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基于可变模糊集的辩证法三大规律数学定理及其应用
引用本文:陈守煜.基于可变模糊集的辩证法三大规律数学定理及其应用[J].大连理工大学学报,2010,50(5):838-844.
作者姓名:陈守煜
作者单位:大连理工大学,建设工程学部,辽宁,大连,116024
基金项目:国家自然科学基金,水利部科技创新资助项目
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.

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

Three mathematical theorems of dialectics based on variable fuzzy sets and their application
CHEN Shouyu.Three mathematical theorems of dialectics based on variable fuzzy sets and their application[J].Journal of Dalian University of Technology,2010,50(5):838-844.
Authors:CHEN Shouyu
Abstract:Based on assurance issue under stochastic interest rate, the endowment assurance policy model which has deposit function is established. The survival annuity, increasing life insurance and repaid principal are introduced. Considering the influence of the actual investment of premiums and the outburst cases on interest rate, the random interest rate is decided by both reflected Brownian motion and Poisson process, and then, a whole value formula of the insurance policy is obtained. Finally, the concise expressions of formula are given in the case that death happens uniformly in every policy year. The cases mentioned in the model correspond with the reality, and this model has theoretical and practical value in solving the problem of insurance company reasonably claiming premiums, insurance payment and crisis management.
Keywords:stochastic rates of interest  annuity  life insurance  actuarial present value
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