Abstract
The focus is on two spaces with a weaker structure than that of a fuzzy topology. The first one is a fuzzy pretopological space, and the second one is a space with an L-fuzzy partition. For a fuzzy pretopological space, we prove that it can be determined by a Čech interior operator and that the latter can be represented by a reflexive fuzzy relation. For a space with an L-fuzzy partition, we show that a lattice-valued \(F^{\downarrow }\)-transform is a strong Čech-Alexandrov fuzzy interior operator. Conversely, we found conditions that guarantee that a given L-fuzzy pretopology determines the L-fuzzy partition and the corresponding \(F^{\downarrow }\)-transform operator.
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Notes
- 1.
Čech interior operator differs from Kuratowski interior operator by the absence of the idempotency.
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Acknowledgement
The work was supported by the project “LQ1602 IT4Innovations excellence in science” and by the Grant Agency of the Czech Republic (project “New approaches to aggregation operators in analysis and processing of data”).
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Perfilieva, I., Tiwari, S.P., Singh, A.P. (2018). Lattice-Valued F-Transforms as Interior Operators of L-Fuzzy Pretopological Spaces. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 854. Springer, Cham. https://doi.org/10.1007/978-3-319-91476-3_14
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