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Ranking of interval type 2 fuzzy numbers using correlation coefficient and Mellin transform

Author

Listed:
  • Avijit De

    (Dr. B. C. Roy Engineering College)

  • Sujit Das

    (National Institute of Technology)

  • Samarjit Kar

    (National Institute of Technology)

Abstract

Ranking of fuzzy numbers exhibits a significant role to solve the multiple attributes group decision making (MAGDM) problems. One of the commonly used indices for MAGDM problems is the correlation coefficient. Type-2 fuzzy numbers (T2FNs) are considered to be more effective than type-1 fuzzy numbers (T1FNs) to handle uncertainties in MAGDM problems. Moreover, T2FNs allow additional freedom to reflect uncertainty. In this paper, we propose a new approach to rank the interval type-2 fuzzy numbers (IT2FNs) using the correlation coefficient, where the correlation coefficient is obtained using the Mellin transform. Initially, we define the correlation coefficient for interval type-2 trapezoidal fuzzy numbers (IT2TrFNs) using Mellin transform and prove some of its major features. Then a new group decision-making method has been recommended using the proposed ranking concept. Eventually, three examples are given to demonstrate the usefulness of the suggested method. Finally, a comparative study is conducted to depict the feasibility of the developed ranking technique.

Suggested Citation

  • Avijit De & Sujit Das & Samarjit Kar, 2021. "Ranking of interval type 2 fuzzy numbers using correlation coefficient and Mellin transform," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1018-1048, December.
    • Handle: RePEc:spr:opsear:v:58:y:2021:i:4:d:10.1007_s12597-020-00504-2
    DOI: 10.1007/s12597-020-00504-2
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    References listed on IDEAS

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    1. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    2. Ye, Jun, 2010. "Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment," European Journal of Operational Research, Elsevier, vol. 205(1), pages 202-204, August.
    3. Yang, Chih-Ching, 2016. "Correlation coefficient evaluation for the fuzzy interval data," Journal of Business Research, Elsevier, vol. 69(6), pages 2138-2144.
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    5. Mohammad Ebrahim Banihabib & Mohammad Hadi Shabestari, 2017. "Fuzzy Hybrid MCDM Model for Ranking the Agricultural Water Demand Management Strategies in Arid Areas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(1), pages 495-513, January.
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