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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Lattice-Valued F-Transforms as Interior Operators of L-Fuzzy Pretopological Spaces
verfasst von : Irina Perfilieva, S. P. Tiwari, Anand P. Singh
Erschienen in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations
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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.