Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

NL-fuzzy拓扑空间中的N-紧性

利用α-远域族定义了NL-fuzzy拓扑空间中的N-紧性,借助α-分子网,模糊滤子以及模糊滤子基的概念给出其等价刻画。证明了N-紧性具有拓扑不变性以及有限多个N-紧集的并仍为N-紧集等性质。

基于改进Fuzzy ART的自适应雷达信号分选

侦察接收机对获取的辐射源波形去交织以分离不同信号,称为信号分选,是电磁频谱战系统的核心技术.复杂电磁环境下脉冲流密度大、时域波形及诸域特征严重交叠,导致多数基于无监督模型的信号分选方法难以胜任.提出一种可自适应调整警戒阈值的模糊自适应共振理论(AVT fuzzy ART)聚类算法,基于对属性差异敏感的曼哈顿距离自适应调整警戒阈值,依据在线累积数据得出的辐射源瞬态聚类概率对警戒阈值动态加权.仿真结果表明,该方法能在无历史先验信息的条件下胜任多类别辐射源信号去交错.

建筑供应链视角下区块链技术应用影响因素分析:基于Fuzzy-DEMATEL-ISM模型

为促进区块链技术赋能建筑供应链数字化转型,从建筑供应链视角探究区块链技术应用影响因素的相互关系与作用方式。基于模糊决策实验室与解释结构模型先后界定因素属性特征、相互作用关系,划分层次结构,并从因素的中心度(M)、原因度(R),层次结构维度进行分析。结果表明:政策导向与法律体系、技术兼容性、技术功能特性、技术运营成本、企业规模等作为原因因素,对区块链技术应用具有驱动作用;竞争者行为、节点企业使用意愿、行业技术认知、专业基础设施、核心人才与技术能力、供应链结构模式等因素作为结果因素,可反映区块链实际应用情况;在建筑供应链的区块链技术应用过程中以改善结果因素为导向的促进策略更为有效。研究结论可为促进区块链在建筑行业中的应用提供策略参考。

矿井带式输送机液压拉紧Fuzzy-PID控制技术研究

针对矿井传统带式输送机拉紧系统响应速度慢、调节能力差、拉紧控制时变性和非线性等问题,提出了一种矿井带式输送机液压拉紧系统Fuzzy-PID控制(基于模糊算法的PID控制)方法。首先,根据液压拉紧装置建立数学模型,其次通过Matlab内置的Simulink仿真库分别对Fuzzy-PID控制器和PID控制器的液压拉紧系统进行仿真,得出输送带拉紧张力启动响应阶段和张力突变的调节响应图,并做出对比分析。最后,通过试验测试来验证算法模型的有效性。仿真结果表明:矿井带式输送机液压拉紧Fuzzy-PID控制系统不仅在启动阶段还有张力突变过程中都具有更好的稳态性能、更快的响应速度。在拉紧装置启动响应阶段的张力超调量降低了13.5%、到达期望值的时间缩短了0.5 s。在拉紧装置张力突变即模拟拉紧和松带阶段,当张力增加时,Fuzzy-PID控制器的调节速度缩短了0.4 s,超调量下降了4%。当张力减少时,Fuzzy-PID控制器的调节速度缩短了0.3 s,超调量降低了2%。试验结果表明:采用Fuzzy-PID控制的效果更佳优异稳定,且损耗更小。对比于PID控制,Fuzzy-PID控制效果更为良好,平均时间缩短31%且总体趋于稳定。对于矿井带式输送机这种连续运输作业的设备,Fuzzy-PID控制技术为矿井带式输送带平稳运行提供了一定保障,不仅减少了电能浪费,也降低了维护保养带式输送机的保养成本。

基于VWM-GRA的新型Fuzzy-FMEA复杂装备风险评估方法

失效模式和影响分析(Failure Mode and Effect Analysis,FMEA)是一种识别和预防复杂装备潜在故障模式的风险评估方法,然而,现有FMEA方法采用等权重和精确数表征不确定情形下的风险因素评估信息,导致风险优先数(Risk Priority Number,RPN)难以准确评估复杂装备故障模式的风险优先级。针对这一难题,文中提出了一种基于变权方法-灰色关联分析(Variable Weight Method-Grey Relation Analysis,VWM-GRA)的新型Fuzzy-FMEA复杂装备风险评估方法。在风险因素权重分配方面,在模糊熵值法的基础上,考虑风险评估信息对风险因素权重的影响,构建风险因素变权综合模型以动态调整风险因素权重值,据此确定风险因素的客观变权重;在风险优先数排序方面,在模糊语言变量表征风险因素评估信息的基础上,考虑风险因素评估信息不确定性量化对故障模式排序精度的影响,构建故障模式模糊灰色关联分析模型,以获取评估信息数据序列间的相对关联度,据此评估故障模式的风险优先级。最后,通过航空发动机主轴轴承的故障模式风险实例,分析验证文中方法的有效性。案例分析表明:该方法能够有效解决不确定情形下准确评估复杂装备故障模式风险优先级的难题。

