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A Normalized Weighted Bonferroni Mean Aggregation Operator Considering Shapley Fuzzy Measure Under Interval-valued Neutrosophic Environment for Decision-Making

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Abstract

Previous theories have suggested that Bonferroni mean (BM) and its extensions can fulfil the desired properties to become a good aggregation operator in managing interrelationship between arguments under fuzzy decision-making environment. However, along with this growth, there are concerns regarding the limitation of the BM and its extensions where interrelationship between arguments is limited to a pair of input arguments. In contrast to previous works, a novel normalized weighted Bonferroni mean aggregation operator considering Shapley fuzzy measure has been introduced, where the overall interactions of input arguments are combined. Unlike other extensions of BM that are mostly considered under fuzzy environment, this aggregation operation introduces the Shapley fuzzy measure to deal with interactions of all arguments under the interval-valued neutrosophic environment. Specifically, the interval-valued neutrosophic Shapley normalized weighted Bonferroni mean (INSNWBM) is proposed in this paper. The properties of INSNWBM such as reducibility, idempotency, monotonicity, commutativity, and boundedness are also presented as to reflect the interrelationship among multiple input arguments. In addition, we have also proposed successive steps of a decision-making procedure in which the proposed INSNWBM is included. Together included is a numerical example as to illustrate the applicability of the INSNWBM in decision-making. The consistency of the ranking results is confirmed by variations of parameters of INSNWBM. It is shown that the ranking results are almost consistent despite the different usages of parameter values. Results obtained appear to support the idea that the proposed aggregation operator is able to address the interrelationship between arguments in decision-making.

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Funding

This study was funded by TAPE-RG Grant No. 55155, Niche Research Grant Scheme (NRGS) Grant No. 53131, Fundamental Research Grant Scheme (FRGS) no. 59522, and MyBrainSC Scholarship under Ministry of Education Malaysia.

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Authors and Affiliations

  1. School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21300, Kuala Nerus, Terengganu, Malaysia

    Azzah Awang, Nur Aidya Hanum Aizam, Ahmad Termimi Ab Ghani & Lazim Abdullah

  2. Department of Fundamental and Applied Sciences, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Malaysia

    Mahmod Othman

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  1. Azzah Awang
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  2. Nur Aidya Hanum Aizam
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  3. Ahmad Termimi Ab Ghani
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Correspondence to Lazim Abdullah.

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Awang, A., Aizam, N.A.H., Ab Ghani, A.T. et al. A Normalized Weighted Bonferroni Mean Aggregation Operator Considering Shapley Fuzzy Measure Under Interval-valued Neutrosophic Environment for Decision-Making. Int. J. Fuzzy Syst. 22, 321–336 (2020). https://doi.org/10.1007/s40815-019-00752-5

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