土壤分类的模糊集成算法与应用

土壤是一个多性状的连续体,其分类的首选方法是模糊聚类分析.但是模糊聚类分析中现有的基于模糊等价关系的动态聚类法和模糊c-均值法各有利弊,采用其中一种方法聚类肯定存在不足.为此集成两种聚类方法的优点,避其缺点,提出了用基于模糊等价关系的动态聚类方法和方差分析方法确定聚类数目和初始聚类中心,再用模糊c-均值法决定最终分类结果的集成算法,并将其应用到松花江流域土壤分类中,得到了较为切合实际的分类结果.     

基于AFS拓扑和FCM的模糊聚类分析

聚类分析是数据挖掘的一个重要研究课题，模糊聚类是聚类分析的一个有效手段。本文在分析AFS方法和FCM算法的基础上，设计了一个基于AFS拓扑和FCM的模糊聚类算法，进行iris数据的聚类实验证明它聚类结果优于传统的FCM聚类算法，具有很好的推广性和实际应用价值。     

基于犹豫模糊语言决策信息的被执行人聚类算法

针对法院“执行难”现状，将模糊聚类分析方法应用于司法执行领域，聚类的数据类型拓展为犹豫模糊语言信息，构建了一套完整的被执行人隐匿财产行为评估体系。通过估测被执行人隐匿财产的量化概率，为执行法官确定查控重点提供了决策支持。对当前的犹豫模糊语言距离测度存在的局限性进行了分析，给出了犹豫模糊语言犹豫度的定义和新的犹豫模糊语言距离计算方法。采用离差最大化思想确定最优属性权重，提出了一种基于离差最大化的犹豫模糊语言凝聚式层次聚类算法。犹豫模糊语言决策信息环境下的被执行人聚类分析算例验证了评估体系和聚类算法的有效性。     

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.     

模糊C均值算法的改进

模糊聚类分析方法具有较强的实用性,但传统的模糊C均值算法对数据集进行分类时有均分的趋势,对于数据集中各类样本数目相差较大的情况,其聚类结果不是很理想.因此,本文对FCM算法进行了改进,使之不但能够达到更好的分类效果,同时也更加适用于样本分类不均衡的聚类问题.文中还结合具体算例进行了聚类分析,得到了理想的分类效果.     

离差最大化特征加权模糊C-划分的聚类分析

聚类分析中每个样本用一个m维向量来表征,每个分量描述样本的一个特征,由于对特征的提取不够完善,使得m维向量的每个分量对聚类贡献不均.基于此本文利用向量间离差最大化对样本的每个分量即特征进行加权,提出一种新的加权模糊c-划分的聚类分析法,一定程度上克服了模糊c-划分的聚类分析对每个特征等同对待不足,又保持其算法的收敛性,最后给出一个算例说明此算法的优越性.     

一种考虑决策者偏向的综合模糊聚类方法

在分析传统模糊聚类分析方法的基础上,提出了一种建立模糊相似矩阵Ｒ的新方法,以及能够充分体现决策者偏好和经验的多向综合模糊聚类方法。该方法简单、实用、能够全面反映事物的特征,具有一定的实用价值。     

基于AFS拓扑和AFCM的模糊聚类分析

在分析AFS方法和AFCM算法的基础上,设计了一个新的模糊聚类算法.它首先应用AFS拓扑理论计算得到数据的相对距离,然后将相对距离应用于改进后的AFCM算法中,并进行了聚类实验.实验结果证明这样的聚类算法优于传统的HCM、FCM聚类算法,而且该方法能应用于含有布尔值或模糊概念的聚类分析中.     

模糊聚类挖掘在综合评价中的应用研究

探讨了聚类分析这一重要的数据挖掘方法在综合评价中的应用,将模糊聚类与综合评价相结合以解决待评价方案数较多的排序问题,并且文中还改进了建立模糊相似矩阵的方法.     

模糊聚类分析的新算法

提出了一种模糊聚类分析的新算法——追踪法 ,解决了以往模糊聚类分析计算量过大以及难于编程实现的问题 .该方法尤其适用于大规模数据的模糊聚类分析 ,对于模糊聚类分析的推广使用有重要意义 .     

