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Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making

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  • Wen Jiang
  • Boya Wei

Abstract

The theory of intuitionistic fuzzy sets (IFS) is widely used for dealing with vagueness and the Dempster--Shafer (D-S) evidence theory has a widespread use in multiple criteria decision-making problems under uncertain situation. However, there are many methods to aggregate intuitionistic fuzzy numbers (IFNs), but the aggregation operator to fuse basic probability assignment (BPA) is rare. Power average (P-A) operator, as a powerful operator, is useful and important in information fusion. Motivated by the idea of P-A power, in this paper, a new operator based on the IFS and D-S evidence theory is proposed, which is named as intuitionistic fuzzy evidential power average (IFEPA) aggregation operator. First, an IFN is converted into a BPA, and the uncertainty is measured in D-S evidence theory. Second, the difference between BPAs is measured by Jousselme distance and a satisfying support function is proposed to get the support degree between each other effectively. Then the IFEPA operator is used for aggregating the original IFN and make a more reasonable decision. The proposed method is objective and reasonable because it is completely driven by data once some parameters are required. At the same time, it is novel and interesting. Finally, an application of developed models to the ‘One Belt, One road’ investment decision-making problems is presented to illustrate the effectiveness and feasibility of the proposed operator.

Suggested Citation

  • Wen Jiang & Boya Wei, 2018. "Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 582-594, February.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:3:p:582-594
    DOI: 10.1080/00207721.2017.1411989
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    Cited by:

    1. Peide Liu & Xiaoxiao Liu & Guiying Ma & Zhaolong Liang & Changhai Wang & Fawaz E. Alsaadi, 2020. "A Multi-Attribute Group Decision-Making Method Based on Linguistic Intuitionistic Fuzzy Numbers and Dempster–Shafer Evidence Theory," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 499-524, April.
    2. Deng, Xinyang & Jiang, Wen & Wang, Zhen, 2019. "Zero-sum polymatrix games with link uncertainty: A Dempster-Shafer theory solution," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 101-112.
    3. Wen, Tao & Jiang, Wen, 2018. "An information dimension of weighted complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 388-399.
    4. Gia Sirbiladze, 2021. "Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment," Mathematics, MDPI, vol. 9(18), pages 1-36, September.
    5. Xiaoxuan Hu & Yanjun Wang & Haiquan Sun & Peng Jin, 2022. "A remote sensing satellite observation scheme evaluation method based on granular computing of intuitionistic linguistic preference relation," Annals of Operations Research, Springer, vol. 316(1), pages 343-364, September.
    6. Bowen Qin & Fuyuan Xiao, 2019. "An improved method to determine basic probability assignment with interval number and its application in classification," International Journal of Distributed Sensor Networks, , vol. 15(1), pages 15501477188, January.

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