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

On Fuzzy Regularly Closed Filters in Michálek Fuzzy Topological Space

C.L. Chang’s introduction of fuzzy topology in 1981 opened up new avenues for parallel theories in topology. However, Chang’s work appears to focus more on the topology of fuzzy sets rather than fuzzy topology itself. In 1975, Michálek presented a functional definition of ordinary topology and later developed fuzzy topology as a distinct extension of this idea, setting it apart from Chang’s approach. While there has been significant research on Chang’s fuzzy topology, Michálek’s version has not received as much attention. This paper introduces the concept of fuzzy regularly closed filters, or FRCM filters, within Michálek’s fuzzy topological space and explores some properties of FRCM ultrafilters.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

A Neuro T-Norm Fuzzy Logic Based System

In this study, we are first examining well-known approach to improve fuzzy reasoning model (FRM) by use of the genetic-based learning mechanism [1]. Later we propose our alternative way to build FRM, which has significant precision advantages and does not require any adjustment/learning. We put together neuro-fuzzy system (NFS) to connect the set of exemplar input feature vectors (FV) with associated output label (target), both represented by their membership functions (MF). Next unknown FV would be classified by getting upper value of current output MF. After that the fuzzy truths for all MF upper values are maximized and the label of the winner is considered as the class of the input FV. We use the knowledge in the exemplar-label pairs directly with no training. It sets up automatically and then classifies all input FV from the same population as the exemplar FVs. We show that our approach statistically is almost twice as accurate, as well-known genetic-based learning mechanism FRM.

Computation Tree Logic Model Checking of Multi-Agent Systems Based on Fuzzy Epistemic Interpreted Systems

Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications.Although there is an extensive literature on qualitative properties such as safety and liveness,there is still a lack of quantitative and uncertain property verifications for these systems.In uncertain environments,agents must make judicious decisions based on subjective epistemic.To verify epistemic and measurable properties in multi-agent systems,this paper extends fuzzy computation tree logic by introducing epistemic modalities and proposing a new Fuzzy Computation Tree Logic of Knowledge(FCTLK).We represent fuzzy multi-agent systems as distributed knowledge bases with fuzzy epistemic interpreted systems.In addition,we provide a transformation algorithm from fuzzy epistemic interpreted systems to fuzzy Kripke structures,as well as transformation rules from FCTLK formulas to Fuzzy Computation Tree Logic(FCTL)formulas.Accordingly,we transform the FCTLK model checking problem into the FCTL model checking.This enables the verification of FCTLK formulas by using the fuzzy model checking algorithm of FCTL without additional computational overheads.Finally,we present correctness proofs and complexity analyses of the proposed algorithms.Additionally,we further illustrate the practical application of our approach through an example of a train control system.

Spherical Functions on Fuzzy Lie Group

Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .

An Integrated Bipolar Picture Fuzzy Decision Driven System to Scrutinize Food Waste Treatment Technology through Assorted Factor Analysis

Food Waste(FW)is a pressing environmental concern that affects every country globally.About one-third of the food that is produced ends up as waste,contributing to the carbon footprint.Hence,the FW must be properly treated to reduce environmental pollution.This study evaluates a few available Food Waste Treatment(FWT)technologies,such as anaerobic digestion,composting,landfill,and incineration,which are widely used.A Bipolar Picture Fuzzy Set(BPFS)is proposed to deal with the ambiguity and uncertainty that arise when converting a real-world problem to a mathematical model.A novel Criteria Importance Through Intercriteria Correlation-Stable Preference Ordering Towards Ideal Solution(CRITIC-SPOTIS)approach is developed to objectively analyze FWT selection based on thirteen criteria covering the industry’s technical,environmental,and entrepreneurial aspects.The CRITIC method is used for the objective analysis of the importance of each criterion in FWT selection.The SPOTIS method is adopted to rank the alternative hassle-free,following the criteria.The proposed model offers a rank reversal-free model,i.e.,the rank of the alternatives remains unaffected even after the addition or removal of an alternative.In addition,comparative and sensitivity analyses are performed to ensure the reliability and robustness of the proposed model and to validate the proposed result.

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.

