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The approach to the development of intelligent decision support systems using ontology knowledge bases consisting of such systems in the article is considered. The classification of such systems in terms of their operation based on ontologies is carried out. The mathematical functioning of intelligent decision support systems and intelligent search system based on ontology is developed. The notion of adaptive ontologies is introduced. An adaptive ontology is proposed to define as an ontology with concepts and relations weighted according to its importance for a given subject domain. This model of ontology defines not only explicit, but also implicit knowledge. The mathematical functioning of intelligent decision support systems using adaptive ontologies formalizes decision making of such a system. Semantic metric based on adaptive ontologies was built, unlike other metrics, takes into account the causal relation between the concepts, not just their taxonomy. For feature problems mathematical software based on automated determination of properties of set concepts was developed, according to the values which the process of decision support was carried out.

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