Equations in a fuzzy distributed lp-structure and the possibility of their application in intelligent systems

Abstract

The algebraic theory of LP-structures proposes and substantiates a formal methodology for knowledge management in intelligent production-type systems. It provides an effective solution to a number of important problems associated with production systems. These include equivalent transformations, verification, optimization of knowledge bases. An important section of the theory is also the method of relevant backward logical inference (LP-inference) aimed at reducing the number of calls to external sources of information. The theoretical basis of the method is the apparatus of production-logical equations in LP-structures. As the statistics of experiments show, when solving the equation and processing a set of solutions, it is possible to reduce the number of external requests during the inference process by an average of 15–20 %. The article defines and investigates an extended class of such equations for an algebraic system (FDLP-structure) that models distributed knowledge systems of production type with fuzzy rules. The results obtained by the author on the solvability of the equations and the method for their solution are announced. Finding a solution to an equation in an FDLP-structure corresponds to backward fuzzy inference in a distributed intelligent system. The considered class of equations creates the basis for advances in the field of optimization of fuzzy distributed inference and in verification of the corresponding knowledge bases. Variants of backward inference strategies using several relevance parameters are proposed. Another possible application of the apparatus of production-logical equations is the verification of knowledge bases of intelligent systems. The paper formulates a methodology and a general algorithm for applying equations to the verification of fuzzy distributed knowledge bases in terms of identifying contradictions and redundancy. The next steps of research in the direction under consideration are the refinement and software implementation of the application of the new relevance parameters of the FDLP-inference, and the statistical analysis of the results.