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# Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making

by 1, 2 and 3,*
1
College of Economics and Management, Beijing University of Technology, Beijing 100124, China
2
Discipline of ICT, School of Technology, Environments and Design, College of Sciences and Engineering, University of Tasmania, Hobart, TAS 7001, Australia
3
College of Economics and Management, Harbin Engineering University, Harbin 150001, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1142; https://doi.org/10.3390/math7121142
Received: 6 November 2019 / Revised: 19 November 2019 / Accepted: 20 November 2019 / Published: 22 November 2019
Q-rung orthopair fuzzy set (q-ROFS) is a powerful tool to describe uncertain information in the process of subjective decision-making, but not express vast objective phenomenons that obey normal distribution. For this situation, by combining the q-ROFS with the normal fuzzy number, we proposed a new concept of q-rung orthopair normal fuzzy (q-RONF) set. Firstly, we defined the conception, the operational laws, score function, and accuracy function of q-RONF set. Secondly, we presented some new aggregation operators to aggregate the q-RONF information, including the q-RONF weighted operators, the q-RONF ordered weighted operators, the q-RONF hybrid operator, and the generalized form of these operators. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Meanwhile, we applied the proposed operators to the multi-attribute decision-making (MADM) problem and established a novel MADM method. Finally, the proposed MADM method was applied in a numerical example on enterprise partner selection, the numerical result showed the proposed method can effectively handle the objective phenomena with obeying normal distribution and complicated fuzzy information, and has high practicality. The results of comparative and sensitive analysis indicated that our proposed method based on q-RONF aggregation operators over existing methods have stronger information aggregation ability, and are more suitable and flexible for MADM problems. View Full-Text
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MDPI and ACS Style

Yang, Z.; Li, X.; Cao, Z.; Li, J. Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making. Mathematics 2019, 7, 1142. https://doi.org/10.3390/math7121142

AMA Style

Yang Z, Li X, Cao Z, Li J. Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making. Mathematics. 2019; 7(12):1142. https://doi.org/10.3390/math7121142

Chicago/Turabian Style

Yang, Zaoli; Li, Xin; Cao, Zehong; Li, Jinqiu. 2019. "Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making" Mathematics 7, no. 12: 1142. https://doi.org/10.3390/math7121142

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