Authors A.N. Tselykh, V.S. Vasilev, L.A. Tselykh
Month, Year 08, 2016 @en
Index UDC 004.891.2
DOI 10.18522/2311-3103-2016-8-122137
Abstract In this paper we present a new approach to the development of the knowledge base of pro-duction Expert System (ES) based on the properties of cause-and-effect relations between the attrib-utes of a logical inference. It is proposed to use fuzzy cognitive maps, which are represented by fuzzy weighted signed directed graphs with feedback cycles; the graph stands as a base to generate antecedents and consequents set of the fuzzy rules to the ES based on the fuzzy inference engine. The resulting knowledge base uses the system qualities to improve the intelligence of logical inference. Modern graphs have a high degree of dimensionality and multiple cycles, which greatly complicate the heuristic definition of attributes of logical inference. The problem of correction of the feedback gear ratio is resolved by reducing the adjacency matrix (as it possible) to the upper (or lower) triangular form using the quadratic functionals of the mechanistic analogy (barrier penalty, "inverse"). The first type is a fixed signed convex functionals, so the minimization process has a unique solution obtained by any methods of the 0-th and 1-th order. Functionals of the second type are unbounded, but, as it is constantly mapping a real-valued solution to integer permutations, so the problem has also a solution that is obtained with the same methods. Minimization algorithm of functional presented by the paired comparisons method is presented. It is shown that the algorithm is computationally efficient, relevant to O(n3) time hardness. We conducted a series of numerical experiments to analyze and compare the quality of the solutions, as well as determine the best functional. The experiment showed efficiency for the matrix size of 103х103. The algorithm would require to solve the problem of accumulation of rounding errors in floating point for very large matrices (big data). Evaluation of the seven types of mechanistic analogies functional based on feasibility, performance, effectiveness and applicability of the subject area has been implemented. The approach of a sequence transformation of the original matrix of fuzzy graph model with two types of qualities functional is described. It allows generating the attributes of production ES.

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Keywords Expert systems; signed directed weighted cyclic graphs; functionals based on a mechanistic analogy.
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