In many Artrificial Intelligence problems an investigated object is considered as a set of its elements {ω₁, . . ., ω_t} and is characterized by properties of these elements and relations between them. These properties and relations may be set by predicates p₁, . . ., pn. The problems appeared with such an approach become NP-complete or NP-hard ones. To decrease the computational complexity of these problems a hierarchical multi-level description of classes was suggested. A logic-predicate recognition network may be constructed according to such a multi-level description. Such a network recognizes only objects which have been presented in the training set, but it may be easily retrained by a new object. After retraining it may change its configuration i.e., the number of levels and the number of nodes in every level. A modification of such a network is offered in this paper. This modification allows to do a fuzzy recognition of a new object and to calculate the degree of certainty that this object or its part belongs to some class of objects.