Interval-Valued Intuitionistic Fuzzy-Rough Sets

This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.

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.

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.

Novelty of Different Distance Approach for Multi-Criteria Decision-Making Challenges Using q-Rung Vague Sets

In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung normal vague weighted averaging(log q-rung NVWA),a log q-rung normal vague weighted geometric(log q-rung NVWG),a log generalized q-rung normal vague weighted averaging(log Gq-rung NVWA),and a log generalized q-rungnormal vagueweightedgeometric(logGq-rungNVWG)operator are discussed in this article.Adescription is provided of the scoring function,accuracy function and operational laws of the log q-rung VS.The algorithms underlying these functions are also described.A numerical example is provided to extend the Euclidean distance and the Humming distance.Additionally,idempotency,boundedness,commutativity,and monotonicity of the log q-rung VS are examined as they facilitate recognizing the optimal alternative more quickly and help clarify conceptualization.We chose five anemia patients with four types of symptoms including seizures,emotional shock or hysteria,brain cause,and high fever,who had either retrograde amnesia,anterograde amnesia,transient global amnesia,post-traumatic amnesia,or infantile amnesia.Natural numbers q are used to express the results of the models.To demonstrate the effectiveness and accuracy of the models we are investigating,we compare several existing models with those that have been developed.

An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets

Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.

On Multi-Granulation Rough Sets with Its Applications

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

All-electron basis sets for H to Xe specific for ZORA calculations:Applications in atoms and molecules

A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions to describe electrons farther away from the nuclei adequately.Using the ZORA-CCSD(T)/QZP-ZORA theoretical model,atomic ionization energies and bond lengths,harmonic vibrational frequencies,and atomization energies of some molecules were calculated.The addition of core-valence corrections has been shown to improve the agreement between theoretical and experimental results for molecular properties.For atomization energies,a similar observation emerges when considering spin-orbit couplings.With the augmented QZP-ZORA set,static mean dipole polarizabilities of a set of atoms were calculated and compared with previously published recommended and experimental values.Performance evaluations of the ZORA and Douglas–Kroll–Hess Hamiltonians were made for each property studied.

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.

基于Rough Sets的中医指症挖掘研究与应用

针对中医病历数据库中指症样本维数较大、数据特征和属性冗余量较多等特征,在对Rough Sets基本理论和属性约简算法研究的基础上,提出了将属性频度和属性重要性相结合的GENRED_GROWTH中医指症挖掘算法,并进行了基于GENRED_GROWTH的中医指症挖掘原型系统设计与实现。通过分析和实验结果表明:该算法能较好地进行中医指症属性约简,分类精度较高,并且能抽取中医指症相关诊断规则以辅助医生的诊断和治疗。

特殊耗材监管系统(SETS)对HIS系统的功能扩展

介绍了特殊耗材监管系统(SETS)的设计理念和具体方案。它是一种针对医院信息系统(HIS)的功能扩展,有效地解决了大中型医院在特殊耗材使用过程中出现的很多问题。

Cardinal Numbers of Fuzzy Sets

Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.

NEW METHOD FOR MEASURING FUZZINESS IN ROUGH SETS

A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.

On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions

The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.

MULTI-PHASE ACTIVE CONTOUR MODEL FOR IMAGE SEGMENTATION BASED ON LEVEL SETS

A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting background （TPBG）, is developed to remove the information of the background, which blocks the detection of weak boundaries in the object; （2） The two-phase level set is applied multiple times for getting the multi-phase segmentation model （n-1 times for the n-phase model, n〉1）; （3） A scaling-based method is introduced to improve the basic model. Experimental results show that the proposed model is effective for detecting weak boundaries.

Strong Uniqueness of Best Approximations from RS-sets in Banach Spaces

The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.

融合Shadowed Sets聚类的离群点检测算法

从数据整体和宏观特点给出了离群点的新的定义,并基于数据宏观模式定义了一种新的离群因子,该因子考虑了数据点偏离数据模式的程度和数据点本身归类的不确定性;提出了一种新的Shadowed Sets优化目标,使得在模糊集阴影化过程中更加关注核的准确性;同时基于Shadowed Sets聚类,提出了一种结合聚类的离群点检测算法,该算法可以同时进行聚类和离群点检测;通过模拟数据和Iris数据测试,显示算法具有较好的检测效果。

Parallel Sets的改进及其在全球恐怖袭击数据分析中的应用

随着恐怖主义愈演愈烈,"反恐"成为当今世界各国军事安全部门的中心任务。使用分类型可视化工具Parallel Sets分析国际恐怖主义数据库中多属性分类值间的关系,揭示数据库中的隐性信息,并针对Parallel Sets任意排列分类值产生较多交叉的不足,提出带降势的启发式分类值布局算法,自动优化分类值布局顺序,减轻视图中的可视混乱,降势策略可以减少参与计算的分类值数目。实验结果表明,改进的ParallelSets可清晰展现国际恐怖主义数据库中各分类值间的关联,从而辅助用户分析不同恐怖组织的行为特征等信息;带降势的启发式分类值布局算法简单高效,适用于数据量较大、分类值较多的数据集。

一种基于Rough Sets和模糊神经网络的规则获取的方法

该文提出了一种基于RoughSets思想获取初始规则，并通过模糊神经网络优化，最后再进行简化获取模糊规则，及模糊系统参数学习的方法。并通过实例进行了自动列车运行系统仿真。文中还基于上述实例，将这种基于模糊神经网络的学习与控制方法与标准的BP网络和基本的模糊系统方法进行了比较，并总结了这种方法的特点。结论表明，该文所提出的模糊规则生成和模糊系统学习方法是行之有效的。

DSets-DBSCAN无参数聚类的雷达信号分选算法

针对现有的很多高效分选算法的性能严重依赖于外界输入的参数问题,例如聚类数目、聚类容差等,将无参数聚类算法DSets-DBSCAN应用于雷达信号分选,提出了一种无参数的雷达信号脉冲聚类算法。该算法无须依赖于任何参数的设置,就能自适应地完成聚类。算法输入直方图均衡化处理过的成对相似性矩阵,使得Dsets(dominant sets)算法不依赖于任何参数;根据得到的超小簇自适应给出DBSCAN的输入参数;利用DBSCAN扩展集群。仿真实验证明,该算法对雷达脉冲描述字特征进行无参数分选的有效性。同时,在虚假脉冲比例(虚假脉冲数/雷达脉冲数)不高于80%的情况下,对雷达信号的聚类准确率在97.56%以上。

Fuzzy description logic based on vague sets

To enable the representation and reasoning for fuzzy ontologies with expressive fuzzy knowledge on the semantic web, a new fuzzy extension of description logics called vague ALC which is based on vague sets is presented. The definition of vague set is introduced and then the syntax and semantics of vague ALC are formally defined. The forms of axioms and assertions in the vague ALC knowledge bases are specified. Finally, the tableau algorithm is developed for the reasoning in the vague ALC. The vague ALC based on vague set uses two degrees of membership instead of a single membership degree in the fuzzy sets and is more accurate in representing the imprecision in the degrees of membership. The vague ALC has more expressive power than ALC and can represent fuzzy knowledge and perform reasoning tasks based on them. Therefore, the vague ALC can enable the representation and reasoning for fuzzy ontologies with expressive fuzzy knowledge on the semantic web.