Methods for Synthesizing Optimal K-Value Correcting Functions

This paper explores the problem of developing correcting functions that replace multiple unreliable (heuristic) recognition algorithms with a single, consistent decision function. The research concept stems from the fact that, in pattern recognition and collective expert decision-making problems, individual algorithms (heuristics) provide inconsistent or incomplete answers, requiring a mathematically sound method for their harmonization (correction) using test data. The methodological content of this paper consists of introducing classes of k-valued logic correcting functions that satisfy the constraints of preserving given sets (Constraint I) and monotonicity (Constraint II), and constructing algorithms for synthesizing a corrector that is optimal with respect to the linear performance functional for each combination of these constraints. The paper also provides a rationale for the optimality of the constructed algorithms (an optimality theorem) and an estimate of their time complexity.