基于可变模糊集的辩证法三大规律数学定理及其应用  

Three mathematical theorems of dialectics based on variable fuzzy sets and their application

作　　者：陈守煜[1] 

机构地区：[1]大连理工大学建设工程学部,辽宁大连116024

出　　处：《大连理工大学学报》2010年第5期838-844,共7页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(50779005);水利部科技创新资助项目(SCXC2005-01)

摘　　要：数学思维辩证化与哲学规律数学化,是数学与哲学领域中的前沿研究命题.基于可变模糊集理论,率先提出对立统一、质量互变与否定的否定定理.突破了长期未能用严密的数学定理表达唯物辩证法哲学的三大基本规律:对立统一、质量互变与否定的否定规律的难题;并将定理用于水资源系统(含陆海空协同系统)评价,提出水资源系统评价的可变模糊集原理与模型.最后将定理用于识别可拓学(物元分析)的数学与逻辑错误.Dialecticization of mathematical thinking and mathematicization of philosophical law are forefront research propositions in the area of mathematics and philosophy.Based on the variable fuzzy set theory,the theorems of unity of opposites,mutual change of quality and quantity and negation of negation are firstly put forward.They break through long-term problems that rigorous mathematical theorems were used to express three dialectical philosophical laws of materialistic dialectics of unity of opposites,mutual change of quality and quantity and negation of negation.The theorems are applied to assessment of water resources system,which includes collaborative system of land,sea and sky,and the variable fuzzy sets＇principle and model about the assessment of water resources system are proposed.Finally,the theorems are used to identify mathematical and logic errors in extenics（matterelement analysis）.

关 键 词：可变模糊集 对立统一定理 质量互变定理 否定的否定定理 水资源评价 可拓学 

分 类 号：O159[理学—数学]