On Felbin-type Fuzzy 2-normed Spacesand Its Fuzzy I-topologies

In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.     

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.     

2-型模糊环境下的能源系统优化

基于模糊可能性理论,建立2-型模糊环境下的能源分配优化模型,其中各种类型能源的成本用2-型模糊变量刻画.用均值简约方法简约2-型模糊成本,建立广义期望值意义下的模糊能源分配优化模型.当成本用相互独立的三角2-型模糊变量刻画时,所建立的模糊能源分配优化模型可以转化为等价的参数线性规划.最后提供一个数值例子表明建模思想.     

二级传递性与二级传递模糊矩阵

推广传递性概念,给出二级传递性的定义;研究二级传递模糊矩阵的性质,给出其若干等价刻画;证明二级传递模糊矩阵或者收敛或者周期为2,指数不大于n 1;讨论二级传递与强传递、k-传递和泛传递等概念之间的关系,指出二级传递是传递性概念的一种新的推广形式。     

二型模糊系统研究与应用

简单介绍模糊系统和二型模糊系统发展,概述二型模糊系统的应用范围、条件和组成,比较详细的介绍了二型模糊集合基础理论,按照二型模糊系统的组成模块描述模糊器,规则库,推理引擎,降型器,精确器的表达式和推导过程,最后还总结了二型模糊系统现阶段存在的不足和可能发展方向。     

基于二型直觉模糊信息的多属性决策方法

模糊数直觉模糊集是直觉模糊集和区间数直觉模糊集的拓展,本文提出了二型直觉模糊数概念,对基于二型直觉模糊信息的多属性决策进行了研究.以结构元理论为基础,给出了二型直觉模糊数的距离公式,然后定义了二型直觉模糊正、负理想点,进而给出了一种基于二型直觉模糊数的多属性决策的步骤.最后通过实例来证明其有效性.     

Fuzzy sets and type 2 under algebraic product and algebraic sum

The concept of fuzzy sets of type 2 has been proposed by L.A. Zadeh as an extension of ordinary fuzzy sets. A fuzzy set of type 2 can be defined by a fuzzy membership function, the grade (or fuzzy grade) of which is taken to be a fuzzy set in the unit interval [0, 1] rather than a point in [0, 1].This paper investigates the algebraic properties of fuzzy grades (that is, fuzzy sets of type 2) under the operations of algebraic product and algebraic sum which can be defined by using the concept of the extension principle and shows that fuzzy grades under these operations do not form such algebraic structures as a lattice and a semiring. Moreover, the properties of fuzzy grades are also discussed in the case where algebraic product and algebraic sum are combined with the well-known operations of join and meet for fuzzy grades and it is shown that normal convex fuzzy grades form a lattice ordered semigroup under join, meet and algebraic product.     

基于Type-2型模糊集的动态生态位模型

复杂生态系统中,由于生物进化的高度非线性,使生物更容易适应环境的变化,生物与环境的交流要求用动态的观点来描述生态位及其相关概念。本文利用T ype-2型模糊集合的“宽带”效应,给出了具有动态特性的生态位模型,并相应的给出宽度和重叠的计算公式。应用于植物的生态位宽度和重叠的计算,与已有公式结果的比较,本文提出的模型可以全面的给出了物种在每个资源状态下的情形,同时反应了物种与环境之间的互动交流。为生物系统的应用研究和理论研究提出统一的数学模型。     

基于模糊Lyapunov函数对带有离散无穷分布时滞的T-S模糊系统的非PDC广义H2控制

基于模糊分段非二次李雅普诺夫(Lyapunov)函数稳定性理论,对一类受外部干扰且带有离散无穷分布时滞的T-S模糊系统的广义H2稳定控制问题进行了讨论.通过设计非PDC (Non-PDC)模糊控制器,充分考虑子邻域Ωi(i=1,2,…,s)之间的转移,给出了保守性较小的使闭环系统广义H2稳定的充分性条件.控制器的设计可以通过线性矩阵不等式(LMI)方法求解得到.仿真例子验证了该方法的有效性.     

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.     

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。     

Universally bad integers and the 2-adics

In his 1964 paper, de Bruijn (Math. Comp. 18 (1964) 537) called a pair (a,b) of positive odd integers good, if , where is the set of nonnegative integers whose 4-adic expansion has only 0's and 1's, otherwise he called the pair (a,b) bad. Using the 2-adic integers we obtain a characterization of all bad pairs. A positive odd integer u is universally bad if (ua,b) is bad for all pairs of positive odd integers a and b. De Bruijn showed that all positive integers of the form u=2^k+1 are universally bad. We apply our characterization of bad pairs to give another proof of this result of de Bruijn, and to show that all integers of the form u=φ_p^k(4) are universally bad, where p is prime and φ_n(x) is the nth cyclotomic polynomial. We consider a new class of integers we call de Bruijn universally bad integers and obtain a characterization of such positive integers. We apply this characterization to show that the universally bad integers u=φ_p^k(4) are in fact de Bruijn universally bad for all primes p>2. Furthermore, we show that the universally bad integers φ_2^k(4), and more generally, those of the form 4^k+1, are not de Bruijn universally bad.     

Fuzzy real valued lacunary I-convergent sequences

In this article, we introduce the concept of lacunary I-convergent sequence of fuzzy real numbers and study some basic properties.