Intuitionistic fuzzy normalized weighted Bonferroni mean and its application in multicriteria decision making
type: Item
instance of: scholarly article
title: Intuitionistic fuzzy normalized weighted Bonferroni mean and its application in multicriteria decision making
zbMATH Open document ID: 1251.90407
DOI: 10.1155/2012/136254
author: Wei Zhou
author: Jianmin He
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 90C70
Mathematics Subject Classification ID: 90B90
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 6106117
zbMATH Keywords: Bonferroni mean
zbMATH Keywords: generalized intuitionistic fuzzy normalized weighted Bonferroni mean
Wikidata QID: Q58905736
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/136254
OpenAlex ID: W2116231621
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description: scientific article; zbMATH DE number 6106117