Traffic Flow Data Forecasting Based on Interval Type-2 Fuzzy Sets Theory

This paper proposes a long-term forecasting scheme and implementation method based on the interval type-2 fuzzy sets theory for traffic flow data. The type-2 fuzzy sets have advantages in modeling uncertainties because their membership functions are fuzzy. The scheme includes traffic flow data preprocessing module, type-2 fuzzification operation module and long-term traffic flow data forecasting output module, in which the Interval Approach acts as the core algorithm. The central limit theorem is adopted to convert point data of mass traffic flow in some time range into interval data of the same time range (also called confidence interval data) which is being used as the input of interval approach. The confidence interval data retain the uncertainty and randomness of traffic flow, meanwhile reduce the influence of noise from the detection data. The proposed scheme gets not only the traffic flow forecasting result but also can show the possible range of traffic flow variation with high precision using upper and lower limit forecasting result. The effectiveness of the proposed scheme is verified using the actual sample application.      

二型直觉模糊粗糙集

将二型直觉模糊集和粗糙集理论融合,建立二型直觉模糊粗糙集模型。首先,在二型直觉模糊近似空间中,定义了一对二型直觉模糊上、下近似算子,并讨论了二型直觉模糊关系退化为普通二型模糊关系和一般等价关系时,上、下近似算子的具体变化形式。然后,将普通二型模糊集之间包含关系的定义推广到了二型直觉模糊集,在此基础上研究了二型直觉模糊上、下近似算子的一些性质。最后,定义了自反的、对称的和传递的二型直觉模糊关系,并讨论了这3种特殊的二型直觉模糊关系与近似算子的特征之间的联系。该结论进一步丰富了二型模糊集理论和粗糙集理论,为二型直觉模糊信息系统的应用奠定了良好的理论基础。     

关于二型模糊集合的一些基本问题

采用集合论的方法给出了单位模糊集合和二型模糊集合及其在一点的限制等定义,使得二型模糊集合更易于理解.通过定义嵌入单位模糊集合来描述一般二型模糊集合,并给出离散、半连通二型模糊集合的表达式.根据论域、主隶属度及隶属函数的特性将二型模糊集合分为四种类型:离散、半连通、连通及复合型,并根据连通的特点将连通二型模糊集合分为单连通及多连通两类.利用支集的闭包（Closure of support,CoS）划分法表述主隶属度及区间二型模糊集合.提出了CoS二、三次划分法分别来表述单、复连通二型模糊集合,并使每一个子区域的上下边界及次隶属函数在该子区域上的限制分别具有相同的解析表述式.最后,探讨了二型模糊集合在一点的限制、主隶属度、支集、嵌入单位模糊集合之间的关系.     

Designing of a type-2 fuzzy logic filter for improving edge-preserving restoration of interlaced-to-progressive conversion

This paper focuses on recently advanced fuzzy models and the application of type-2 fuzzy sets in video deinterlacing. The final goal of the proposed deinterlacing algorithm is to exactly determine an unknown pixel value while preserving the edges and details of the image. To begin, we will discuss some artefacts of spatial, temporal, and spatio-temporal domain deinterlacing methods. In order to address the aforementioned issues, we adopted type-2 fuzzy sets concepts to design a weight evaluating approach. In the proposed method, the upper and lower fuzzy membership functions of the type-2 fuzzy logic filters are derived from the type-1 (or primary) fuzzy membership function. The weights from upper and lower membership functions are considered to be multiplied with the candidate deinterlaced pixels. Experimental results proved that the performance of the proposed method was superior, both objectively and subjectively to other different conventional deinterlacing methods. Moreover, the proposed method preserved the smoothness of the original image edges and produced a high-quality progressive image.     

Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets

In this paper, we present a new method to handle fuzzy multiple attributes group decision-making problems based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. First, we present the arithmetic operations between interval type-2 fuzzy sets. Then, we present a fuzzy ranking method to calculate the ranking values of interval type-2 fuzzy sets. We also make a comparison of the ranking values of the proposed method with the existing methods. Based on the proposed fuzzy ranking method and the proposed arithmetic operations between interval type-2 fuzzy sets, we present a new method to handle fuzzy multiple attributes group decision-making problems. The proposed method provides us with a useful way to handle fuzzy multiple attributes group decision-making problems in a more flexible and more intelligent manner due to the fact that it uses interval type-2 fuzzy sets rather than traditional type-1 fuzzy sets to represent the evaluating values and the weights of attributes.     

Type-2 Fuzzy Control for Driving State and Behavioral Decisions of Unmanned Vehicle

In this paper, interval type-2 fuzzy sets, fuzzy comprehensive evaluation and the fuzzy control rules are synthesized to realize the control of unmanned vehicle in driving state and behavioral decisions. Compared to the type-1 fuzzy set, type-2 fuzzy sets have more advantages in handling the model based on uncertainties, linguistic information because the membership functions are fuzzy sets. Different membership functions are established for each factor when the unmanned vehicle is driving at different speed intervals. In addition, a new evaluation method is developed to analyze unmanned vehicle’s driving state. Finally, a set of dynamic fuzzy rules are sorted out, which can be applied to the unmanned vehicle’s behavioral decision-making and provide a new idea to related research.      

二型模糊相似度及其应用

二型模糊集可以直接处理高度不确定性,并且具有很强的实际应用背景。基于二型模糊相似度的公理化定义,给出了新的二型模糊相似度计算公式。进一步,将二型模糊相似度与Yang-Shih方法相结合,用于二型模糊数据的聚类分析,聚类结果与Yang-Lin的结果进行了比较,实例表明新的相似度更合理。此外,基于二型模糊相似度,讨论了二型模糊信息系统的属性约简问题,给出了相应约简的分辨函数法,并通过实例说明了该方法的具体计算步骤。     

Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets

In this paper, we present a new method to deal with fuzzy multiple attributes group decision-making problems based on ranking interval type-2 fuzzy sets. First, we propose a new method for ranking interval type-2 fuzzy sets. Then, we propose a new method for fuzzy multiple attributes group decision-making based on the proposed ranking method of interval type-2 fuzzy sets. We also use some examples to illustrate the fuzzy multiple attributes group decision-making process of the proposed method. The proposed method is simpler than the methods presented in [Chen and Lee, 2010a] and [Lee and Chen, 2010b] for fuzzy multiple attributes group decision-making based on interval type-2 fuzzy sets. It provides us with a useful way for dealing with fuzzy multiple attributes group decision-making problems based on interval type-2 fuzzy sets.     

Supplier selection using a clustering method based on a new distance for interval type-2 fuzzy sets: A case study

Supplier selection is a decision-making process to identify and evaluate suppliers for making contracts. Here, we use interval type-2 fuzzy values to show the decision makers’ preferences and also introduce a new formula to compute the distance between two interval type-2 fuzzy sets. The performance of the proposed distance formula in comparison with the normalized Hamming, normalized Hamming based on the Hausdorff metric, normalized Euclidean and the signed distances is evaluated. The results show that the signed distance has the same trend as our method, but the other three methods are not appropriate for interval type-2 fuzzy sets. Using this approach, we propose a hierarchical clustering-based method to solve a supplier selection problem and find the proximity of the suppliers. To illustrate the applicability of the proposed method, first a case study of supplier selection problem with 8 criteria and 8 suppliers are illustrated and next, an example taken from the literature is worked through. Then, to test the hierarchical clustering-based method and compare with the obtained results by two other methods, a comparative study using experimental analysis is designed. The results show that while the proposed hierarchical clustering algorithm provides acceptable results, it is also conveniently appropriate for using interval type-2 fuzzy sets and obtaining proximity of suppliers.     

