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A new approach to similarity and inclusion measures between general type-2 fuzzy sets

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Abstract

Interval type-2 fuzzy similarity and inclusion measures have been widely studied. In this paper, the axiomatic definitions of general type-2 fuzzy similarity and inclusion measures are given on the basis of interval type-2 fuzzy similarity and inclusion measures. To improve the shortcomings of the existing general type-2 fuzzy similarity and inclusion measures, we define two new general type-2 fuzzy similarity measures and two new general type-2 fuzzy inclusion measures based on \(\alpha \)-plane representation theory, respectively, and discuss their related properties. Unlike some existing measures, one of the proposed similarity and inclusion measures are expressed as type-1 fuzzy sets, and therefore these definitions are consistent with the highly uncertain nature of general type-2 fuzzy sets. The theoretical proof is also given to illustrate that the proposed measures are natural extensions of the most popular type-1 fuzzy measures. In the end, the performances of the proposed similarity and inclusion measures are examined.

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Acknowledgments

The authors would like to thank reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China(51177137,61134001) and the Fundamental Research Funds for the Central Universities(SWJTU11CX034).

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Authors and Affiliations

  1. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, 610031, China

    Tao Zhao

  2. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Jian Xiao, YiXing Li & XueSong Deng

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  1. Tao Zhao
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  2. Jian Xiao
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  3. YiXing Li
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  4. XueSong Deng
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Correspondence to Tao Zhao.

Additional information

Communicated by H. Hagras.

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Zhao, T., Xiao, J., Li, Y. et al. A new approach to similarity and inclusion measures between general type-2 fuzzy sets. Soft Comput 18, 809–823 (2014). https://doi.org/10.1007/s00500-013-1101-z

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