Abstract
We observe that a Q-fuzzy topology, see e.g., Chen and Zhang (Fuzzy Sets Syst 161:2505–2514, 2010, [2]), on a set X is a ordinary subset (contained constants and closed under arbitrary sups and finite infs) of \(Q^X\), the latter is a set of all Q-fuzzy subsets of X. We use an analogy with the way how a fuzzy subgroupoid was introduced in Höhle (Non-classical logics and their applications to fuzzy subsets: a handbook on the mathematical foundations of fuzzy set theory. Kluwer Academic Publishers, Dordrecht, pp 53–105, 1995, [1]), and propose a new notion of an Q-fuzzy subtopology on X. In this contribution, we give an example of one important Q-fuzzy subtopology and discuss useful applications.
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Acknowledgements
The work has been partially supported by the project “LQ1602 IT4Innovations excellence in science” and by the Grant Agency of the Czech Republic (project No. 18-06915S). The author thanks anonymous reviewers for their help in improving the style of this article.
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Perfilieva, I. (2022). Q-Fuzzy Subtopology. In: Harmati, I.Á., Kóczy, L.T., Medina, J., Ramírez-Poussa, E. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems 3. Studies in Computational Intelligence, vol 959. Springer, Cham. https://doi.org/10.1007/978-3-030-74970-5_1
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DOI: https://doi.org/10.1007/978-3-030-74970-5_1
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