Ⅱ型模糊控制综述

Ⅱ型模糊集合是传统Ⅰ型模糊集合的扩展,其特征是隶属度值本身为模糊集合.基于Ⅱ型模糊集合的Ⅱ型模糊控制器可以同时有效地处理语言和数据不确定性,在高小确定场合具有明显超过相应Ⅰ型控制器的性能表现.本文首先对Ⅱ型模糊集合及系统理论进行了概述,然后对Ⅱ型非自适应模糊控制器Ⅱ型自适应模糊控制器和Ⅱ型自组织模糊控制器的研究进展分别...     

二型直觉模糊集

二型模糊集和直觉模糊集都具有很强的实际应用背景.二型模糊集增强了系统处理不确定性的能力,直觉模糊集为解决人们判断问题所出现的犹豫信息提供了理论依据.本文在二型模糊集和直觉模糊集的基础上,给出了二型直觉模糊集的概念,证明了二型直觉模糊集是一型模糊集、直觉模糊集、区间值模糊集、区间值直觉模糊集的广义形式,讨论了二型直觉模糊集的基本运算和二型直觉模糊关系.最后,研究了基于二型直觉模糊理论的近似推理,并实例说明了二型直觉模糊集的实际应用背景.     

二型模糊粗糙集

基于二型模糊关系,研究二型模糊粗糙集.首先,在二型模糊近似空间中定义了二型模糊集的上近似和下近似;然后,研究二型模糊粗糙上下近似算子的基本性质,讨论二型模糊关系与二型模糊粗糙近似算子的特征联系;最后,给出二型模糊粗糙近似算子的公理化描述.     

Long-term Traffic Volume Prediction Based on K-means Gaussian Interval Type-2 Fuzzy Sets

This paper uses Gaussian interval type-2 fuzzy set theory on historical traffic volume data processing to obtain a 24- hour prediction of traffic volume with high precision. A K-means clustering method is used in this paper to get 5 minutes traffic volume variation as input data for the Gaussian interval type-2 fuzzy sets which can reflect the distribution of historical traffic volume in one statistical period. Moreover, the cluster with the largest collection of data obtained by K-means clustering method is calculated to get the key parameters of type-2 fuzzy sets, mean and standard deviation of the Gaussian membership function. Using the range of data as the input of Gaussian interval type-2 fuzzy sets leads to the range of traffic volume forecasting output with the ability of describing the possible range of the traffic volume as well as the traffic volume prediction data with high accuracy. The simulation results show that the average relative error is reduced to 8% based on the combined K-means Gaussian interval type-2 fuzzy sets forecasting method. The fluctuation range in terms of an upper and a lower forecasting traffic volume completely envelopes the actual traffic volume and reproduces the fluctuation range of traffic flow.      

Interval type-2 fuzzy expert system for prediction of carbon monoxide concentration in mega-cities

This paper presents an indirect approach to interval type-2 fuzzy logic system modeling to forecaste the level of air pollutants. The type-2 fuzzy logic system permits us to model the uncertainties among rules and the parameters related to data analysis. In this paper, we propose an indirect method to create an interval type-2 fuzzy logic system from a historical data, where Footprint of Uncertainties of fuzzy sets are extracted by implementation of an interval type-2 FCM algorithm and based on an upper and lower value for the level of fuzziness m in FCM. Finally, the proposed model is applied for prediction of carbon monoxide concentration in Tehran air pollution. It is shown that the proposed type-2 fuzzy logic system is superior in comparison to type-1 fuzzy logic systems in terms of two performance indices.     

基于包含度的区间二型模糊粗糙集

基于区间二型模糊包含度的公理化定义,给出了新的区间二型模糊包含度计算公式.进一步,通过包含度定义了区间二型模糊粗糙集,并讨论了它的一些基本性质.最后,利用区间二型模糊粗糙集研究了连续域决策信息系统的属性约简,给出了新的约简方法.实例说明了该约简方法的具体计算步骤,并且通过实验验证了该算法的有效性和可行性.     

