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New Method for Solving a General Multiple Criteria Decision-Making Problem Under Risk in Fuzzy Environment

Author

Listed:
  • N. Thillaigovindan

    (Department of Mathematics, College of Natural Sciences, Arba Minch University, Arba Minch, Ethiopia)

  • S. Anita Shanthi

    (Department of Mathematics, Annamalai University, Annamalainagar — 608002, Tamilnadu, India)

  • J. Vadivel Naidu

    (Department of Mathematics, Annamalai University, Annamalainagar — 608002, Tamilnadu, India)

Abstract

This paper considers a multiple criteria decision-making (MCDM) problem under risk in fuzzy environment in its general form. There are m alternatives which need to be ranked on the basis of a set of n criteria. The alternatives and the criteria are evaluated based on a set of l characteristics. The entire data is presented in the form of interval valued intuitionistic fuzzy soft set of root type. In addition each criterion is assigned a subjective criterion weight based on expert’s evaluation and each characteristic is assigned a probability weight on the basis of decision maker’s knowlege and understanding of the importance of the characteristic. This problem may be called as a MCDM problem under risk in fuzzy environment in its general form. A method for ranking the alternatives using the new score functions, prospect theory and method of determining the optimum criteria weights is explained. An algorithm is developed for this purpose and its working illustrated with a suitable example.

Suggested Citation

  • N. Thillaigovindan & S. Anita Shanthi & J. Vadivel Naidu, 2016. "New Method for Solving a General Multiple Criteria Decision-Making Problem Under Risk in Fuzzy Environment," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1157-1179, September.
    • Handle: RePEc:wsi:ijitdm:v:15:y:2016:i:05:n:s0219622016500279
    DOI: 10.1142/S0219622016500279
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    References listed on IDEAS

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    1. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    2. Peng, Yi & Kou, Gang & Wang, Guoxun & Shi, Yong, 2011. "FAMCDM: A fusion approach of MCDM methods to rank multiclass classification algorithms," Omega, Elsevier, vol. 39(6), pages 677-689, December.
    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Gang Kou & Yanqun Lu & Yi Peng & Yong Shi, 2012. "Evaluation Of Classification Algorithms Using Mcdm And Rank Correlation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 197-225.
    5. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
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    Cited by:

    1. Mustafa Batuhan Ayhan, 2018. "A New Decision Making Approach for Supplier Selection: Hesitant Fuzzy Axiomatic Design," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1085-1117, July.
    2. Paulo Cesar Schotten & Danielle Costa Morais, 2019. "A group decision model for credit granting in the financial market," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 5(1), pages 1-19, December.

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