Application of the Bipolar Neutrosophic Hamacher Averaging Aggregation Operators to Group Decision Making: An Illustrative Example

被引:10
作者
Jamil, Muhammad [1 ]
Abdullah, Saleem [2 ]
Khan, Muhammad Yaqub [1 ]
Smarandache, Florentin [3 ]
Ghani, Fazal [2 ]
机构
[1] Riphah Int Univ, Dept Math & Stat, Islamabad 44000, Pakistan
[2] Abdul Wali Khan Univ, Dept Math, Mardan 23200, Pakistan
[3] Univ New Mexico, Dept Math & Sci, 705 Gurley Ave, Gallup, NM 87301 USA
来源
SYMMETRY-BASEL | 2019年 / 11卷 / 05期
关键词
BNHWA aggregation operator; BNHOWA aggregation operator; BNHHA aggregation operator; score function; accuracy function; certainty function; group decision making; FUZZY NUMBERS; SETS;
D O I
10.3390/sym11050698
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
The present study aims to introduce the notion of bipolar neutrosophic Hamacher aggregation operators and to also provide its application in real life. Then neutrosophic set (NS) can elaborate the incomplete, inconsistent, and indeterminate information, Hamacher aggregation operators, and extended Einstein aggregation operators to the arithmetic and geometric aggregation operators. First, we give the fundamental definition and operations of the neutrosophic set and the bipolar neutrosophic set. Our main focus is on the Hamacher aggregation operators of bipolar neutrosophic, namely, bipolar neutrosophic Hamacher weighted averaging (BNHWA), bipolar neutrosophic Hamacher ordered weighted averaging (BNHOWA), and bipolar neutrosophic Hamacher hybrid averaging (BNHHA) along with their desirable properties. The prime gain of utilizing the suggested methods is that these operators progressively provide total perspective on the issue necessary for the decision makers. These tools provide generalized, increasingly exact, and precise outcomes when compared to the current methods. Finally, as an application, we propose new methods for the multi-criteria group decision-making issues by using the various kinds of bipolar neutrosophic operators with a numerical model. This demonstrates the usefulness and practicality of this proposed approach in real life.
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页数:18
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