On the Local Coordination of Fuzzy Valuations

Abstract

The paper is devoted to the model-theoretic formalization of the semantic model of the object domain. The article discusses the concept of a fuzzy model, which is a model where the truth function exhibits properties of a fuzzy measure. We demonstrate that a fuzzy model is a generalization of the concept of fuzzification of a precedent (semantic) model to include a countable number of precedents. In practice, it is common to have partial expert knowledge about the set of events in the object domain, making it difficult to immediately describe the fuzzy model. Additionally, since expert valuations are subjective, they may be incorrect and inconsistent with any fuzzy model. In the article, we introduce the concepts of coordinated and locally coordinated valuation of a set of sentences, and provide proofs for interval theorems and an analogue of the compactness theorem.