Information technologies play a crucial role in the modern world. Computer systems are becoming big, critically significant. As a result, importance and relevance of the theoretical justification of correctness and reliability of information processing in various application areas are increasing. The basis for formal construction and research of computer systems based on various technologies is provided by algebraic structures. This fully applies to knowledge engineering, including production systems widely used in computer science. In the last decade, the author and his students have obtained a number of results related to logical systems of the production type. On the basis of algebraic lattices, there was developed a theory of LP structures (lattice production structures), which substantiates and effectively solves the problems of equivalent transformations, verification and minimization of knowledge bases. The method of backward inference (LP-inference), significantly reducing the number of appeals to external information sources, was introduced and studied. Subsequently, this theory was expanded for distributed production systems modeling. An important feature of modern intelligent systems is the fuzzy nature of knowledge and reasoning. In this circumstance, it seems to be relevant to extend the theory of LP structures to fuzzy production systems. The first steps in this direction were taken in two previous works with the authors participation. The concepts characterizing the fuzziness of the LP structure were introduced, and some useful properties of the fuzzy LP-inference were studied. The present work is devoted to the development of the theory of fuzzy LP structures for managing fuzzy knowledge bases and modeling fuzzy logical inference. The terminology of FLP structures (Fuzzy LP structures) with fuzzy logical relation is introduced. The definition of the logical closure of a fuzzy binary relation on a lattice is given; a theorem on its existence is presented. The theorem allows to introduce the concept of equivalent FLP structures and, respectively, in applications — of equivalent knowledge bases. The theorem on equivalent transformations of the FLP structure is proved. Its applied value is the method and its justification for automated transformations of fuzzy knowledge bases. Finally, a definition is introduced and a statement on the reduction of a fuzzy LP structure to a canonical form is proved. In applications, this format corresponds to a set of Horn fuzzy rules.