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Open AccessArticle

Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

1
Department of Mathematics and Statistic, International Islamic University, Islamabad 44000, Pakistan
2
School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, Shandong, China
3
Department of Mathematics and Sciences, University of New Mexico, 705 Gurley Ave, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 459; https://doi.org/10.3390/sym10100459
Received: 16 August 2018 / Revised: 27 September 2018 / Accepted: 28 September 2018 / Published: 2 October 2018
The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter. View Full-Text
Keywords: interval neutrosophic sets; Bonferroni mean; power operator; multi-attribute decision making (MADM) interval neutrosophic sets; Bonferroni mean; power operator; multi-attribute decision making (MADM)
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MDPI and ACS Style

Khan, Q.; Liu, P.; Mahmood, T.; Smarandache, F.; Ullah, K. Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making. Symmetry 2018, 10, 459. https://doi.org/10.3390/sym10100459

AMA Style

Khan Q, Liu P, Mahmood T, Smarandache F, Ullah K. Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making. Symmetry. 2018; 10(10):459. https://doi.org/10.3390/sym10100459

Chicago/Turabian Style

Khan, Qaisar; Liu, Peide; Mahmood, Tahir; Smarandache, Florentin; Ullah, Kifayat. 2018. "Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making" Symmetry 10, no. 10: 459. https://doi.org/10.3390/sym10100459

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