2-型供应链网络设计优化

基于模糊可能性理论,研究了2-型模糊供应链网络设计问题。考虑到运输费用和顾客需求的不确定性,我们用2-型模糊变量来刻画,建立了2-型模糊环境下的期望值供应链网络设计模型。当2-型模糊变量相互独立且服从三角分布时,我们将原模型转化为等价的确定模型。等价模型是一个0-1混合整数参数规划,因此可采用Lingo软件求解。最后,我们通过数值例子演示所提建模思想。实验结果证明了所建模型的有效性。     

含模糊变量的水污染控制系统研究

在水流量为模糊变量且河流中工业污水含量标准给定的条件下,分别建立了水污染控制系统问题的模糊期望值模型和模糊机会约束规划模型来满足不同的优化需求.为了有效求解优化模型,采用了将模糊模拟、神经元网络及遗传算法相结合的混合智能算法.最后用算例进行了验证,结果表明该算法是有效可行的.     

结构的失效可能度及模糊概率计算方法

依据模糊可能性理论,系统地建立含模糊变量时结构的可靠性计算模型。旨在解决模糊结构、模糊-随机结构和模糊状态假设下结构的可靠性计算问题。所建模型可给出模糊结构失效的可能度和模糊-随机结构失效概率的可能性分布。研究表明:对同时含模糊变量和随机变量的混合可靠性计算问题,把失效概率(或可靠度)作为模糊变量,能更客观地反映系统的安全状况。算例分析说明了文中方法的合理性和有效性。     

模糊随机环境下的企业综合实力评价模型研究

建立随机环境下的定量指标评价模型、模糊随机环境下的定性指标评价模型和权重为模糊变量的综合评价模型,研究定量评价指标、定性评价指标分别为随机变量和模糊随机变量的企业综合实力评价模型和评价分析方法.最后,以制造业中HX行业的CA企业为例,实证模拟验证了模型的有效性和可操作性.     

模糊环境下可控提前期供应链库存优化的Stackelberg模型研究

为了有效地缩短提前期与降低库存成本,研究了模糊环境下可控提前期的供应链库存优化问题.利用三角形模糊数描述需求的不确定性,建立了一类模糊需求条件下可控提前期供应链库存优化的Stackelberg模型.利用三角形模糊数描述成本系数的不确定性,建立了模糊成本系数条件下可控提前期供应链库存优化的Stackelberg模型,并提出利用均值面积度量法来解模糊化.通过数值分析来验证两类模型的优化效果.     

基于可信性安全准则的模糊动态投资组合模型

研究了模糊环境下的动态投资组合模型,将证券的收益率描述为模糊变量,提出了基于可信性测度的安全准则,可信性安全准则反映了投资者对灾难事件的容忍水平.建立了基于可信性安全准则的模糊动态投资组合模型,对建立的模型设计了基于模糊模拟的混合智能算法进行求解,并在Visual C++环境下,用C语言实现了对实例的求解,证明了混合智能算法的有效性和合理性.     

一种算子模糊逻辑系统及其Petri网推理算法

定义一种只带模糊文字以及模糊算子的模糊逻辑，讨论了该逻辑的λ-归结的相容性、完备性及其若干逻辑性质。为了实现算子模糊逻辑的归结推理，给出了算子模糊逻辑的Petri网模型：Horn型，进一步讨论了推理算法：T-不变量算法，得到了算法的完备性定理，最后用实例进行了验证。     

单失效模式双变量函数复杂系统模糊随机可靠性广义模型研究

在综合考虑系统功能函数变量不同属性的基础上 ,建立了单一失效模式下复杂系统模糊随机可靠性的广义模型 ,并讨论了广义模型与各个单一模型之间的关系 ,为产品在复杂状态下的可靠性求解提供了统一的数学模型 .分析讨论表明 :所建立的模糊随机可靠性广义模型更具有一般性 .     

模糊批量生产计划问题的可信性规划模型与算法

描述模糊单位利润、模糊生产能力以及模糊需求下的批量生产计划,并应用可信性规划建立了模型.当模糊变量是梯形模糊数时,我们将模糊模型转化为确定意义下的模型.为了求解优化模型,我们设计了基于模糊模拟的遗传算法.最后,通过一个数值例子说明算法的有效性.     

基于二型模糊逻辑的元胞自动机模型

将二型模糊逻辑推理引入到元胞自动机模型中,把二型模糊逻辑推理与经典的元胞自动机模型结合起来,建立一种新的推理演化模型,基于二型模糊逻辑的元胞自动机模型.元胞自动机模型的关键部分是演化规则和元胞状态.将元胞自动机模型中的演化规则二型模糊化,将经典元胞自动机模型中的元胞状态模糊化为二型模糊状态,建立基于二型模糊逻辑的元胞自动机模型.     

随机值Ⅱ-型模糊集及其不确定性知识表示

针对人工智能中的不确定性问题,在研究了Ⅱ-型模糊集理论的基础上,提出了一种随机值Ⅱ-型模糊集概念,给出了正态随机值Ⅱ-型模糊集数学模型及其生成算法,并对正态随机值Ⅱ-型模糊集的参数及形态特征进行解析.实例证明随机值Ⅱ-型模糊集可以用来处理社会和自然科学中诸多不确定性问题.     

