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Interval-valued intuitionistic fuzzy jenson-shannon divergence and its application in multi-attribute decision making

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Abstract

Interval-Valued Intuitionistic Fuzzy Set (IVIFS) is an effective tool to model uncertainty, and has received much attention. When applying IVIFS to solve real problems such as Multi-Attribute Decision Making (MADM) problem, how to measure the distance between two Interval-Valued Intuitionistic Fuzzy Values (IVIFVs) is an essential problem. In this paper, a novel distance of IVIFS called Interval-Valued Intuitionistic Fuzzy Jenson-Shannon (IVIFJS) divergence is proposed, which can measure the difference or dissimilarity between IVIFSs. First, we propose a new Evaluation Score Function of the IVIFV, the score function considering the weight of membership and non-membership, which is more flexible than other existing score functions of IVIFV. Then, we find that the Evaluation Score Function is enclosed in a fixed interval, denoted as the largest possible range. Additionally, we find that the Evaluation Score Function can be approximately regarded to have Gaussian distribution over its largest range. Based on this, we propose a novel divergence measure operator for IVIFS named Interval-valued Intuitionistic Fuzzy Jenson-Shannon (IVIFJS) divergence by extending from discrete Jenson-Shannon (JS) divergence. Some useful mathematical properties of JS divergence, including boundness, symmetric and triangular inequality, are maintained in the proposed IVIFJS divergence. Next, we design a novel MADM method based on the proposed divergence operator. Further, some numerical examples are evaluated to illustrate the applicability and plausibility of the proposed method by comparing with other existing MADM methods. Then, the robustness and stability of the proposed MADM method are verified through sensitivity analysis on numerical examples. Finally, the proposed MADM method is applied in the applications of medical diagnosis and network system selection to verify the practicability of the proposed method.

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Acknowledgment

The authors would like to express the sincere appreciation to the editor and anonymous reviewers for their insightful comments, which greatly improve the quality of this paper, and also greatly appreciate research assistant Yangyang Zhao who discussed many issues of this work and support this work. This research is supported by the National Natural Science Foundation of China under Grants 62003280 and 61976120, Chongqing Talents: Exceptional Young Talents Project (CQYC202105031), and the Natural Science Foundation of Jiangsu Province under Grant BK20191445, and the Qing Lan Project of Jiangsu Province.

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  1. School of Big Data and Software Engineering, Chongqing University, Chongqing, 401331, China

    Zhe Wang & Fuyuan Xiao

  2. School of Information Science and Technology, Nantong University, Nantong, 226019, China

    Weiping Ding

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  1. Zhe Wang
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  2. Fuyuan Xiao
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Correspondence to Fuyuan Xiao.

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Wang, Z., Xiao, F. & Ding, W. Interval-valued intuitionistic fuzzy jenson-shannon divergence and its application in multi-attribute decision making. Appl Intell 52, 16168–16184 (2022). https://doi.org/10.1007/s10489-022-03347-0

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