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Synthesis of Optimal Correction Functions in the Class of Disjunctive Normal Forms

Author

Listed:
  • Anvar Kabulov

    (School of Mathematics and Natural Sciences, New Uzbekistan University, Mustaqillik Ave. 54, Tashkent 100007, Uzbekistan
    Applied Mathematics and Intelligent Technologies Faculty, National University of Uzbekistan, Tashkent 100174, Uzbekistan)

  • Abdussattar Baizhumanov

    (Department of Mathematics, O. Zhanibekov South Kazakhstan State Pedagogical University, A. Baitursynov Street No.13, Shymkent City 160012, Kazakhstan)

  • Islambek Saymanov

    (School of Mathematics and Natural Sciences, New Uzbekistan University, Mustaqillik Ave. 54, Tashkent 100007, Uzbekistan
    Applied Mathematics and Intelligent Technologies Faculty, National University of Uzbekistan, Tashkent 100174, Uzbekistan)

Abstract

The paper proposes to consider individual heuristics as unreliably operating parts of the information processing system. In a separate case, several different heuristics are adopted to solve the same problem, and the results obtained are adjusted in a certain way. In this case, problems arise that are close in methodology to the problems of synthesizing reliable circuits from unreliable elements or making a collective expert decision. The work solves the problem of constructing an optimal correction function based on control material; classes of functions of k -valued logic under monotonicity restrictions are studied. A theorem on the completeness of the class of monotonic functions of k -valued logic for arbitrary k is proved, and a basis in the given class is proved and constructed. The problem of constructing an optimal corrector in the class of disjunctive normal forms of k -valued functions is solved.

Suggested Citation

  • Anvar Kabulov & Abdussattar Baizhumanov & Islambek Saymanov, 2024. "Synthesis of Optimal Correction Functions in the Class of Disjunctive Normal Forms," Mathematics, MDPI, vol. 12(13), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2120-:d:1429901
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