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Properties of the solution set of a fuzzy relation equation from the viewpoint of attainability

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Abstract

 In a fuzzy relation equation, many properties of the solution set are known, especially when the basic spaces are all finite sets. However, when the basic spaces are infinite, only a few properties are known. In this paper, we introduce a new binary relation that is weaker than the ordinary one defined on fuzzy sets, and we show that an unattainable solution is partly characterized by the proposed binary relation.

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Authors and Affiliations

  1. Division of Systems and Information Engineering, Hokkaido University, Sapporo, 060-8628, Japan, , , , , , JP

    H. Imai, M. Miyakoshi & Y. Sato

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  1. H. Imai
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  2. M. Miyakoshi
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  3. Y. Sato
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Imai, H., Miyakoshi, M. & Sato, Y. Properties of the solution set of a fuzzy relation equation from the viewpoint of attainability. Soft Computing 6, 87–91 (2002). https://doi.org/10.1007/s005000100145

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  • DOI: https://doi.org/10.1007/s005000100145