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A Novel Two Dimensional Pythagorean Fuzzy Sets Model with Its Application in Multi-attribute Decision Making

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Machine Learning for Cyber Security (ML4CS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12488))

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Abstract

Pythagorean fuzzy set (PFS) is a generalization of intuitionistic fuzzy set (IFS), which can express and handle uncertainty in uncertain environment more capable and is widely used in various fields. In the past, several methods of uncertainty measurement of PFSs have been proposed, however, some methods can not provide counterintuitive examples. Therefore, how to measure the uncertainty of PFSs is still an open question. Z-number is a new way to treat uncertainty and reliability of information, Z-number can greatly improve the accuracy and effectiveness of the information fusion process. However, one-dimensional index is not sufficient to express the expert’s assessment. On account of this point, this paper proposes a new uncertainty measurement method between two-dimensional Pythagorean fuzzy sets by using Deng entropy. This method is based on the operation distribution of membership function, non-membership function and hesitation function of two PFSs. Numerical examples show that the proposed method can produce higher identification with more feasible, reasonable and superior result. In addition, by comparing the application of different methods in medical diagnosis, we find that the new algorithm is as effective as other methods. These results prove the practicability of this method in dealing with medical diagnosis problems.

This research is supported by the National Natural Science Foundation of China (No. 62003280), Research Project of Education and Teaching Reform in Southwest University (No. 2019JY053), Fundamental Research Funds for the Central Universities (No. XDJK2019C085) and Chongqing Overseas Scholars Innovation Program (No. cx2018077).

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Authors and Affiliations

  1. School of Computer and Information Science, Southwest University, No. 2 Road, Beibei District, Chongqing, 400715, China

    Yi Fan & Fuyuan Xiao

Authors
  1. Yi Fan
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  2. Fuyuan Xiao
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Corresponding author

Correspondence to Fuyuan Xiao .

Editor information

Editors and Affiliations

  1. Xidian University, Xi'an, China

    Xiaofeng Chen

  2. Guangzhou University, Guangzhou, China

    Hongyang Yan

  3. Michigan State University, East Lansing, MI, USA

    Qiben Yan

  4. Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science, Thuwal, Saudi Arabia

    Xiangliang Zhang

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Fan, Y., Xiao, F. (2020). A Novel Two Dimensional Pythagorean Fuzzy Sets Model with Its Application in Multi-attribute Decision Making. In: Chen, X., Yan, H., Yan, Q., Zhang, X. (eds) Machine Learning for Cyber Security. ML4CS 2020. Lecture Notes in Computer Science(), vol 12488. Springer, Cham. https://doi.org/10.1007/978-3-030-62463-7_39

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  • DOI: https://doi.org/10.1007/978-3-030-62463-7_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62462-0

  • Online ISBN: 978-3-030-62463-7

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