Connected Components in Bipolar Fuzzy Digital Plane

The concepts of connectedness play a critical role in digital picture segmentation and analyses. However, the crisp nature of set theory imposes hard boundaries that restrict the extension of the underlying topological notions and results. Whilst fuzzy set theory was introduced to address this inherent drawback, most human processes are not just fuzzy but also double-sided. Most phenomena will exhibit both a positive side and a negative side. Therefore, it is not enough to have a theory that addresses imprecision, uncertainty and ambiguity;rather, the theory must also be able to model polarity. Hence the study of bipolar fuzzy theory is of potential significance in an attempt to model real-life phenomena. This paper extends some concepts of fuzzy digital topology to bipolar fuzzy subsets including some important basic properties such as connectedness and surroundedness.

Fuzzy Difference Equations in Diagnoses of Glaucoma from Retinal Images Using Deep Learning

The intuitive fuzzy set has found important application in decision-making and machine learning.To enrich and utilize the intuitive fuzzy set,this study designed and developed a deep neural network-based glaucoma eye detection using fuzzy difference equations in the domain where the retinal images converge.Retinal image detections are categorized as normal eye recognition,suspected glaucomatous eye recognition,and glaucomatous eye recognition.Fuzzy degrees associated with weighted values are calculated to determine the level of concentration between the fuzzy partition and the retinal images.The proposed model was used to diagnose glaucoma using retinal images and involved utilizing the Convolutional Neural Network(CNN)and deep learning to identify the fuzzy weighted regularization between images.This methodology was used to clarify the input images and make them adequate for the process of glaucoma detection.The objective of this study was to propose a novel approach to the early diagnosis of glaucoma using the Fuzzy Expert System(FES)and Fuzzy differential equation(FDE).The intensities of the different regions in the images and their respective peak levels were determined.Once the peak regions were identified,the recurrence relationships among those peaks were then measured.Image partitioning was done due to varying degrees of similar and dissimilar concentrations in the image.Similar and dissimilar concentration levels and spatial frequency generated a threshold image from the combined fuzzy matrix and FDE.This distinguished between a normal and abnormal eye condition,thus detecting patients with glaucomatous eyes.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

A Quality Evaluation System for Dissertation Based on Fuzzy Analytic Hierarchy Process

A dissertation is a research report or scientific paper written by an author to obtain a certain degree. It reflects postgraduates’ research achievements and the educational quality of an institute, even a country. To construct an optimized quality evaluation system for postgraduate dissertation (QESPD), we summarized the influencing factors and invited 10 experienced specialists to rate and prioritize them based on fuzzy analytic hierarchy process. Four primary indicators (innovation, integrity, scientificity and normativity) and 16 sub-indicators were selected to form the evaluation system. The order of primary indicators by weight, was innovation (0.4269), scientificity (0.2807), integrity (0.1728) and normativity (0.1196). The top five sub-dimensions were theoretical originality, scientific value, data reliability, design rationality and evidence credibility. To demonstrate the effectiveness of the proposed system, a case study was performed. In the case study, it was demonstrated that the established two-index-hierarchy QESPD in this study was a more scientific and reasonable evaluation system worthy of promotion and application.

Evaluation of Industrial IoT Service Providers with TOPSIS Based on Circular Intuitionistic Fuzzy Sets

Industrial Internet of Things(IIoT)service providers have become increasingly important in the manufacturing industry due to their ability to gather and process vast amounts of data from connected devices,enabling manufacturers to improve operational efficiency,reduce costs,and enhance product quality.These platforms provide manufacturers with real-time visibility into their production processes and supply chains,allowing them to optimize operations and make informed decisions.In addition,IIoT service providers can help manufacturers create new revenue streams through the development of innovative products and services and enable them to leverage the benefits of emerging technologies such as Artificial Intelligence(AI)and machine learning.Overall,the implementation of IIoT platforms in the manufacturing industry is crucial for companies seeking to remain competitive and meet the ever-increasing demands of customers in the digital age.In this study,the evaluation criteria to be considered in the selection of IIoT service provider in small andmedium-sized(SME)manufacturing enterprises will be determined and IIoT service providers alternatives will be evaluated using the technique for order preference by similarity to an ideal solution(TOPSIS)method based on circular intuitionistic fuzzy sets.Based on the assessments conducted in accordance with the literature review and expert consultations,a set of 8 selection criteria has been established.These criteria encompass industry expertise,customer support,flexibility and scalability,security,cost-effectiveness,reliability,data analytics,as well as compatibility and usability.Upon evaluating these criteria,it was observed that the security criterion holds the highest significance,succeeded by cost-effectiveness,data analytics,flexibility and scalability,reliability,and customer support criteria,in descending order of importance.Following the evaluation of seven distinct alternatives against these criteria,it was deduced that the A6 alternative,a German service provider,emerged as the most favorable option.The identical issue was addressed utilizing sensitivity analysis alongside various multi-criteria decision-making(MCDM)methods,and after comprehensive evaluation,the outcomes were assessed.Spearman’s correlation coefficient was computed to ascertain the association between the rankings derived from solving the problem using diverse MCDM methods.