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Mixed Solution Strategy for MCGDM Problems Using Entropy/Cross Entropy in Interval-Valued Intuitionistic Fuzzy Environment

Author

Listed:
  • Anjana Gupta

    (Department of Mathematics, Delhi Technological University, Bawana Road, Rohini Sector-16, Delhi, India)

  • Aparna Mehra

    (Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India)

  • S. S. Appadoo

    (Department of Supply Chain Management, Asper School of Business, University of Manitoba, Winnipeg, MB R3T5V4 Canada, Canada)

Abstract

Although several weight determining methods have been studied for multiple criteria group decision making (MCGDM) problems under intuitionistic fuzzy environment, in the present study, besides the criteria values provided by the decision makers (DMs), we propose to also use the historical data of alternatives-criteria to compute the criteria weights. This is a reasonable thought as the past information may influence the decision makers' choice of entries in their respective alternatives-criteria decision matrices. To this aim, we introduce a novel mixed solution strategy to derive the criteria final weight vector. Initially, the alternatives-criteria decision matrices provided by the DMs are taken to involve interval-valued intuitionistic fuzzy numbers (IVIFNs). The entropy measure for IVIFNs, studied by Ye [2010a], is used to aggregate these decision matrices. We also introduce a new definition of cross entropy for IVIFNs and used it to rank the alternatives. Finally, an example is presented to illustrate the proposed approach.

Suggested Citation

  • Anjana Gupta & Aparna Mehra & S. S. Appadoo, 2015. "Mixed Solution Strategy for MCGDM Problems Using Entropy/Cross Entropy in Interval-Valued Intuitionistic Fuzzy Environment," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-22.
    • Handle: RePEc:wsi:igtrxx:v:17:y:2015:i:01:n:s0219198915400071
    DOI: 10.1142/S0219198915400071
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    Cited by:

    1. Arunodaya Raj Mishra & Pratibha Rani, 2018. "Interval-Valued Intuitionistic Fuzzy WASPAS Method: Application in Reservoir Flood Control Management Policy," Group Decision and Negotiation, Springer, vol. 27(6), pages 1047-1078, December.

    More about this item

    Keywords

    Multiple criteria group decision making; interval-valued intuitionistic fuzzy number; weight vector; entropy; cross entropy; 90B50; 62C25;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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