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

This paper uses Gaussian interval type-2 fuzzy se 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.

Entropy measures of type-2 intuitionistic fuzzy sets and type-2 triangular intuitionistic trapezodial fuzzy sets

In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.

Modelling spatial vagueness based on type-2 fuzzy set

The modelling and formal characterization of spatial vagueness plays an increasingly important role in the imple- mentation of Geographic Information System (GIS). The concepts involved in spatial objects of GIS have been investigated and acknowledged as being vague and ambiguous. Models and methods which describe and handle fuzzy or vague (rather than crisp or determinate) spatial objects, will be more necessary in GIS. This paper proposes a new method for modelling spatial vagueness based on type-2 fuzzy set, which is distinguished from the traditional type-1 fuzzy methods and more suitable for describing and implementing the vague concepts and objects in GIS.

New Approaches to the Prognosis and Diagnosis of Breast Cancer Using Fuzzy Expert Systems

Breast cancer remains a significant global health challenge, necessitating effective early detection and prognosis to enhance patient outcomes. Current diagnostic methods, including mammography and MRI, suffer from limitations such as uncertainty and imprecise data, leading to late-stage diagnoses. To address this, various expert systems have been developed, but many rely on type-1 fuzzy logic and lack mobile-based applications for data collection and feedback to healthcare practitioners. This research investigates the development of an Enhanced Mobile-based Fuzzy Expert system (EMFES) for breast cancer pre-growth prognosis. The study explores the use of type-2 fuzzy logic to enhance accuracy and model uncertainty effectively. Additionally, it evaluates the advantages of employing the python programming language over java for implementation and considers specific risk factors for data collection. The research aims to dynamically generate fuzzy rules, adapting to evolving breast cancer research and patient data. Key research questions focus on the comparative effectiveness of type-2 fuzzy logic, the handling of uncertainty and imprecise data, the integration of mobile-based features, the choice of programming language, and the creation of dynamic fuzzy rules. Furthermore, the study examines the differences between the Mamdani Inference System and the Sugeno Fuzzy Inference method and explores challenges and opportunities in deploying the EMFES on mobile devices. The research identifies a critical gap in existing breast cancer diagnostic systems, emphasizing the need for a comprehensive, mobile-enabled, and adaptable solution by developing an EMFES that leverages Type-2 fuzzy logic, the Sugeno Inference Algorithm, Python Programming, and dynamic fuzzy rule generation. This study seeks to enhance early breast cancer detection and ultimately reduce breast cancer-related mortality.

红外图像的一种Type-Ⅱ模糊增强算法

提出了一种基于Type-Ⅱ模糊集的红外图像增强算法,该算法首先根据像素的邻域相关性对图像进行预处理,然后以Ostu分割阈值为基础,构造了红外图像的Type-Ⅱ模糊特征平面;然后,采用不同的变换规则对图像进行模糊增强,并将结果进行融合;最后,通过Type reduction和去模糊化操作得到增强后的输出图像。对几幅典型的红外图像的增强实验表明,提出的方法能够有效地提高红外图像的对比度。

Study of Interval Type-2 Fuzzy Controller for the Twin-tank Water Level System

For dealing with large static error due to poor immunity of the traditional fuzzy control, a novel interval type-2 fuzzy control system is proposed. By extending the typical membership functions to interval type-2 membership functions, the proposed control system can efficiently reduce the uncertain disturbance from real environment without increasing the design complexity. The simulation results on the water tank level control system showed that the proposed method succeeded in better static and dynamic control with stronger robust performance than the traditional fuzzy control method.

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.

A simplified adaptive interval Type-2 fuzzy control in practical industrial application

Adaptive Type-2 fuzzy control possesses control performance better than the traditional adaptive fuzzy control.However,heavy computation burden obviously blocks the utilization of adaptive Type-2 fuzzy control in industrial application.By adopting novel piecewise fuzzy sets and center-average type-reduction,a simplified adaptive interval Type-2 fuzzy controller involving less computation is developed for practical industrial application.In the proposed controller,the inputs are divided into several subintervals and then two piecewise fuzzy sets are used for each subinterval.With the manner of piecewise fuzzy sets and a novel fuzzy rules inference engine,only part of fuzzy rules are simultaneously activated in one control loop,which exponentially decreases the computation and makes the controller appropriate in industrial application.The simulation and experimental study,involving the popular magnetic levitation platform,shows the predicted system with theoretical stability and good tracking performance.The analysis indicates that there is far less computation of the proposed controller than the traditional adaptive interval Type-2 fuzzy controller,especially when the number of fuzzy rules and fuzzy sets is large,and the controller still maintains good control performance as the traditional one.

A Novel Green Supplier Selection Method Based on the Interval Type-2 Fuzzy Prioritized Choquet Bonferroni Means

In view of the environment competencies,selecting the optimal green supplier is one of the crucial issues for enterprises,and multi-criteria decision-making(MCDM)methodologies can more easily solve this green supplier selection(GSS)problem.In addition,prioritized aggregation(PA)operator can focus on the prioritization relationship over the criteria,Choquet integral(CI)operator can fully take account of the importance of criteria and the interactions among them,and Bonferroni mean(BM)operator can capture the interrelationships of criteria.However,most existing researches cannot simultaneously consider the interactions,interrelationships and prioritizations over the criteria,which are involved in the GSS process.Moreover,the interval type-2 fuzzy set(IT2FS)is a more effective tool to represent the fuzziness.Therefore,based on the advantages of PA,CI,BM and IT2FS,in this paper,the interval type-2 fuzzy prioritized Choquet normalized weighted BM operators with fuzzy measure and generalized prioritized measure are proposed,and some properties are discussed.Then,a novel MCDM approach for GSS based upon the presented operators is developed,and detailed decision steps are given.Finally,the applicability and practicability of the proposed methodology are demonstrated by its application in the shared-bike GSS and by comparisons with other methods.The advantages of the proposed method are that it can consider interactions,interrelationships and prioritizations over the criteria simultaneously.

