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Picture inference system: a new fuzzy inference system on picture fuzzy set

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Abstract

In this paper, we propose a novel fuzzy inference system on picture fuzzy set called picture inference system (PIS) to enhance inference performance of the traditional fuzzy inference system. In PIS, the positive, neutral and negative degrees of the picture fuzzy set are computed using the membership graph that is the combination of three Gaussian functions with a common center and different widths expressing a visual view of degrees. Then, the positive and negative defuzzification values, synthesized from three degrees of the picture fuzzy set, are used to generate crisp outputs. Learning in PIS including training centers, widths, scales and defuzzification parameters is also discussed. The system is adapted for all architectures such as the Mamdani, the Sugeno and the Tsukamoto fuzzy inferences. Experimental results on benchmark UCI Machine Learning Repository datasets and an example in control theory - the Lorenz system are examined to verify the advantages of PIS.

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Acknowledgments

The authors wish to thank the Editor-in-chief and anonymous reviewers for their valuable comments and suggestions. We acknowledge the Center for High Performance Computing, VNU University of Science for executing the program on the IBM 1350 cluster server.

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Authors and Affiliations

  1. Division of Data Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Le Hoang Son

  2. Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Le Hoang Son

  3. VNU University of Science, Vietnam National University, Hanoi, Vietnam

    Pham Van Viet

  4. School of Information and Communication Technology, Hanoi University of Science and Technology, Hanoi, Vietnam

    Pham Van Viet & Pham Van Hai

Authors
  1. Le Hoang Son
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  2. Pham Van Viet
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  3. Pham Van Hai
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Corresponding author

Correspondence to Le Hoang Son.

Additional information

This work is dedicated to Prof. Bui Cong Cuong (Institute of Mathematics, VAST) for 3-year presence of the picture fuzzy set.

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Son, L.H., Van Viet, P. & Van Hai, P. Picture inference system: a new fuzzy inference system on picture fuzzy set. Appl Intell 46, 652–669 (2017). https://doi.org/10.1007/s10489-016-0856-1

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  • DOI: https://doi.org/10.1007/s10489-016-0856-1

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