The formalization of knowledge remains one of the main problems of informatization. Special, applied knowledge can be streamlined, brought to a logical level and used to solve specific problems of a qualitative nature. The problems of applied fuzzy knowledge formalization from the point of view of mathematical logic and the theory of fuzzy sets are considered. Use of the applied calculus of fuzzy predicates of the first order was developed and proposed for the representation of knowledge and problem solving. The developed methods were used in the expert system for scientific research in the field of molecular spectroscopy, as well as other subject areas.
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