必要与可能(下)--四谈高中开设"模糊数学初步"选修课

1　“数学怎能模糊”2　“教材应该成熟”3　“中学生学习模糊数学 ,会不会太难”4　家长的看法5　从集合到模糊集合“数学就是要精确、严密 ,怎么与模糊混为一谈了 ,真是乱弹琴 !”这是一般人看到“模糊数学”的第一反应 .确实 ,长期以来人们一直把模糊看成贬义词 ,而只对精密与严格充满敬意 .在模糊数学的初创时期 ,它曾被美欧的许多专家权威认为是伪科学 ,是头脑发热的产物而遭到排斥 ,应用模糊数学的研究也不得不转入“地下” .模糊数学的先驱L A 扎德教授曾感叹地说 :“有一段时间 ,我觉得自己就象生活在狗窝里…”但这一页 ,早在十几…     

基于相对隶属度的织物风格模糊聚类分析

分析比较了统计数学、模糊数学和灰色数学在织物风格分析中的缺陷.特别针对模糊数学需人为确定隶属函数的缺陷提出采用基于相对隶属度的织物风格模糊聚类分析方法.以相对隶属度矩阵和模糊聚类中心矩阵的迭代求解为依据,对苎麻等十种织物的风格测试参数进行了聚类分析.通过聚类计算得到了织物相对类别特征值的聚类结果.经验证认为该结果符合客观实际和人们的感知经验.     

Fuzzy区间数的一种排序方法及综合评判模型

根据模糊数学的原理,给出了区间数的一种排序方法,引入了可信度的概念,并就区间数fuzzy综合评判进行了数学建模.     

第三类模糊事件的模糊概率

研究第三类模糊概率--模糊事件模糊概率的数学描述.在区间概率和第二类模糊概率的基础上,进一步给出了第三类离散型模糊概率的随机变量及其模糊分布函数和模糊分布列的定义和性质以及数字特征,并研究了连续型模糊概率随机变量的模糊数学期望和模糊方差的定义,进一步完善了模糊概率理论.     

用模糊集合描述模糊信息的无效性

用模糊集合描述模糊信息无效的原因是,把原本是论域与状态空间上二元函数的模糊隶属函数看成是论域上的一元函数,用模糊集合描述的模糊信息,不能支持模糊集合转换;使得通过模糊集合转换处理模糊信息的模糊数学,不得不借用不是数学计算、无缘数学模型的"取大取小"实现模糊集合转换;结果是背离数学计算的模糊数学,不能为处理模糊信息提供算法支持,导致大量需要处理的模糊信息滞留至今.还原模糊信息是高维状态空间上分类数据的真实面目,把处理模糊信息明确为由指标隶属度确定目标隶属度的隶属度转换,是模糊数学回归数学的唯一正确途径.     

2007模糊数学与模糊系统专业委员会常务委员会暨《模糊系统与数学》杂志创刊20周年庆典纪要

2007年5月17日,由中国系统工程学会模糊数学与模糊系统专业委员会、国防科技大学理学院联合主办的中国系统工程学会模糊数学与模糊系统专业委员会常务委员会暨《模糊系统与数学》杂志创刊20周年庆典在湖南长沙召开.     

高等院校数学课程教学质量的模糊综合评价研究

本文以某中医药院校开设的数学类专业基础课程为例,参照国内的高校课程教学质量评价标准,基于模糊数学理论,建立教学质量的多指标模糊综合评价模型,确定符合教学质量的隶属函数.通过MATLAB R2010b数学软件实现流程,结果表明,该模型能够较为科学、客观地反映教师的综合教学水平.     

模糊决策在航空维修工程中的应用

本文以模糊数学和规划论为工具，对航空维修工程中一类决策问题的决策方法进行了探讨，给出了具有普遍意义的建模思想，通过实例分析，证明了这种方法的可行性和先进性。     

数学建模是开启数学大门的金钥匙

作为大学《数学建模》课程的导言,对什么是数学建模,以及数学建模在推动数学学科发展及培养创新型人才方面的重要性,作充分的阐述.同时,针对数学建模的特点,对数学建模课程的教学,提出一些必要的建议.     

