[1]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(04):656-664.[doi:10.11992/tis.201706057]
 BAO Yanke,WANG Peizhuang,GUO Sicong.Structure of factor space and the dual convolution theorem[J].CAAI Transactions on Intelligent Systems,2018,13(04):656-664.[doi:10.11992/tis.201706057]
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因素空间的结构与对偶回旋定理(/HTML)
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《智能系统学报》[ISSN:1673-4785/CN:23-1538/TP]

卷:
第13卷
期数:
2018年04期
页码:
656-664
栏目:
出版日期:
2018-07-05

文章信息/Info

Title:
Structure of factor space and the dual convolution theorem
作者:
包研科 汪培庄 郭嗣琮
辽宁工程技术大学 智能工程与数学研究院, 辽宁 阜新 123000
Author(s):
BAO Yanke WANG Peizhuang GUO Sicong
Institute of Intelligent Engineering and Mathematics, Liaoning Technical University, Fuxin 123000, China
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
Keywords:
factor spacestructurestaggered automorphism transformconvolution latticedual convolution theorem
分类号:
TP18;O29
DOI:
10.11992/tis.201706057
摘要:
基于概念的内涵与外延的对合性与反变关系,以及概念形成过程中概括与解析的辩证统一性,深入讨论了因素空间的数学结构问题。系统梳理了由认知本体论原理构造出的因素空间的基本概念与核心命题,为基于因素空间的知识发现理论与技术的研究提供了一种新的思想框架。首次提出了格上的交错自同构变换与回旋格的概念,证明了因素空间上的对偶回旋定理,揭示出因素空间数学结构的几何表象是一个麦乌比斯环,为阐释人类思维与概念形成过程的动力学机制提供了一个新的数学模型。
Abstract:
Based on two expressions consistency and the reverse-change relation of conceptual connotation and extension, 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 framework for both the theoretical and technological research of knowledge discovery based on factor space. We propose novel 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.

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备注/Memo

备注/Memo:
收稿日期:2017-06-16。
基金项目:国家自然科学基金项目(71371091);中国工程院2017年重点咨询项目(2017-XZ-23).
作者简介:包研科,男,1962年生,副教授,主要研究方向为工程数据分析、统计预测与决策、统计机器学习以及基于因素空间的知识发现理论与应用。发表学术论文20余篇,出版著作3部;汪培庄,男,1936年生,教授,博士生导师,主要研究方向为模糊数学和人工智能的理论与应用,创立模糊落影表示、真值流推论和因素空间理论,近年主要关注因素空间在人工智能和数据科学中的应用。获国家级奖励多项和国际奖项1项。发表学术论文200余篇,出版著作多部;郭嗣琮,男,1951年生,教授,博士生导师,国家政府特殊津贴获得者,主要研究方向为模糊数学、模糊预测与决策技术以及模糊运筹学理论与应用,创立了基于模糊结构元方法的模糊值函数分析学理论。发表学术论文200余篇,出版著作3部。
通讯作者:包研科.E-mail:baoyanke_9257@163.com.
更新日期/Last Update: 2018-08-25