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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, Hindawi, vol. 2012, pages 1-22, September.
  • Handle: RePEc:hin:jnljam:136254
    DOI: 10.1155/2012/136254
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    Cited by:

    1. Changxing Fan & Keli Hu & Sheng Feng & Jun Ye & En Fan, 2019. "Heronian mean operators of linguistic neutrosophic multisets and their multiple attribute decision-making methods," International Journal of Distributed Sensor Networks, , vol. 15(4), pages 15501477198, April.
    2. Sayyid Ali Banihashemi & Mohammad Khalilzadeh & Edmundas Kazimieras Zavadskas & Jurgita Antucheviciene, 2021. "Investigating the Environmental Impacts of Construction Projects in Time-Cost Trade-Off Project Scheduling Problems with CoCoSo Multi-Criteria Decision-Making Method," Sustainability, MDPI, vol. 13(19), pages 1-17, September.
    3. Yi Yang & Lei Hua & Mengqi Jie & Biao Shi, 2024. "Large-Scale Satisfaction Rating-Driven Selection of New Energy Vehicles: A Basic Uncertain Linguistic Information Bonferroni Mean-Based MCGDM Approach Considering Criteria Interaction," Sustainability, MDPI, vol. 16(16), pages 1-27, August.
    4. Peide Liu & Xi Liu, 2017. "Multiattribute Group Decision Making Methods Based on Linguistic Intuitionistic Fuzzy Power Bonferroni Mean Operators," Complexity, Hindawi, vol. 2017, pages 1-15, January.

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