhatia, T.K., Kumar, A., Appadoo, S.S. (2023). A Note on “Parameter Estimation and Optimization of Multi-objective Capacitated Stochastic Transportation Problem for Gamma Distribution”. In: Sahoo, L., Senapati, T., Yager, R.R. (eds) Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain. Studies in Fuzziness and Soft Computing, vol 420. Springer, Singapore. https://doi.org/10.1007/978-981-19-4929-6_27
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DOI: https://doi.org/10.1007/978-981-19-4929-6_27
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