Representation of Tolerance Relations and Granulation of Information with Respect to Substructural Logic

The paper investigates fuzzy tolerance relations with membership function valued in a noncommutative residuated lattice. Such tolerance relations appear in the context of the theory of formal concepts. The paper shows that given a fuzzy tolerance relation, it is possible to identify a system of attr...

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Bibliographic Details
Published in2019 XXII International Conference on Soft Computing and Measurements (SCM) pp. 12 - 14
Main Authors Volkova, E. S., Gisin, V. B.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2019
Subjects
concept lattice
Lattices
Logic
Object recognition
residuated lattice
substructural logic
tolerance relation
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DOI10.1109/SCM.2019.8903804

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Summary:The paper investigates fuzzy tolerance relations with membership function valued in a noncommutative residuated lattice. Such tolerance relations appear in the context of the theory of formal concepts. The paper shows that given a fuzzy tolerance relation, it is possible to identify a system of attributes and an object-to-attribute relationship, so that the objects are similar to the extent they have common attributes. For this purpose the tolerance classes can be taken as attributes. The paper presents the general description of the structure of fuzzy tolerance classes.
DOI:10.1109/SCM.2019.8903804