Functors Among Categories of L-fuzzy Partitions, L-fuzzy Pretopological Spaces and L-fuzzy Closure Spaces
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.
This research was partially supported by the project 18-06915S provided by the Grant Agency of the Czech Republic.
- 5.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)Google Scholar
- 6.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)Google Scholar
- 9.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)Google Scholar
- 10.Singh, A.P., Tiwari, S.P., Perfilieva, I.: \(F\)-transform, \(L\)-fuzzy partitions and \(l\)-fuzzy pretopological spaces: an operator oriented view (Submitted)Google Scholar