两类新的基于T／S范数的模糊神经元模型及其应用

基于T范数和S范数提出了F1型和F2型两类神经元模型，并研究了它们的性质和应用(F1型灵敏性强而鲁棒性弱，而F2型神经元灵敏性弱而鲁棒性强)；给出了一个基于F1型神经元的广义AND／OR运算为T／S范数簇的充分必要条件；首先提出了弱界三角范数的概念，并发现F2型的一个特例模型能实现弱界三角范数，经分析，F1型更适合用于工业控制系统，而F2型更适合用于面向用语言描述知识的医学和人文社会领域的计算机应用系统，该文把一个由特殊的F2型神经元组成的神经网络用于模糊推理，发现该推理方法是Zadeh的CRI法的推广，且能满足假言推理，通过权值的调整，该推理法能满足若干推理原则的要求。     

泛逻辑泛运算模型之间的关系*

研究泛逻辑的泛与运算模型、泛或运算模型与模糊非之间的关系。证明了零级泛与运算模型T(x,y,h)、零级泛或运算模型S(x, y, h)与强非N(x)=1-x形成De Morgan三元组,当h∈(0, 0.75), 零级泛或运算S(x, y, h)=(min(xm+ym, 1))1/m, N(x)=(1-xm)1/m时, T, S, N形成一个强De Morgan三元组。进一步证明了一级泛与运算模型T(x, y, h, k)、一级泛或运算模型S(x, y, h, k)与N(x)=(1-xn)1/n满足De Morgan定律;特别当h∈(0, 075), 一级泛或运算模型S(x, y, h, k)=(min(xnm+ynm, 1))1/nm, N(x)=(1-xnm)1/nm时, T, S, N形成一个强De Morgan三元组。     

两类新的基于T/S范的模糊神经元模型及其应用

基于T范数和S范数提出了F1型和F2型两类神经元模型,并研究了它们的性质和应用(F1型灵敏性强而鲁棒性弱,而F2型神经元灵敏性弱而鲁棒性强);给出了一个基于F1型神经元的广义AND/OR运算为T/S范数簇的充分必要条件;首先提出了弱界三角范的概念,并发现F2型的一个特例模型能实现弱界三角范.经分析,F1型更适合用于工业控制系统,而F2型更适合用于面向用语言描述知识的医学和人文社会领域的计算机应用系统.该文把一个由特殊的F2型神经元组成的神经网络用于模糊推理,发现该推理方法是Zadeh的CRI法的推广,且能满足假言推理.通过权值的调整,该推理法能满足若干推理原则的要求.     

基于Schweizer算子簇的柔性概率逻辑算子的研究

Schweizer算子簇是泛逻辑学研究零级非相容T/S范数完整簇的数学基础,由它构造的与/或运算具有连续单调可变性.基于Schweizer算子簇构造的概率逻辑算子,既可满足概率测度的基本公理,又可实现概率逻辑运算的连续单调可变.     

[0，∞)值柔性逻辑中平均运算模型的研究

在柔性逻辑中,不仅命题真值的连续可变性对命题连接词运算模型有影响,而且命题间关系的连续可变性对命题连接词运算模型也有影响。柔性逻辑中的逻辑算子是在其定义域上随广义自相关系数k和广义相关系数h连续变化的算子簇。详细研究了柔性逻辑平均算子,定义了[0,∞)值零级和一级柔性逻辑平均运算模型。为保证逻辑运算模型的零级完整性,该模型在其定义域内,从最大算子经过概率算子和中心算子,到最小算子单调连续变化,证明了该区间上的4个特殊算子形式。     

基于幂零泛与运算模型的命题模糊逻辑

本文讨论了泛与运算模型T(x，y．h)(h∈(o，0．75))的一些性质；证明了泛与运算模型T(x,y,h)(h∈(0，O.75))是一个幂零三角范数；而且泛与运算模型T(x，y．h)(h∈(0，0．75))与泛蕴涵运算模型，(x，y，h)(h∈(0，0.75))是一个伴随对；进一步证明了([0，1].∨，∧．*，→．0，1)作成一个MV-代数。给出了基于幂零泛与运算模型T(x，y,h)(h∈(0，0.75))的模糊命题演算系统PC(T),证明了此命题演算系统与Lukasiewicz逻辑命题演算系统是等价的。     

基于一类严格三角范数的命题逻辑

剩余模糊逻辑演算与连续三角范数是紧密相关的,三角范数是合取联结词的真值函数,三角范数的剩余是蕴涵联结词的真值函数. 在这些逻辑中,非运算都是由蕴涵和真值常量0定义的,即(→)P∶P→0-.在本文中,我们引入一种具有对合性质的强非运算联结词"～"和投影联结词"Δ",证明基于严格泛与运算模型T(x,y,h)(h∈(0.75,1))的命题演算逻辑PC(T)系统是基本严格模糊逻辑SBL;PC(T)～是基本严格模糊逻辑SBL的扩张SBL～.     

