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Certain information granule system as a result of sets approximation by fuzzy context. (English) Zbl 1460.68107
Summary: This paper presents the application of abstraction methods in creating concepts that allow to describe and solve more complex problems of knowledge representation in semantic networks. In the Semantic Web, knowledge is represented by the attributive language AL. There are many information granules theories formulated in different theories such as set theory, probability theory, possible data sets in the evidence systems, shadowed sets, fuzzy set theory, and rough set theory. In order to equally interpret AL language expressions in different information granules theories within the Semantic Web, it is assumed that AL language expressions are interpreted in the chosen relational system called a granule system. This paper formally describes information granule system and shows the example how to formulate such granule system in the theory of the contextual rough sets [E. Bryniarski and U. Wybraniec-Skardowska, J. Appl. Non-Class. Log. 8, No. 1–2, 9–26 (1998; Zbl 0957.03052)] which describes inclusions of fuzzy context relations with some error. Defined granule system allows to interpret AL languages. It is shown that there is such subsystem of this granule system that is adequate i.e. it is homomorphic within some ordered set algebra.

68T37 Reasoning under uncertainty in the context of artificial intelligence
68T30 Knowledge representation
Full Text: DOI
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