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

Author

Listed:
  • Zaoli Yang

    (College of Economics and Management, Beijing University of Technology, Beijing 100124, China)

  • Xin Li

    (College of Economics and Management, Beijing University of Technology, Beijing 100124, China)

  • Zehong Cao

    (Discipline of ICT, School of Technology, Environments and Design, College of Sciences and Engineering, University of Tasmania, Hobart, TAS 7001, Australia)

  • Jinqiu Li

    (College of Economics and Management, Harbin Engineering University, Harbin 150001, China)

Abstract

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.

Suggested Citation

  • Zaoli Yang & Xin Li & Zehong Cao & Jinqiu Li, 2019. "Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making," Mathematics, MDPI, vol. 7(12), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1142-:d:289879
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    References listed on IDEAS

    as
    1. Runtong Zhang & Jun Wang & Xiaomin Zhu & Meimei Xia & Ming Yu, 2017. "Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making," Complexity, Hindawi, vol. 2017, pages 1-16, August.
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    3. Jian-qiang Wang & Peng Zhou & Kang-jian Li & Hong-yu Zhang & Xiao-hong Chen, 2014. "Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1103-1122, October.
    4. Ping Wang & Jie Wang & Guiwu Wei & Cun Wei, 2019. "Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications," Mathematics, MDPI, vol. 7(4), pages 1-23, April.
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