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Multiple attribute group decision making using J-divergence and evidential reasoning theory under intuitionistic fuzzy environment

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Abstract

The theory of intuitionistic fuzzy sets has been proved to be an effective and convenient tool in the construction of fuzzy multiple attribute group decision-making models to deal with the uncertainty in developing complex decision support systems. Concerning this topic, the current studies mainly focus on their attention on two aspects including aggregation operators on intuitionistic fuzzy sets and determining the weights of both decision makers and attributes. However, some challenges have not been fully considered including existing aggregation operators which may induce unreasonable results in some situations and how to objectively determine the weights of both attributes and decision makers to meet different decision-making demands. To overcome the challenges of existing decision-making models and to satisfy much more decision-making situations, a novel intuitionistic fuzzy multiple attribute group decision-making method via J-divergence and evidential reasoning theory is proposed in this paper as a supplement of conventional models. On the one hand, a weighted J-divergence of intuitionistic fuzzy sets and a J-divergence between two intuitionistic fuzzy matrices are introduced. Following the two concepts, two consensus-based approaches are proposed to determine the weights of both decision makers and attributes. The weights obtained from the proposed method can more accurately reflect the importance levels of both attributes and decision makers from the perspective of consensus by comparison with existing models. On the other hand, an evidential reasoning theory-based operator is established to replace conventional operators for aggregating intuitionistic fuzzy information. The fusion result via this operator is consistent with most of intuitionistic fuzzy numbers. With these works, the proposed method can provide more accurate and reasonable decision results than existing algorithms.

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Notes

  1. Concerning Examples 5 and 6, both IFWA-based method and IFWG-based method have employed score function to rank all the alternatives (see Definition 4). In addition, the problem of determining the weights has not been considered in some models, we have adopted the weights from JDER to these models.

Abbreviations

IFS:

Intuitionistic fuzzy set

IFSs:

Intuitionistic fuzzy sets

IFN:

Intuitionistic fuzzy number

IFNs:

Intuitionistic fuzzy numbers

MADM:

Multiple attribute decision making

MAGDM:

Multiple attribute group decision making

ER:

Evidential reasoning

DM:

Decision maker

DMs:

Decision makers

DM’s:

Decision maker’s

TOPSIS:

Technique for Order Preference by Similarity to an Ideal Solution

K–L divergence:

Kullback–Leibler divergence

D–S theory:

Dempster–Shafer theory

ERTIFA operator:

Evidential reasoning theory-based intuitionistic fuzzy averaging operator

IFWA:

Intuitionistic fuzzy weighted averaging

IFOWA:

Intuitionistic fuzzy ordered weighted averaging

IFPWA:

Intuitionistic fuzzy power weighted average

IFHWA:

Intuitionistic fuzzy Hamacher weighted averaging

IFHOWA:

Intuitionistic fuzzy Hamacher ordered weighted averaging

IFEWA:

Intuitionistic fuzzy Einstein weighted averaging

IFEOWA:

Intuitionistic fuzzy Einstein ordered weighted averaging

IFWGA:

Intuitionistic fuzzy weighted geometric averaging

IFOWGA:

Intuitionistic fuzzy ordered weighted geometric averaging

IFWG:

Intuitionistic fuzzy weighted geometric

IFHGWA:

Intuitionistic fuzzy Hamacher geometric weighted averaging

IFHGOWA:

Intuitionistic fuzzy Hamacher geometric ordered weighted averaging

IFEGA:

Intuitionistic fuzzy Einstein geometric averaging

IFEOGA:

Intuitionistic fuzzy Einstein ordered geometric averaging

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Acknowledgement

The authors are grateful to the editors and anonymous referees for their valuable comments and efforts, which have improved this paper. This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant 2018JBM013, the National Key R&D Program of China under Grant 2017YFF0108300, and the National Natural Science Foundation of China under Grants 51827813 and 61572063.

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Authors and Affiliations

  1. School of Computer and Information Technology, Beijing Jiaotong University, Beijing, 100044, China

    Yingjun Zhang, Shaohai Hu & Wei Zhou

  2. Beijing Key Lab of Traffic Data Analysis and Mining, Beijing Jiaotong University, Beijing, 100044, China

    Yingjun Zhang & Wei Zhou

  3. Institute of Information Science, Beijing Jiaotong University, Beijing, 100044, China

    Shaohai Hu

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  1. Yingjun Zhang
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Correspondence to Yingjun Zhang.

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Zhang, Y., Hu, S. & Zhou, W. Multiple attribute group decision making using J-divergence and evidential reasoning theory under intuitionistic fuzzy environment. Neural Comput & Applic 32, 6311–6326 (2020). https://doi.org/10.1007/s00521-019-04140-w

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