State feedback control of interval type-2 Takagi–Sugeno fuzzy systems via interval type-2 regional switching fuzzy controllers

The interval type-2 Takagi–Sugeno fuzzy systems have been proposed to handle nonlinear systems subject to parameter uncertainties. In this paper, a new type of state feedback controller, namely, interval type-2 regional switching fuzzy controller, is proposed to conceive less-conservative stabilisation conditions, which is switched by basing on the values of system states. To further reduce the conservativeness in the stability analysis, the information of lower and upper membership functions is also considered. Stability conditions for the interval type-2 fuzzy closed-loop systems are presented in the form of linear matrix inequalities (LMIs). Simulation examples are provided to illustrate the effectiveness of the proposed method.     

二型模糊集的模糊熵研究

研究基于质心的二型模糊集的模糊熵和加权模糊熵,构造了两个二型模糊集的模糊熵度量.针对二型模糊集的特殊情形,提出一种新的区间值模糊集的模糊熵度量,既弥补了现有区间值模糊集退化为普通模糊集时熵为零的不足,又克服了两个明显不同的区间值模糊集熵相等的缺点.数值实例和仿真实验表明了所提出模糊熵的合理性和实用性.     

Type-2 fuzzy Gaussian mixture models

This paper presents a new extension of Gaussian mixture models (GMMs) based on type-2 fuzzy sets (T2 FSs) referred to as T2 FGMMs. The estimated parameters of the GMM may not accurately reflect the underlying distributions of the observations because of insufficient and noisy data in real-world problems. By three-dimensional membership functions of T2 FSs, T2 FGMMs use footprint of uncertainty (FOU) as well as interval secondary membership functions to handle GMMs uncertain mean vector or uncertain covariance matrix, and thus GMMs parameters vary anywhere in an interval with uniform possibilities. As a result, the likelihood of the T2 FGMM becomes an interval rather than a precise real number to account for GMMs uncertainty. These interval likelihoods are then processed by the generalized linear model (GLM) for classification decision-making. In this paper we focus on the role of the FOU in pattern classification. Multi-category classification on different data sets from UCI repository shows that T2 FGMMs are consistently as good as or better than GMMs in case of insufficient training data, and are also insensitive to different areas of the FOU. Based on T2 FGMMs, we extend hidden Markov models (HMMs) to type-2 fuzzy HMMs (T2 FHMMs). Phoneme classification in the babble noise shows that T2 FHMMs outperform classical HMMs in terms of the robustness and classification rate. We also find that the larger area of the FOU in T2 FHMMs with uncertain mean vectors performs better in classification when the signal-to-noise ratio is lower.     

Adaptive sliding mode control for interval type-2 stochastic fuzzy systems subject to actuator failures

This paper investigates the problem of adaptive sliding mode control for a class of interval type-2 Itô stochastic fuzzy systems, where the actuator failures may happen. The sliding function is firstly constructed, whose key feature is its dependence on the upper membership functions. And then, an adaptive scheme is proposed to estimate the effectiveness lose values of faulty actuators, and a sliding mode controller based on estimating scheme is designed such that the reachability of the specified sliding surface can be guaranteed even in the presence of actuator failures, in which the lower and upper membership functions are involved. Moreover, the stability conditions of sliding mode dynamics are derived, which involve some coupling terms of Lyapunov matrix and the sliding matrix. By introducing additional matrix variables and employing the cone complementary linearisation algorithm, the above nonlinear stability criterions are decoupled and lastly converted to a minimisation problem with linear constraints. Finally, a numerical example demonstrates the validity of the proposed method.     

基于区间二型模糊集合的语言动力系统稳定性

运用区间二型模糊集合(Interval type-2 fuzzy sets, IT2 FSs) 的扩展原理将常规的数值函数转化为对应的区间二型模糊函数, 并给出了相应的词计算(Computing with words, CW)方法与算法,最后分析了严格单调情况下基于区间二型模糊集合的单输入单输出系统的语言动力系统(Linguistic dynamic systems, LDS)稳定性.