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Open AccessArticle

Relational Variants of Lattice-Valued F-Transforms

Institute for Research and Applications of Fuzzy Modelling, NSC IT4Innovations, University of Ostrava, 702 00 Ostrava, Czech Republic
Received: 3 November 2019 / Revised: 13 December 2019 / Accepted: 17 December 2019 / Published: 19 December 2019
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications)
Two categories of lower and upper lattice-valued F-transforms with fuzzy relations as morphisms are introduced, as generalisations of standard categories of F-transforms with maps as morphisms. Although F-transforms are defined using special structures called spaces with fuzzy partitions, it is shown that these categories are identical to the relational variants of the two categories of semimodule homomorphisms where these fuzzy partitions do not occur. This a priori independence of the F-transform on spaces with fuzzy partitions makes it possible, for example, to use a simple matrix calculus to calculate F-transforms, or to determine the image of F-transforms in relational morphisms of the two categories. View Full-Text
Keywords: spaces with fuzzy partition; F-transform; semimodule; semimodule homomorphism; residuated lattice; MV-algebra; morphisms; functors spaces with fuzzy partition; F-transform; semimodule; semimodule homomorphism; residuated lattice; MV-algebra; morphisms; functors
MDPI and ACS Style

Močkoř, J. Relational Variants of Lattice-Valued F-Transforms. Axioms 2020, 9, 1.

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