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.

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.

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 .

Research on θ -Intuitionistic Fuzzy Homomorphism Theory

Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.

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.

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.

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.

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.

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.

Fuzzy Multi-Criteria Decision Support System for the Best Anti-Aging Treatment Selection Process through Normal Wiggly Hesitant Fuzzy Sets

This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine.

Novel Adaptive Memory Event-Triggered-Based Fuzzy Robust Control for Nonlinear Networked Systems via the Differential Evolution Algorithm

This article mainly investigates the fuzzy optimization robust control issue for nonlinear networked systems characterized by the interval type-2(IT2)fuzzy technique under a differential evolution algorithm.To provide a more reasonable utilization of the constrained communication channel,a novel adaptive memory event-triggered(AMET)mechanism is developed,where two event-triggered thresholds can be dynamically adjusted in the light of the current system information and the transmitted historical data.Sufficient conditions with less conservative design of the fuzzy imperfect premise matching(IPM)controller are presented by introducing the Wirtinger-based integral inequality,the information of membership functions(MFs)and slack matrices.Subsequently,under the IPM policy,a new MFs intelligent optimization technique that takes advantage of the differential evolution algorithm is first provided for IT2 TakagiSugeno(T-S)fuzzy systems to update the fuzzy controller MFs in real-time and achieve a better system control effect.Finally,simulation results demonstrate that the proposed control scheme can obtain better system performance in the case of using fewer communication resources.

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.

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.

Optical Fibre Communication Feature Analysis and Small Sample Fault Diagnosis Based on VMD-FE and Fuzzy Clustering

To solve the problems of a few optical fibre line fault samples and the inefficiency of manual communication optical fibre fault diagnosis,this paper proposes a communication optical fibre fault diagnosis model based on variational modal decomposition(VMD),fuzzy entropy(FE)and fuzzy clustering(FC).Firstly,based on the OTDR curve data collected in the field,VMD is used to extract the different modal components(IMF)of the original signal and calculate the fuzzy entropy(FE)values of different components to characterize the subtle differences between them.The fuzzy entropy of each curve is used as the feature vector,which in turn constructs the communication optical fibre feature vector matrix,and the fuzzy clustering algorithm is used to achieve fault diagnosis of faulty optical fibre.The VMD-FE combination can extract subtle differences in features,and the fuzzy clustering algorithm does not require sample training.The experimental results show that the model in this paper has high accuracy and is relevant to the maintenance of communication optical fibre when compared with existing feature extraction models and traditional machine learning models.

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.

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.

Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction

As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.

Multi-Granularity Neighborhood Fuzzy Rough Set Model on Two Universes

The two universes multi-granularity fuzzy rough set model is an effective tool for handling uncertainty problems between two domains with the help of binary fuzzy relations. This article applies the idea of neighborhood rough sets to two universes multi-granularity fuzzy rough sets, and discusses the two-universes multi-granularity neighborhood fuzzy rough set model. Firstly, the upper and lower approximation operators are defined in the two universes multi-granularity neighborhood fuzzy rough set model. Secondly, the properties of the upper and lower approximation operators are discussed. Finally, the properties of the two universes multi-granularity neighborhood fuzzy rough set model are verified through case studies.

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。

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.