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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 56

Pairwise Independence of the Blurry Model Submodels

Author(s)

Gulnara E. Yakhyaeva

Novosibirsk State Technical University, Novosibirsk, Russian Federation

Abstract
This paper is devoted to research in the theory of blurry models, which serves as a methodology for the logical formalization of subject domains under conditions of imprecision and incompleteness of knowledge about these domains. The article introduces the concept of a submodel of a blurry model as an extension of the notion of a submodel of a classical model, and also defines pairwise independence of submodels: submodels are independent if the events described by the signature of one model are independent from the events described by the signature of another model. The independence of submodels can be interpreted as the mutual independence of groups of objects within the subject domain, i.e., their autonomy and lack of influence on each other. A theorem is proven that formalizes the criterion (i.e., necessary and sufficient condition) for pairwise independence of submodels. Based on the property of submodel independence, blurry models are divided into separable models and entangled models. Each separable model decomposes into a separable union of its submodels. There may be several such decompositions for a given model, among which a “minimal” decomposition, called normal, is selected; a theorem on the uniqueness of the normal decomposition is proven. An algorithm for finding the normal decomposition of a blurry model into a separable union of submodels is presented, and the correctness of this algorithm is proven.
About the Authors
Gulnara E. Yakhyaeva, Cand. Sci. (Phys.-Math.), Assoc. Prof., Novosibirsk State Technical University, Novosibirsk, 630073, Russian Federation, gul nara@mail.ru
For citation
Yakhyaeva G. E. Pairwise Independence of the Blurry Model Submodels. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 56, pp. 160–175. (in Russian) https://doi.org/10.26516/1997-7670.2026.56.160
Keywords
blurry model, pairwise independent submodels, separable model, entangled model
UDC
004.827
MSC
68T27, 68T30
DOI
https://doi.org/10.26516/1997-7670.2026.56.160
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