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Intuitionistic Fuzzy Normalized Weighted Bonferroni Mean and Its Application in Multicriteria Decision Making

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  • Wei Zhou
  • Jian-min He

Abstract

The Bonferroni mean (BM) was introduced by Bonferroni six decades ago but has been a hot research topic recently since its usefulness of the aggregation techniques. The desirable characteristic of the BM is its capability to capture the interrelationship between input arguments. However, the classical BM and GBM ignore the weight vector of aggregated arguments, the general weighted BM (WBM) has not the reducibility, and the revised generalized weighted BM (GWBM) cannot reflect the interrelationship between the individual criterion and other criteria. To deal with these issues, in this paper, we propose the normalized weighted Bonferroni mean (NWBM) and the generalized normalized weighted Bonferroni mean (GNWBM) and study their desirable properties, such as reducibility, idempotency, monotonicity, and boundedness. Furthermore, we investigate the NWBM and GNWBM operators under the intuitionistic fuzzy environment which is more common phenomenon in modern life and develop two new intuitionistic fuzzy aggregation operators based on the NWBM and GNWBM, that is, the intuitionistic fuzzy normalized weighted Bonferroni mean (IFNWBM) and the generalized intuitionistic fuzzy normalized weighted Bonferroni mean (GIFNWBM). Finally, based on the GIFNWBM, we propose an approach to multicriteria decision making under the intuitionistic fuzzy environment, and a practical example is provided to illustrate our results.

Suggested Citation

  • Wei Zhou & Jian-min He, 2012. "Intuitionistic Fuzzy Normalized Weighted Bonferroni Mean and Its Application in Multicriteria Decision Making," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:136254
    DOI: 10.1155/2012/136254
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    References listed on IDEAS

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    1. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
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    Cited by:

    1. Ya-ming Shi & Jian-min He, 2013. "The Interval‐Valued Intuitionistic Fuzzy Optimized Weighted Bonferroni Means and Their Application," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Wei Zhou, 2014. "On Hesitant Fuzzy Reducible Weighted Bonferroni Mean and Its Generalized Form for Multicriteria Aggregation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Dejian Yu, 2014. "Hydrogen Production Technologies Evaluation Based on Interval‐Valued Intuitionistic Fuzzy Multiattribute Decision Making Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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