智能系统学报2018，Vol.13Issue(4)：656-664,9.DOI:10.11992/tis.201706057
因素空间的结构与对偶回旋定理
Structure of factor space and the dual convolution theorem
摘要
Abstract
Based on two expressions consistency and the reverse-change relation of conceptual connotation and exten-sion,as well as the dialectical unity of summary and parsing in the concept formation process,in this paper,we present a detailed discussion of the mathematical structure of factor space.We systematically identify the basic concepts and core propositions of factor space,as constructed by the principle of cognitive ontology,and provide a new ideological frame-work for both the theoretical and technological research of knowledge discovery based on factor space.We propose nov-el concepts related to the staggered automorphism transform and the convolution lattice,prove the dual entanglement theorem of factor space,and introduce a geometrical representation of the mathematical structure of factor space as a Mobius strip,thereby establishing a new mathematical model for illustrating the dynamics mechanism of the formation of human thinking and conceptualization.关键词
因素空间/结构/交错自同构变换/回旋格/对偶回旋定理Key words
factor space/structure/staggered automorphism transform/convolution lattice/dual convolution theorem分类
信息技术与安全科学引用本文复制引用
包研科,汪培庄,郭嗣琮..因素空间的结构与对偶回旋定理[J].智能系统学报,2018,13(4):656-664,9.基金项目
国家自然科学基金项目(71371091) （71371091）
中国工程院2017年重点咨询项目(2017-XZ-23). （2017-XZ-23）
