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Mathematics 2019, 7(1), 97; https://doi.org/10.3390/math7010097

Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment

1
Department of Computer Science, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
2
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
*
Author to whom correspondence should be addressed.
Received: 23 November 2018 / Revised: 9 January 2019 / Accepted: 11 January 2019 / Published: 17 January 2019
(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)
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Abstract

In real applications, most decisions are fuzzy decisions, and the decision results mainly depend on the choice of aggregation operators. In order to aggregate information more scientifically and reasonably, the Heronian mean operator was studied in this paper. Considering the advantages and limitations of the Heronian mean (HM) operator, four Heronian mean operators for bipolar neutrosophic number (BNN) are proposed: the BNN generalized weighted HM (BNNGWHM) operator, the BNN improved generalized weighted HM (BNNIGWHM) operator, the BNN generalized weighted geometry HM (BNNGWGHM) operator, and the BNN improved generalized weighted geometry HM (BNNIGWGHM) operator. Then, their propositions were examined. Furthermore, two multi-criteria decision methods based on the proposed BNNIGWHM and BNNIGWGHM operator are introduced under a BNN environment. Lastly, the effectiveness of the new methods was verified with an example. View Full-Text
Keywords: bipolar neutrosophic number (BNN); BNN improved generalized weighted HM (BNNIGWHM) operator; BNN improved generalized weighted geometry HM (BNNIGWGHM) operator; decision-making bipolar neutrosophic number (BNN); BNN improved generalized weighted HM (BNNIGWHM) operator; BNN improved generalized weighted geometry HM (BNNIGWGHM) operator; decision-making
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Fan, C.; Ye, J.; Feng, S.; Fan, E.; Hu, K. Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment. Mathematics 2019, 7, 97.

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