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L-fuzzy concept analysis for three-way decisions: basic definitions and fuzzy inference mechanisms

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Abstract

In this paper, the basic ideas underlying fuzzy logic are introduced into the study of three-way formal concept analysis. This leads naturally to the notion of L-fuzzy three-way concepts. The L-fuzzy three-way operators and their inverse are defined and their properties are given. Based on these operators, two types of L-fuzzy three-way concepts are defined and the corresponding three-way concept lattices are constructed. A possibility theory reading of L-fuzzy three-way concepts is also provided. Moreover, the corresponding fuzzy inference method is studied. Two coherent fuzzy inference methods, the lower approximate fuzzy inference and the upper approximate fuzzy inference, are proposed, respectively.

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, China

    Xiaoli He & Ling Wei

  2. College of Science, Xi’an Shiyou University, Xi’an, 710065, China

    Xiaoli He & Yanhong She

Authors
  1. Xiaoli He
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  2. Ling Wei
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  3. Yanhong She
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Correspondence to Ling Wei.

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This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61772021, 11371014, 61472471 and 11531009) and the Innovation Talent Promotion Plan of Shaanxi Province for Young Sci-Tech New Star (No.2017KJXX-60).

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He, X., Wei, L. & She, Y. L-fuzzy concept analysis for three-way decisions: basic definitions and fuzzy inference mechanisms. Int. J. Mach. Learn. & Cyber. 9, 1857–1867 (2018). https://doi.org/10.1007/s13042-018-0857-y

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  • DOI: https://doi.org/10.1007/s13042-018-0857-y

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