日本“模糊”产品简介

模糊集合理论自1965年算起,至今已有了26年的历史,在这26年的风风雨雨中,模糊数学的应用也日趋成熟,国外特别是日本应用模糊数学原理生产的产品已大量上市。下面简单地介绍一下日本的“模糊”产品情况。     

Bell-shaped Fuzzy Soft Sets and Their Application in Medical Diagnosis

A soft set theory is a new general mathematical tool to dealing with imprecision. The theory differs from traditional mathematical tools to dealing with uncertainties in which many mathematical theories failed. In this paper, we proposed the concept of Bell shaped fuzzy soft set and its application in medical diagnosis using arithmetic operations of discrete- Gaussian fuzzy number, triangular-Cauchy fuzzy number and Gaussian-Cauchy fuzzy number. As an integral part of this paper, we discuss the parametric form of Gaussian membership function is discussed with some important properties.     

基于Fuzzy推理的时变系统建模

提出一种基于Fuzzy推理的时变系统建模方法,其基本思想是:对时间维度进行分割,在每个较短的时间间隔内用时不变模型代替时变模型,将这些时不变模型组合在一起,最终获得一个整体非线性时变的微分方程模型.分别研究了输入输出型时变系统和状态空间型时变系统的模型建立方法,除了从理论上保证了所获得的模型对系统的逼近性,还从仿真实验验证了用该方法建立的模型对非线性时变系统有很好的逼近效果.     

On the modeling of nonlinear interactions in large complex systems

This work deals with the modeling of large systems of interacting entities in the framework of the mathematical kinetic theory for active particles. The contents are specifically focused on the modeling of nonlinear interactions which is one of the most important issues in the mathematical approach to modeling and simulating complex systems, and which includes a learning–hiding dynamics. Applications are focused on the modeling of complex biological systems and on immune competition.     

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using micro-analysis to examine modeling processes. The findings and the MTDs were used to critically question the implications of using modeling cycles as a theory of mathematical modeling processes.     

From generalized kinetic theory to discrete velocity modeling of vehicular traffic. A stochastic game approach

This work reports on vehicular traffic modeling by methods of the discrete kinetic theory. The purpose is to detail a reference mathematical framework for some discrete velocity kinetic models recently introduced in the literature, which proved capable of reproducing interesting traffic phenomena without using experimental information as modeling assumptions. To this end, we firstly derive a general discrete velocity kinetic framework with binary nonlocal interactions. Then, resorting to some ideas of stochastic game theory, we outline specific modeling guidelines for vehicular traffic, and finally we discuss the derivation of the above-mentioned vehicular traffic models from these mathematical structures.     

Modeling the hiding–learning dynamics in large living systems

This paper deals with the modeling of large systems of interacting entities in the framework of the mathematical kinetic theory for active particles. Various mathematical structures of the hiding–learning dynamics are derived at the mesoscopic scale. Subsequently, these structures are further detailed referring to modeling issues and, in particular, to the learning-hiding competition among tumors and the immune system cells.     

最优渡江路线的理论解和非线性规划解

探讨了2003年全国大学生数学建模竞赛D题主要问题的求解,从理论上得出了一个有用的结论,在已知江中各处流速分布的情况下,由该结论可以算出渡江路线的理论最优解.作为对比,文章还建立了非线性规划模型,用LINGO软件求出了近似解.     

面向独立学院学生的线性代数课程“可视化”教学研究

针对独立学院培养目标和学生的特点,研究如何通过案例教学,具体将线性代数的概念、定理、应用、习题"可视化",完成将枯燥数学知识由抽象到直观的转化,使得线性代数理论与数学建模紧密结合,培养应用型人才.     

Stochastic flows and finite block frames

With the aim of understanding the mathematical structure of the fluctuation-dissipation theorem in non-equilibrium statistical physics and then constructing a mathematical principle in the modeling problem for time series analysis, we have developed the theory of KM₂O-Langevin equations for discrete time stochastic processes. In this paper, as a new method for model analysis in the theory of KM₂O-Langevin equations, we show that block frames provide a natural mathematical language for dealing with minimum norm expansions of multi-dimensional stochastic processes which do not necessarily satisfy stationarity and non-degeneracy conditions.