具有模糊信息的多目标运输问题求解

提出一种求解具有模糊信息的多目标运输问题的方法。利用专家意见通过模糊算法集给从各产地到各目的地运送单位物资的模糊综合指标值,运用一种对模糊数排序的方法,将模糊多目标运输问题转化为单目标的运输问题进行求解,最后给出了一个数值例子。     

Optimum Radius of Robust Stability for Schur Polynomials

The paper investigates the problem of the robust stability of Schur polynomials. Recently, a new approach based on the Rouche theorem of classical complex analysis has been adopted for the solution of this problem. In this paper, an improvement of the previous solution is presented. This is the optimum solution of the robust stability problem for Schur polynomials, which is obtained by solving a minimization problem and is better than other methods in robust stability literature. Three numerical examples are given to illustrate the proposed method.     

需求区间型运输问题的求解算法

为了便于建立与需求区间型运输问题有关的决策支持系统，本给出了一个求解需求区间型运输问题的数值算法，证明了算法的理论依据，并举例说明算法的应用，该算法能求得问题的最优解，并具有易于编程实现、收敛性好等优点，大量数值实验表明该算法有较高的计算效率。     

Fuzzy goal programming for multiobjective transportation problems

Several fuzzy approaches can be considered for solving multiobjective transportation problem. This paper presents a fuzzy goal programming approach to determine an optimal compromise solution for the multiobjective transportation problem. We assume that each objective function has a fuzzy goal. Also we assign a special type of nonlinear (hyperbolic) membership function to each objective function to describe each fuzzy goal. The approach focuses on minimizing the negative deviation variables from 1 to obtain a compromise solution of the multiobjective transportation problem. We show that the proposed method and the fuzzy programming method are equivalent. In addition, the proposed approach can be applied to solve other multiobjective mathematical programming problems. A numerical example is given to illustrate the efficiency of the proposed approach.     

求解网络最大流问题的一个算法

为了便于建立与网络最大流问题有关的决策支持系统，本给出一个求解网络最大流问题的数值算法。证明了算法的理论依据，并举例说明了算法的应用。该算法能求出网络最大流和最小截，并具有易于编程实现、收敛性好等优点，大量数值实验表明该算法非常实用有效。     

Time minimizing transportation problems

A procedure for time minimization in a transportation problem is developed and consists of a finite number of interactions and is based on moving from a basic feasible solution to another till the last solution is arrived at. A numerical example is given in support of the theory.     

Dijkstra’s Algorithm for Solving the Shortest Path Problem on Networks Under Intuitionistic Fuzzy Environment

In this paper, a well known problem called the Shortest Path Problem (SPP) has been considered in an uncertain environment. The cost parameters for traveling each arc have been considered as Intuitionistic Fuzzy Numbers (IFNs) which are the more generalized form of fuzzy numbers involving a degree of acceptance and a degree of rejection. A heuristic methodology for solving the SPP has been developed, which aim to exploit tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness and low cost solution corresponding to the minimum-cost path or the shortest path. The Modified Intuitionistic Fuzzy Dijkstra’s Algorithm (MIFDA) has been proposed in this paper for solving Intuitionistic Fuzzy Shortest Path Problem (IFSPP) using the Intuitionistic Fuzzy Hybrid Geometric (IFHG) operator. A numerical example illustrates the effectiveness of the proposed method.     

A computational method for large‐scale differential symmetric Stein equation

We propose a numerical method for solving large‐scale differential symmetric Stein equations having low‐rank right constant term. Our approach is based on projection the given problem onto a Krylov subspace then solving the low dimensional matrix problem by using an integration method, and the original problem solution is built by using obtained low‐rank approximate solution. Using the extended block Arnoldi process and backward differentiation formula (BDF), we give statements of the approximate solution and corresponding residual. Some numerical results are given to show the efficiency of the proposed method.     

Panel clustering method and restriction matrices for symmetric Galerkin BEM

In the framework of Symmetric Galerkin Boundary Element Method, different techniques in these last years have been proposed to reduce the computational cost of the Galerkin matrix evaluation: in particular, the Panel Clustering Method [25,26] it is now largely used. On the other side, very recently a theory on restriction matrices has been developed to take computational advantage of possible symmetry properties of the differential or integral problem at hand [4,5]. Here we couple Panel Clustering Method with restriction matrices, presenting the most important algorithms employed and showing several examples, comparisons and numerical results. AMS subject classification 65F30, 65N38     

A numerical method for solving optimal control problems using state parametrization

A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.