An algebraic model of the distributedproduction system with fuzzy rules

Abstract

The algebraic theory of LP-structures is intended for modeling and optimization of production and similar systems in computer science. One of its areas of application is intelligent systems based on rules in production form of. In previous studies, the authors obtained results that substantiate and automate the solution of a number of problems for production systems: equivalent transformations, elimination of redundancy, verification, acceleration of backward inference.In this paper, we introduce and study the LP structure, the semantics of which incorporates (covers) distributed fuzzy production systems. The terminology of FDLP structures (Fuzzy Distributed LP structures) with a fuzzy binary relation is introduced. A definition of the logical closure of a fuzzy binary relation is given, a theorem on its existence is presented. The theorem allows you to introduce the concept of equivalent FDLP structures, respectively, in applications – equivalent knowledge bases. A theorem on equivalent transformations of an FDLP structure is formulated. Its applied value is the method and its justification for automated transformations of distributed fuzzy knowledge bases. A statement on the reduction of the FDLP structure to a canonical form is also presented. In applications this format corresponds to the set of Horn rules.Within the framework of the constructed extended model, the possibilities of the theory of LP structures are available in the construction and study of distributed intelligent systems with fuzzy rules.