Prediction of retinopathy in diabetic patients using type-2 fuzzy regression model

Due to the small sample size of data available in medical research and the levels of uncertainty and ambiguity associated with medical data, some researchers have employed fuzzy regression models to find the relationship between outcomes and explanatory variables in medical decision-making. The advantages of regression models are their ability to handle small sample sizes while fuzzy logic can model vagueness, thus making fuzzy regression a popular model among researchers. In addition, the high levels of uncertainty in medical data encourage the use of type-2 fuzzy which is capable of handling such uncertainty. The current paper proposes an interval type-2 fuzzy regression model for predicting retinopathy in diabetic patients. The results of the present work shall prevent unnecessary testing of diabetic patient. This study also aims to assist patients and the healthcare community to reduce the cost of diabetes control and treatment by optimizing the number of check-ups.     

Methods of critical value reduction for type-2 fuzzy variables and their applications

A type-2 fuzzy variable is a map from a fuzzy possibility space to the real number space; it is an appropriate tool for describing type-2 fuzziness. This paper first presents three kinds of critical values (CVs) for a regular fuzzy variable (RFV), and proposes three novel methods of reduction for a type-2 fuzzy variable. Secondly, this paper applies the reduction methods to data envelopment analysis (DEA) models with type-2 fuzzy inputs and outputs, and develops a new class of generalized credibility DEA models. According to the properties of generalized credibility, when the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we can turn the proposed fuzzy DEA model into its equivalent parametric programming problem, in which the parameters can be used to characterize the degree of uncertainty about type-2 fuzziness. For any given parameters, the parametric programming model becomes a linear programming one that can be solved using standard optimization solvers. Finally, one numerical example is provided to illustrate the modeling idea and the efficiency of the proposed DEA model.     

基于Nie-Tan算法的区间二型模糊集质心计算:改变主变量采样个数

计算区间二型模糊集的质心(也称降型)是区间二型模糊逻辑系统中的一个重要模块。Karnik-Mendel(KM)迭代算法通常被认为是计算区间二型模糊集质心的标准算法。尽管如此,KM算法涉及复杂的计算过程,不利于实时应用。在各种改进类算法中,非迭代的Nie-Tan(NT)算法可节省计算消耗。此外,连续版本NT(CNT,continuous version of NT)算法被证明是计算质心的准确算法。本文比较了离散版本NT算法中求和运算和连续版本NT算法中求积分运算,通过四个计算机仿真例子证实了当适度增加区间二型模糊集主变量采样个数时,NT算法的计算结果可以精确地逼近CNT算法。     

Differentiability of type-2 fuzzy number-valued functions

In this paper, we define a differentiability of the type-2 fuzzy number-valued functions. The definition is based on type-2 Hukuhara difference which is defined in the paper as well. The related theorem of the differentiability of the type-2 fuzzy number-valued functions is derived. In addition, a parametric closed form of the perfect triangular quasi type-2 fuzzy numbers is introduced, and finally, the applicability and an approach to solving type-2 fuzzy differential equations are illustrated using some examples and cases.     

Exact calculations of extended logical operations on fuzzy truth values

In this paper we propose computationally simple, pointwise formulas for extended t-norms and t-conorms on fuzzy truth values. The complex convolutions of the extended operations are shown to be equivalent to simple pointwise expressions for several special cases. Linear fuzzy truth values are defined and it is shown that the extended Łukasiewicz operations preserve linearity. Since linear fuzzy truth values are common in representing linguistic modifiers, the results simplify fuzzy truth value-based reasoning methods. The results can also be applied immediately to type-2 fuzzy set operations.     

基于T2FCM-FE-HMMs的隐马氏模型参数估计算法

把2型模糊集的思想引入到了基于模糊聚类的离散HMM参数训练中,提出了改进的T 2FCM-FE-HMM s算法。     

Type-2 fuzzy fractional derivatives

In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann–Liouville and Caputo derivative of order β ∊ (0, 1), and based on type-2 Hukuhara difference and H₂-differentiability. The existence and uniqueness of the solutions of type-2 fuzzy fractional differential equations (T2FFDEs) under Caputo type-2 fuzzy fractional derivative and the definition of Laplace transform of type-2 fuzzy number-valued functions are also given. Moreover, the approximate solution to T2FFDE by a Predictor-Evaluate–Corrector-Evaluate (PECE) method is presented. Finally, the approximate solutions of two examples of linear and nonlinear T2FFDEs are obtained using the PECE method, and some cases of T2FFDEs applications in some sciences are presented.     

几类广义模糊集的关系

经过近五十年的发展,模糊集在理论与应用两个领域的研究都已经取得长足的进展,特别地,在模糊决策等应用领域,涌现了几类重要的广义模糊集,包括区间值模糊集,直觉模糊集,区间值直觉模糊集,II型模糊集,Vague集,灰集等。本文简要介绍关于这些广义模糊集之间关系的研究成果,以及国外关于直觉模糊集术语问题的争议。     

A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets

Soft set theory, originally proposed by Molodtsov, has become an effective mathematical tool to deal with uncertainty. A type-2 fuzzy set, which is characterized by a fuzzy membership function, can provide us with more degrees of freedom to represent the uncertainty and the vagueness of the real world. Interval type-2 fuzzy sets are the most widely used type-2 fuzzy sets. In this paper, we first introduce the concept of trapezoidal interval type-2 fuzzy numbers and present some arithmetic operations between them. As a special case of interval type-2 fuzzy sets, trapezoidal interval type-2 fuzzy numbers can express linguistic assessments by transforming them into numerical variables objectively. Then, by combining trapezoidal interval type-2 fuzzy sets with soft sets, we propose the notion of trapezoidal interval type-2 fuzzy soft sets. Furthermore, some operations on trapezoidal interval type-2 fuzzy soft sets are defined and their properties are investigated. Finally, by using trapezoidal interval type-2 fuzzy soft sets, we propose a novel approach to multi attribute group decision making under interval type-2 fuzzy environment. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.