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Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection

Author

Listed:
  • Suizhi Luo

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Lining Xing

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

Abstract

Picture fuzzy numbers (PFNs), as the generalization of fuzzy sets, are good at fully expressing decision makers’ opinions with four membership degrees. Since aggregation operators are simple but powerful tools, this study aims to explore some aggregation operators with PFNs to solve practical decision-making problems. First, new operational rules, the interaction operations of PFNs, are defined to overcome the drawbacks of existing operations. Considering that interrelationships may exist only in part of criteria, rather than all of the criteria in reality, the partitioned Heronian aggregation operator is modified with PFNs to deal with this condition. Then, desirable properties are proved and several special cases are discussed. New decision-making methods with these presented aggregation operators are suggested to process hotel selection issues. Last, their practicability and merits are certified by sensitivity analyses and comparison analyses with other existing approaches. The results indicate that our methods are feasible to address such situations where criteria interact in the same part, but are independent from each other at different parts.

Suggested Citation

  • Suizhi Luo & Lining Xing, 2019. "Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection," Mathematics, MDPI, vol. 8(1), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:3-:d:299427
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    References listed on IDEAS

    as
    1. Weizhang Liang & Bing Dai & Guoyan Zhao & Hao Wu, 2019. "Assessing the Performance of Green Mines via a Hesitant Fuzzy ORESTE–QUALIFLEX Method," Mathematics, MDPI, vol. 7(9), pages 1-19, August.
    2. Guiwu Wei, 2018. "Uncertain Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making," International Journal of Decision Support System Technology (IJDSST), IGI Global, vol. 10(2), pages 40-64, April.
    3. Peide Liu & Peng Wang, 2017. "Some Improved Linguistic Intuitionistic Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 817-850, May.
    4. Guiwu Wei, 2016. "Picture fuzzy cross-entropy for multiple attribute decision making problems," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 17(4), pages 491-502, July.
    Full references (including those not matched with items on IDEAS)

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