一种鲁棒性较强的神经元在模糊规则发生摄动时的有效控制

一种基于弱T-范数和弱S-范数的神经元,可以实现与、或和混合-并模糊逻辑运算,并且拥有较强的鲁棒性。将它所组成的神经网络运用到模糊推理系统中,不仅可以简化网络,实现模糊推理最基本的一致性要求,还可以控制在模糊推理过程中当规则发生摄动时对推理结果的影响程度。     

泛逻辑的一级泛运算模型的代数性质

论文讨论泛逻辑的一级泛运算模型的基本代数性质。证明了T(x,y,h,k)(h∈(0,0.75),k∈(0,1))是幂零的阿基米德型三角范数,T(x,y,h,k)(h∈(0.75,1),k∈(0,1))是严格的阿基米德型三角范数;泛与运算模型与泛蕴涵运算模型形成一个伴随对。当h∈(0,0.75),k∈(0,1)时,有界格(眼0,1演,∨,∧,觹,→,0,1)做成一个MV-代数;当h∈(0.75,1),k∈(0,1)时,有界格(眼0,1演,∨,∧,觹,→,0,1)做成一个乘积代数。进一步,给出了一级泛与运算模型与泛或运算模型的加性生成元与乘性生成元。     

[0,∞]区间N范数的定义及生成定理

柔性逻辑学的研究目标是探索逻辑的一般规律,它指出命题真值误差用连续变化的广义自相关系数k∈[0,1]来刻画。在柔性逻辑的不确定推理中,N范数是一级运算的数理模型。由于在现实生活中,很多逻辑推理控制必须在其自身的定义域内完成,因此以三角范数作为柔性逻辑学研究的数学工具,定义了[0,∞]区间上的N范数和N性生成元,并研究了相关主要性质;证明了N范数生成定理;给出了广义自相关系数的计算方法;证明了[0,∞]区间上指数(幂)型N性生成元为N性生成元完整簇;从而为柔性逻辑中[0,∞]区间的一级运算模型提供了重要的理论基础。     

Applying weakest t-norm based approximate intuitionistic fuzzy arithmetic operations on different types of intuitionistic fuzzy numbers to evaluate reliability of PCBA fault

This research addresses system reliability analysis using weakest t-norm based approximate intuitionistic fuzzy arithmetic operations, where failure probabilities of all components are represented by different types of intuitionistic fuzzy numbers. Due to the incomplete, imprecise, vague and conflicting information about the component of system, the present study evaluates the reliability of system in terms of membership function and non-membership function by using weakest t-norm (T_w) based approximate intuitionistic fuzzy arithmetic operations on different types of intuitionistic fuzzy numbers. In general, interval arithmetic (α-cut arithmetic) operations have been used to analyze the fuzzy system reliability. In complicated systems, interval arithmetic operations may occur the accumulating phenomenon of fuzziness. In order to overcome the accumulating phenomenon of fuzziness, this research adopts approximate intuitionistic fuzzy arithmetic operations under the weakest t-norm arithmetic operations (T_w) to analyze fuzzy system reliability. The approximate intuitionistic fuzzy arithmetic operations employ principle of interval arithmetic under the weakest t-norm arithmetic operations. The proposed novel fuzzy arithmetic operations may obtain fitter decision values, which have smaller fuzziness accumulating and successfully analyze the system reliability. Also weakest t-norm arithmetic operations provide more exact fuzzy results and effectively reduce fuzzy spreads (fuzzy intervals). Using proposed approach, fuzzy reliability of series system and parallel system are also constructed. For numerical verification of proposed approach, a malfunction of printed circuit board assembly (PCBA) is presented as a numerical example. The result of the proposed method is compared with the listing approaches of reliability analysis methods.     

Generalized triangular norm and conorm aggregation operators on ordinal spaces

We describe the basic features of the t-norm operator and then introduce a family of t-norm operators that are defined on an ordinal space. We then do the same for the t-conorms. We note the strong limitation that the requirement of associativity places on the t-norm and t-conorm operators. We particularly note how it limits our ability to model different types of reinforcement. We then define a generalization of the t-conorm aggregation operator, which relaxes the requirement of associativity, we denote these operators as GENOR operators. We show that these operators have the same functionality as the t-conorm. We provide some examples of GENOR operators which allow us to control the reinforcement process. We define a related extension for the t-norm, the GENAND operator and provide some examples.     