General Type-2 Fuzzy Topological Spaces

In this paper, a presented definition of type-2 fuzzy sets and type-2 fuzzy set operation on it was given. The aim of this work was to introduce the concept of general topological spaces were extended in type-2 fuzzy sets with the structural properties such as open sets, closed sets, interior, closure and neighborhoods in topological spaces were extended to general type-2 fuzzy topological spaces and many related theorems are proved.

PSO type-reduction method for geometric interval type-2 fuzzy logic systems

In a special case of type-2 fuzzy logic systems （FLS）, i.e. geometric inteIval type-2 fuzzy logic systems （GIT-2FLS）, the crisp output is obtained by computing the geometric center of footprint of uncertainly （FOU） without type-reduction, but the defuzzifying method acts against the corner concepts of type-2 fuzzy sets in some cases. In this paper, a PSO type-reduction method for GIT-2FLS based on the particle swarm optimization （PSO） algorithm is presented. With the PSO type-reduction, the inference principle of geometric interval FLS operating on the continuous domain is consistent with that of traditional interval type-2 FLS operating on the discrete domain. With comparative experiments, it is proved that the PSO type-reduction exhibits good performance, and is a satisfactory complement for the theory of GIT-2FLS.

Type-2 Fuzzy Point

The important role of the concept of type-2 fuzzy point in the formation of type-2 fuzzy open sets such as type-2 fuzzy δ≈-closed?set this important role make the main objective of this paper is to introduce the concept type-2 fuzzy point of type-2 fuzzy set an important definitions in the composition of this concept as α≈-plane?and the support of type-2 fuzzy set after preliminaries we present the definition of type-1 fuzzy set (fuzzy set) and fuzzy point and the special concepts that helped to configure them as support.

FuzzyⅡ—仿紧性与分离性

文 [1 ]曾在 L -fuzzy拓扑空间中引入了 —仿紧集的概念 .文 [2 ]指出这种 —仿紧集定义不以分明情形为特款 ,并修正了这一定义 .因此文 [1 ]中许多结论均需重新论证 .本文的目的就是重证 [1

基于改进NSGA-Ⅱ算法的电厂多目标负荷分配

针对电厂负荷分配通常以经济性单目标进行优化的局限性,综合国内外研究情况。确定了以负荷分配中的经济性和快速性为目标建立多目标优化的数学模型。运用改进的NSGA-Ⅱ算法求解负荷分配问题,得到Pareto最优解集,并引入模糊优化理论将优化得到的Pareto最优解集进行隶属度计算得到最优解。实例运行结果表明,该优化方法是正确的、有效的。

基于Ⅱ型模糊集的车辆图像二值化算法

车辆图像二值化是车牌识别系统中一个关键的部分,其性能的好坏直接影响到后续的工作的效果.本文提出了一种新的针对于车辆图像的二值化算法:基于Ⅱ型模糊集的二值化算法,此算法是在I型模糊隶属度的基础上,建立了Ⅱ型模糊集,同时基于Ⅰ型隶属度函数的选择,采用灰度遍历搜寻在最小模糊度意义下的最佳灰度值作为分块后的车辆图像的二值化阈值.此算法保持了原有模糊集所具有的鲁棒性,减少了后续工作中图像背景对图像目标的影响,实验结果证明此算法的性能要优于Otsu等二值化算法.

基于Ⅱ型模糊集的工程参数的评判

提出了一种基于Ⅱ型模糊集的工程参数模糊综合评判方法。将单因素评判的隶属度和各因素的权数均视为模糊数,应用模糊数的运算规则,建立了相应的模糊综合评判算法。考虑到模糊数运算后展形大大增加的情况,提出了既节省计算又保证精度的展形截断措施。总评判指标的模糊性,以其隶属度为权数进行加权平均处理,从而得到最终的评判结果。并给出了具体算例。

Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of differ- ent proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable prop- erties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Lim- itations of existing ranking methods have been studied. Fur- ther for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example.

Comments on ＂Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems＂

In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets （T2FSs） as provided by Singh （Frontiers of Computer Science, 2014, 8（5）, 741-752）, are incorrect by a counterexample. Further, these propositions have been corrected in the present manuscript by giving a correct relation between the T2FSs and validating it with a numerical example.

基于POP NSGA-Ⅱ的配电网故障恢复重构

快速的非支配排序遗传算法（NSGA-Ⅱ）可以使每次进化过程中得到的个体分布均匀，具有较好的收敛性和鲁棒性。本文分析了当前遗传算法（GA）的缺陷，将NSGA-Ⅱ应用到配电网的故障恢复重构中，并提出通过一种Pareto寻优路径（POP）控制选择操作的方法，一方面可以扩大搜索面积、避免陷入局部最优；另一方面可以适时地停止进化、减少多余的计算。另外，本文根据模糊集理论确定故障恢复重构的最终解决方案，使NSGA-Ⅱ算法适用于恢复重构问题。算例结果表明，POPNSGA-Ⅱ算法与GA、NSGA-Ⅱ算法相比具有更强的寻优能力，是一种解决配电网故障恢复重构问题的新方法。

Image Segmentation Based on Intuitionistic Type-2 FCM Algorithm

Due to using the fuzzy clustering algorithm,the accuracy of image segmentation is not high enough.So one hybrid clustering algorithm combined with intuitionistic fuzzy factor and local spatial information is proposed.Experimental results show that the proposed algorithm is superior to other methods in image segmentation accuracy and improves the robustness of the algorithm.