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Advances in Computer Communication and Computational Sciences pp 199–210Cite as

A Parametric Method for Knowledge Measure of Intuitionistic Fuzzy Sets

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 924))

Abstract

Entropy is an important tool in measuring the uncertainty research of fuzzy system, in which many achievements have been obtained. Due to the hesitant degree, intuitionistic fuzzy sets (IFS) is more complex than the traditional fuzzy sets in ambiguity and uncertainty. Therefore, there are many challenges in the research of intuitionistic fuzzy entropy and intuitionistic fuzzy knowledge measure, especially the lack of deep research on the axiom system, unified theory, and method. Hence, this paper firstly studies the Szmidt and Kacprzyk’s axiom system, which is composed of order, non-negative boundedness, and symmetry. Meanwhile, we put forward some necessary and sufficient conditions and necessary conditions for order property. Simultaneously, the order property of some traditional and classical operators is proved by using the necessary and sufficient conditions. Then, a simple and convenient knowledge measure with parameter is proposed based on the order condition. Finally, based on intuitionistic fuzzy set, an experiment to test the order property is proposed. The simulation demonstrates that the results of the presented method are widely similar to that of the traditional algorithm under different parameter values, and in some special values, the results of this parametric method are more accurate than those of most classic methods.

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Acknowledgements

This paper is funded by the National statistical research key projects (No. 2016LZ18), Soft Science Project (No. 2015A070704051) and Natural Science Projects (No. 2016A030313688, No. 2016A030310105, No. 2018A030313470) and Quality engineering and teaching reform project (No. 125-XCQ16268) of Guangdong Province.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, 510006, China

    Zhen-hua Zhang

  2. Department of Informatics, University of Leicester, Leicester, LE1 7RH, UK

    Zhen-hua Zhang

  3. School of Economics and Statistics, Guangzhou University, Guangzhou, 510006, China

    Shen-guo Yuan

  4. Department of Computer Science and Technology, University of Cambridge, Cambridge, CB3 0FD, UK

    Chao Ma

  5. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85281, USA

    Jin-hui Xu

  6. Education Technology Center, Guangdong University of Foreign Studies, Guangzhou, 510006, China

    Jing Zhang

Authors
  1. Zhen-hua Zhang
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  2. Shen-guo Yuan
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  3. Chao Ma
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  4. Jin-hui Xu
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  5. Jing Zhang
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Corresponding authors

Correspondence to Zhen-hua Zhang or Jing Zhang .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Missouri–St. Louis, St. Louis, MO, USA

    Sanjiv K. Bhatia

  2. CSED, ABES Engineering College, Ghaziabad, Uttar Pradesh, India

    Shailesh Tiwari

  3. Department of Computer Science and Engineering, Motilal Nehru National Institute of Technology, Allahabad, Uttar Pradesh, India

    Krishn K. Mishra

  4. Department of Information Technology, Rajkiya Engineering College, Azamgarh, Uttar Pradesh, India

    Munesh C. Trivedi

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© 2019 Springer Nature Singapore Pte Ltd.

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Zhang, Zh., Yuan, Sg., Ma, C., Xu, Jh., Zhang, J. (2019). A Parametric Method for Knowledge Measure of Intuitionistic Fuzzy Sets. In: Bhatia, S., Tiwari, S., Mishra, K., Trivedi, M. (eds) Advances in Computer Communication and Computational Sciences. Advances in Intelligent Systems and Computing, vol 924. Springer, Singapore. https://doi.org/10.1007/978-981-13-6861-5_18

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