Fuzzy linear regression and its applications to forecasting in uncertain environment

Linear regression has been used for many years in developing mathematical models for application in marketing, management, and sales forecasting. In this paper, two different sales forecasting techniques are discussed. The first technique involves non-fuzzy abstract methods of linear regression and econometrics. A study of the international market sales of cameras, done in 1968 by John Scott Armstrong, utilized these non-fuzzy forecasting techniques. The second sales forecasting technique uses fuzzy linear regression introduced by H. Tanaka, S. Uejima, and K. Asai, in 1980. In this paper, a study of the computer and peripheral equipment sales in the United States is discussed using fuzzy linear regression. Moreover, fuzzy linear regression is applied to forecasting in an uncertain environment. Finally, some possible improvements and suggestions for further study are mentioned.     

Probability of fuzzy events defined as denumerable additivity measure

In this paper the probability of fuzzy events is defined as a denumerable additivity measure. This definition is based on a non-conventional approach of separativity between fuzzy subsets. The presented measure fulfils all properties analogous to the properties of classical probability in the crisp case. Further, the notion of conditional probability of fuzzy events, complete fuzzy repartition and independent fuzzy events are defined by means of the probability measure considered here. Connections between all the above notions are presented in this paper, too. Finally, the Bayes formula is proved for the fuzzy case.     

Type-2 T–S fuzzy impulsive control of nonlinear systems

A novel impulsive control approach based on interval Type-2 T–S fuzzy model has been presented for nonlinear systems in this paper. This approach makes up for the drawback of Type-1 fuzzy impulsive control, which cannot fully handle the uncertainties in describing the complex nonlinear systems by Type-1 fuzzy membership functions and cannot give rigorous fuzzy rules. Further more, this approach uses the “broad band” effect of the Type-2 membership functions to solve the noise of training data and exterior disturbance of the Type-1 fuzzy impulsive control. By using Lyapunov theory and Lipschitz condition, which is combined with integrated approaches such as comparison methods and linear matrix inequalities, the Type-2 fuzzy impulsive controller is designed and the general asymptotical stability analysis of the systems is given. Finally, the simulation of the inverted pendulum model demonstrates the validity and superiority of the proposed method by easily determining the membership functions and choosing minimum number of fuzzy rules and the method can handle random disturbance and data uncertainties very well.     

模糊相似关系传递核获取算法

针对模糊相似关系传递核的获取问题进行研究.首先给出模糊相似关系传递核的一些基本性质.之后,利用这些性质构造了三个算法来获取可能为传递核的模糊等价关系.最后,通过实验比较并分析这三种算法在获取传递核时的能力.     

Fuzzy control of original UPOs of unknown discrete chaotic systems

This paper presents a fuzzy algorithm for controlling original unstable periodic orbits of unknown discrete chaotic systems. In the modeling phase, only input–output data pairs provided from the true system are required. The fuzzy model is developed using Gaussian membership functions and consequent functions where the Levenberg–Marquardt computational algorithm is employed for the model parameters calculation. In the controller design phase, the L₂-stability criterion is used, which forms the basis of the main design principle. Simulation results are given to illustrate the effectiveness and control performance of the proposed method.     

max-zero t-模复合意义下的模糊矩阵幂序列的收敛性

主要讨论模糊矩阵在max-zro t-模(以下简称为max-t0)复合意义下的收敛性。证明了模糊矩阵在,max-t0复合意义下只有有限收敛,无限收敛,有限振荡及无限振荡这四种情况。并主要以一种特殊且重要的zero t-模：lukasiewice t-模为例,研究了max-lukasiewiez t模(以下简称为max-lu)复合意叉下的模糊矩阵的收敛性。证明了在max-lu复合意义下．模糊矩阵要么有限收敛要么有限振荡。且比较了在max-lu复合意义下以及在,max-product复合意义下,模糊矩阵收敛性的相同之处与不同之处,并揭示其原因。     

一般化合成模糊对策的势指标

定义了一种新的合成模糊对策模型,我们称之为一般化合成模糊对策模型．并研究了这种模型的Shapley值和Banzhaf-Coleman势指标。     

群中模糊同余关系下的模糊粗糙群

在模糊同余关系下,首次提出了群中模糊同余关系下的模糊粗糙集和模糊粗糙群的概念,并讨论了它的一系列的性质,得到了一些有意义的结果。     

单调集函数的连续性与可测函数序列的收敛

引了单调集函数的几种连续性并且讨论了它们与可测函数依测度收敛之间的关系,给出可加测度论中的Lesbegue定理在单调测度空间上的4种推广形式。讨论单调集函数的连续性和模糊积分与Choquet积分的单调收敛定理之间的等价性。证明Choquet积分的控制收敛定理。     

Fractional time-varying energy distributions of ECG signals

We introduce here fractional Cohen class of time-frequency distributions (FCCTFDs) containing fractional modulations which is kernel of fractional Fourier transform (FFT). The fractional modulation depends on angular parameter α and can be interpreted as a rotation by an angle α in time-frequency plane. This distribution promotes to track time-variant energy of a biological signals and represents it in time-frequency domain. It uses the fractional ambiguity function (FAF) of signal multiplied by a suitable kernel which is designed for the biological signals generally having multi-non-stationary components. This result improves and generalizes some of the previous time-frequency distributions derived in the literature.