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Generalized Archimedean Intuitionistic Fuzzy Averaging Aggregation Operators and their Application to Multicriteria Decision-Making

Author

Listed:
  • Chunqiao Tan

    (School of Business, Central South University, Changsha 410083, China2Mobile E-business Collaborative Innovation Center of Hunan Province, Changsha 410205, China)

  • Xiaohong Chen

    (Key Laboratory of Hunan Province for Mobile Intelligence, Hunan University of Commerce, Changsha 410205, China)

Abstract

Aggregation operators play a key role in multiple criteria decision-making (MCDM). Extensions of aggregation operators to intuitionistic fuzzy sets (IFSs) usually involve replacing the standard arithmetic operations with those defined over the membership and nonmembership of IFS, which is essentially a pair of special Archimedean triangular norm (t-norm) and triangular conorm (t-conorm), called probabilistic sum t-conorm and product t-norm, on the membership and nonmembership of IFS, respectively. In this paper, we first introduce some operations on IFSs by means of Archimedean t-norm and t-conorm. Then some generalized Archimedean intuitionistic fuzzy aggregation operators are proposed, such as generalized Archimedean intuitionistic fuzzy weighted averaging operator, generalized Archimedean intuitionistic fuzzy ordered weighted averaging (GAIFOWA) operator, and generalized Archimedean intuitionistic fuzzy hybird averaging operator. Some desirable properties of these operators are investigated. The relations between these operators and the existing intuitionistic fuzzy aggregation operators are discussed. Finally, applying these proposed operators, we develop an approach for multi-criteria decision-making with intuitionistic fuzzy information, an illustrative example is used to verify the developed approach and to demonstrate its practicality and effectiveness.

Suggested Citation

  • Chunqiao Tan & Xiaohong Chen, 2016. "Generalized Archimedean Intuitionistic Fuzzy Averaging Aggregation Operators and their Application to Multicriteria Decision-Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 311-352, March.
    • Handle: RePEc:wsi:ijitdm:v:15:y:2016:i:02:n:s0219622016500048
    DOI: 10.1142/S0219622016500048
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    References listed on IDEAS

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    4. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    5. Chunqiao Tan & Wentao Yi & Xiaohong Chen, 2015. "Generalized intuitionistic fuzzy geometric aggregation operators and their application to multi-criteria decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1919-1938, November.
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