Abstract
In the present work we consider several categories with a weaker structure than that of an L-valued topology, namely the categories of Čech L-fuzzy interior spaces, Čech L-fuzzy closure spaces, categories of L-fuzzy pretopological spaces and L-fuzzy co-pretopological spaces, the category of reflexive L-fuzzy relations and, finally, the category of spaces with L-fuzzy partitions. We connect all these categories and some of their subcategories using commutative diagrams of functors.
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References
Höhle, U.: Fuzzy sets and sheaves. Part I, basic concepts. Fuzzy Sets Syst. 158, 1143–1174 (2007)
Močkoř, J.: Spaces with fuzzy partitions and fuzzy transform. Soft Comput. 13(21), 3479–3492 (2017)
Novák, V., Perfilijeva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Boston (1999)
Perfilieva, I., Singh, A.P., Tiwari, S.P.: On the relationship among \(F\)-transform, fuzzy rough set and fuzzy topology. Soft Comput. 21, 3513–3523 (2017)
Perfilieva, I., Hurtik, P.: The \(F\)-transform plus PCA dimensionality reduction with application to pattern recognition in large databases. In: Proceedings of 2018 IEEE Symposium Series on Computational Intelligence (SSCI 2018), pp. 1020–1026 (2018)
Perfilieva, I.: F-transform-based optimization for image restoration (inpainting). In: Proceedings of 2018 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2018, 8–13 July 2018, Rio de Janeiro, Brazil (2018)
Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006)
Ramadan, A.A., Li, L.: Categories of lattice-valued closure (interior) operators and Alexandroff L-fuzzy topologies. Iranian J. Fuzzy Syst. (2018). https://doi.org/10.22111/IJFS.2018.4239
Rodabaugh, S.E.: Powerset operator foundation for poslat fuzzy SST theories and topologies. In: Höhle, U., Rodabaugh, S.E. (eds.) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, The Handbook of Fuzzy Sets Series, vol. 3, pp. 91–116. Kluwer Academic Publishers, Boston (1999)
Singh, A.P., Tiwari, S.P., Perfilieva, I.: \(F\)-transform, \(L\)-fuzzy partitions and \(l\)-fuzzy pretopological spaces: an operator oriented view (Submitted)
Zhang, D.: Fuzzy pretopological spaces, an extensional topological extension of FTS. Chin. Ann. Math. 3, 309–316 (1999)
Acknowledgements
This research was partially supported by the project 18-06915S provided by the Grant Agency of the Czech Republic.
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Močkoř, J., Perfilieva, I. (2019). Functors Among Categories of L-fuzzy Partitions, L-fuzzy Pretopological Spaces and L-fuzzy Closure Spaces. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_35
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DOI: https://doi.org/10.1007/978-3-030-21920-8_35
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