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Fuzzy objects in spaces with fuzzy partitions

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Abstract

A theory of fuzzy objects is derived in the category SpaceFP of spaces with fuzzy partitions, which generalize classical fuzzy sets and extensional maps in sets with similarity relations. It is proved that fuzzy objects in SpaceFP can be characterized by some morphisms in the category of sets with similarity relations. A powerset object functor \({\mathcal {F}}\) in the category SpaceFP is introduced and it is proved that \({\mathcal {F}}\) defines a CSLAT-powerset theory in the sense of Rodabaugh.

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Acknowledgements

This study was funded by the Centre of Excellence Project LQ1602.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Jiří Močkoř & Michal Holčapek

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  1. Jiří Močkoř
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  2. Michal Holčapek
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Correspondence to Jiří Močkoř.

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Communicated by A. Di Nola.

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Močkoř, J., Holčapek, M. Fuzzy objects in spaces with fuzzy partitions. Soft Comput 21, 7269–7284 (2017). https://doi.org/10.1007/s00500-016-2431-4

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