The function structure analysis theory based on the factor space and space fault tree

In order to analyze system function structure, the system function structure analysis theory is put forward based on factor space theory. Factors space is more suitable for describing cognition process of intelligence science than the qualitative cartesian space. Based on factor logic, the justice system of the function structure analysis was built. It is proved that the system function logic structure is a minimal disjunctive normal form from the system function analysis. The relationship is discussed between the classification reasoning method of inward analysis of system structure in space fault tree (SFT) and the function structure analysis. The process of inward analysis of system function structure in SFT is realized by the function structure analysis theory. The original classification reasoning method is enhanced to the level of logic mathematics. The system function structures of both incomplete information and complete information are analyzed with the method respectively, and the minimal disjunctive normal forms obtained from the analyses are T=x1x4+x3x5+x1x2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T = x_{1}x_{4} + x_{3}x_{5} + x _{1}x_{2}$$\end{document} and T=x1x4+x3x5+x1x2x3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T = x_{1}x_{4} + x_{3}x_{5} +x_{1}x_{2} x_{3}$$\end{document}. The findings indicate that there are some implicit relationships between A3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{3}$$\end{document} and A2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{2}$$\end{document} , A1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{1}$$\end{document}. They added the phase set to the background sets and converted uncertain problems to certain ones.