勾股模糊H平均算法应用于多媒体图像系统选择

提出了一种勾股模糊H平均算法应用多媒体图像系统选择问题。首先,定义了基于t-模和t-余模的勾股模糊数运算;讨论了勾股模糊Heronian平均算法的三个特征性质和经常使用的特例;然后构建了新的勾股模糊决策模型,该模型在构建过程中能够挖掘输入数据之间关联性,还提高了决策的使用范围;最后,将构建的模型应用于多媒体图像系统选择案例来验证有效性。     

正则FBR_0-代数的弱t-模及其应用

吴望名教授建立的FI-代数(模糊蕴涵代数)是重要的基础逻辑代数,且通过弱化WBR0-代数建立的FBR0-代数与FI-代数有相同的代数结构。对FBR0-代数进行了较细致的研究。首先,证明了正则的FBR0-代数与RBR0-代数有相同的代数结构;其次,讨论了正则FBR0代数中弱t-模的基本性质;最后,给出了正则FBR0-代数的弱t-模表示形式。     

Transitive approximation of fuzzy relations by alternating closures and openings

 In this paper, a new method is proposed for approximating a fuzzy relation on a finite universe by a min-transitive fuzzy relation that is `close' to it. The method consists of a cascade of T-transitive closure and opening operations, where the t-norm T gradually progresses from the Lukasiewicz t-norm W to the minimum operator M. The underlying T-transitive opening heuristic is particularly interesting for t-norms T that belong to the class of copulas.     

A neural net for extracting knowledge from natural language databases

A model of a fuzzy neuron, one which increases the computational power of the artificial neuron, turning it also into a symbolic processing device, is presented. The model proposes the synapsis to be symbolically and numerically defined, by means of the assignment of tokens to the presynaptic and postsynaptic neurons. The matching or concatenation compatibility between these tokens is used to decide about the possible connections among neurons of a given net. The strength of the compatible synapsis is made dependent on the amount of the available presynaptic and postsynaptic tokens. The symbolic and numeric processing capacity of the new fuzzy neuron is used to build a neural net (JARGON) to disclose the existing knowledge in natural language databases such as medical files, sets of interviews and reports about engineering operations.     

一种基于多主体技术的分布式图像聚类算法

针对医学图像具有对比度较低,不同组织之间的模糊性较高的特点,给出一种基于多主体和数学形态学灰度形态运算的聚类算法。算法采用agent技术和多结构元素结合的模式,用结构元素做智能个体,每个不同类型的agents随机散布在离散空间格点上,在同时刻控制系统驱动下agents根据其自身结构元素的类型用给出的邻域平均算子自主选择作相应的运算进而实现图像聚类。算法无须先验知识和预处理操作,对初始聚类点不敏感,无须事先输入聚类簇数。算法具有分布式并行计算功能和自主分析能力。实验结果验证了该算法的可行性和可靠性。     

Neural network learning with generalized-mean based neuron model

The advances in biophysics of computations and neurocomputing models have brought the foreground importance of dendritic structure of neuron. These structures are assumed as basic computational units of the neuron, capable of realizing the various mathematical operations. The well structured higher order neurons have shown improved computational power and generalization ability. However, these models are difficult to train because of a combinatorial explosion of higher order terms as the number of inputs to the neuron increases. In this paper we present a neural network using new neuron architecture i.e., generalized mean neuron (GMN) model. This neuron model consists of an aggregation function which is based on the generalized mean of all the inputs applied to it. The resulting neuron model has the same number of parameters with improved computational power as the existing multilayer perceptron (MLP) model. The capability of this model has been tested on the classification and time series prediction problems.     

Fast solving method of fuzzy relational equation and itsapplication to lossy image compression/reconstruction

A fast solving method of the solution for max continuous t-norm composite fuzzy relational equation of the type G(i, j)=(R^T□A_i)^T□B_j , i=1, 2, ..., I, j=1, 2, ..., J, where A_i∈F(X)X={x₁, x₂, ..., x_M }, Bj∈F(Y) Y={y₁, y₂, ..., y_N}, R∈F(X×Y), and □: max continuous t-norm composition, is proposed. It decreases the computation time IJMN(L+T+P) to JM(I+N)(L+P), where L, T, and P denote the computation time of min, t-norm, and relative pseudocomplement operations, respectively, by simplifying the conventional reconstruction equation based on the properties of t-norm and relative pseudocomplement. The method is applied to a lossy image compression and reconstruction problem, where it is confirmed that the computation time of the reconstructed image is decreased to 1/335.6 the compression rate being 0.0351, and it achieves almost equivalent performance for the conventional lossy image compression methods based on discrete cosine transform and vector quantization     

Robust Computation of Intersection Graph between Two Solids

We propose a new robust algorithm for Boolean operations on solid models. The algorithm produces a consistent intersection graph between two input solids whose geometrical data are represented in floating point numbers. In order to prevent numerical calculation errors and inaccuracy of input data from causing inconsistency of the output, we put higher priority on symbolical connectivity of the edge-face intersection points than their numerical nearness. Each edge-face intersection point is symbolically represented using face names, which generate connectivity relations between the intersection points and the intersection line segments. The symbols with the same connectivity are made into clusters. The intersection line segments connected together at their end clusters form the intersection graph of two solids. Inconsistency of the connectivity of the clusters is detected and the intersection graph is corrected automatically. We describe the algorithm in detail for polyhedral solids, discuss extension to curves solids, and show its effectiveness by some examples of Boolean operations for two solids whose faces intersect at a very small angle.