Abstract:
The paper is devoted to research in the field of fuzzy model theory. The paper introduces the notion of a coordinated valuation of sentences of a given signature, which can be considered as a generalisation of the notion of a realizable set of sentences to the fuzzy case. By analogy with the classical case, classes of fuzzy models generated by coordinated valuations are considered, and the notion of axiomatised class of fuzzy models is introduced.
Fuzzy truth values of different sentences can be considered as a formalisation of subjective evaluative knowledge of experts about object domain. To formalise such knowledge, interval and point valuations are considered in this paper, and model-theoretic properties of classes of fuzzy models generated by such valuations are described.
Often, at formalisation of some system it is necessary to take into account also the environment in which this system is located and with which it inevitably interacts. In this case it is necessary to include in the fuzzy model the formalisation of knowledge not only about the system itself, but also about the environment in which it lives. The system itself can be considered as a submodel of the full model. The paper introduces the concept of submodel of a fuzzy model and also the concept of factorisation of a class of fuzzy models by fixed submodels. It is proved that equivalence classes of such factorisation are axiomatised classes of fuzzy models.
Keywords:fuzzy model, fuzzy model theory, coordinated valuation, interval valuation, axiomatised class of fuzzy models.
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