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Notes on Intuitionistic Fuzzy Sets最新文献

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Intuitionistic fuzzy probability and convergence of intuitionistic fuzzy observables 直觉模糊观测值的直觉模糊概率与收敛性
Pub Date : 2022-12-12 DOI: 10.7546/nifs.2022.28.4.381-396
K. Čunderlíková
The aim of this contribution is to define a convergence in distribution, a convergence in measure and an almost everywhere convergence with respect to an intuitionistic fuzzy probability. We prove a version of Central limit theorem, a version of Weak law of large numbers and a version of Strong law of large numbers for intuitionistic fuzzy observables with respect to the intuitionistic fuzzy probability. We study a connection between convergence of intuitionistic fuzzy observables with respect to the intuitionistic fuzzy probability and a convergence of random variables, too.
这一贡献的目的是定义分布上的收敛,度量上的收敛和关于直觉模糊概率的几乎处处收敛。针对直觉模糊概率,证明了直觉模糊观测的一个中心极限定理、一个弱大数定律和一个强大数定律。我们还研究了直觉模糊观测值相对于直觉模糊概率的收敛性与随机变量的收敛性之间的联系。
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引用次数: 0
Digital transformation project selection using Interval Valued Type-2 Intuitionistic Fuzzy TOPSIS 区间值2型直觉模糊TOPSIS在数字化转型项目选择中的应用
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.334-342
Başar Öztayşi, Sezi Cevik Onar, C. Kahraman, S. Çebi
Digital transformation necessitates fundamental changes in business processes, business models, and even cultures of the companies. DT projects provide a substantial value to the business competition and effect their market shares. In order to reach these results, digital transformation projects should be carefully analyzed and evaluated. In this paper, we focus on digital transformation project prioritization problem under multiple criteria. Just like many other technology related decisions, digital transformation problems are inherently uncertain, which leads researchers to employ the fuzzy set theory. Interval Valued Type-2 Intuitionistic Fuzzy Sets (IVT2IFS) are a relatively new extension of fuzzy sets which take into account membership and non-membership values as an interval. In this paper, we utilize Interval Valued Type-2 Intuitionistic Fuzzy TOPSIS method for a digital transformation project prioritization problem and apply the model to a real-world example.
数字化转型需要对业务流程、业务模型甚至公司文化进行根本性的改变。DT项目为商业竞争提供了巨大的价值,并影响了他们的市场份额。为了达到这些结果,应该仔细分析和评估数字化转型项目。本文主要研究多准则下数字化转型项目的优先级问题。与许多其他与技术相关的决策一样,数字化转型问题具有固有的不确定性,这导致研究人员采用模糊集理论。区间值型-2直觉模糊集(IVT2IFS)是模糊集的一个较新的扩展,它将隶属度值和非隶属度值作为一个区间。本文利用区间值型-2直觉模糊TOPSIS方法求解一个数字化转型项目的优先级问题,并将该模型应用于一个实际实例。
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引用次数: 0
On some classes of Tchebychev distance based on intuitionistic fuzzy cardinality and intuitionistic fuzzy statistical description 基于直觉模糊基数和直觉模糊统计描述的切比切夫距离
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.238-258
Romuald Thierry Dzati Kamga, Bertrand Mbama Engoulou, Siméon Fotso, L. Fono
The Tchebychev distance on fuzzy sets (FSs) has been proposed to construct a measure of proximity between two modalities in a two-dimensional statistical description. The parameterized symmetric difference operations and cardinality for intuitionistic fuzzy sets (IFSs) has been proposed. This paper extends to intuitionistic fuzzy set the Tchebychev distance and possibility measure on fuzzy sets. More precisely, we firstly use the parameterized symmetric difference operations and the cardinality on IFSs to propose a Tchebychev distance measure for IFSs. From these, we then deduce two examples of metrics. Secondly, we introduce an intuitionistic fuzzy mapping that preserves the properties of the fuzzy mapping. We use this mapping to propose a Tchebychev possibility measure based on IF-cardinality. This leads to define a proximity measure between two modalities of a given character in a two-dimensional intuitionistic fuzzy statistical description.
提出了模糊集上的切比切夫距离(Tchebychev distance)来构造二维统计描述中两个模态之间的接近度度量。提出了直觉模糊集的参数化对称差分运算和基数。本文将模糊集上的切比切夫距离和可能性测度推广到直觉模糊集。更精确地说,我们首先利用参数化对称差分操作和ifs上的基数提出了ifs的Tchebychev距离度量。从这些,我们推导出两个度量的例子。其次,我们引入了一种保持模糊映射性质的直觉模糊映射。我们利用这个映射提出了一个基于IF-cardinality的Tchebychev可能性测度。这导致在二维直觉模糊统计描述中定义给定字符的两种模式之间的接近度量。
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引用次数: 0
Clustering stock price volatility using intuitionistic fuzzy sets 基于直觉模糊集的股价波动聚类
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.343-352
Georgy Urumov, P. Chountas
Clustering involves gathering a collection of objects into homogeneous groups or clusters, such that objects in the same cluster are more similar when compared to objects present in other groups. Clustering algorithms that generate a tree of clusters called dendrogram which can be either divisive or agglomerative. The partitional clustering gives a single partition of objects, with a predefined K number of clusters. The most popular partition clustering approaches are: k-means and fuzzy C-means (FCM). In k-means clustering, data are divided into a number of clusters where data elements belong to exactly one cluster. The k-means clustering works well when data elements are well separable. To overcome the problem of non-separability, FCM and IFCM clustering algorithm were proposed. Here we review the use of FCM/IFCM with reference to the problem of market volatility.
聚类涉及将一组对象聚集到同质组或集群中,这样,与其他组中的对象相比,同一集群中的对象更加相似。聚类算法生成一个称为树形图的聚类树,它可以是分裂的,也可以是聚集的。分区聚类给出对象的单个分区,具有预定义的K个聚类。最流行的划分聚类方法是:k-means和模糊C-means (FCM)。在k-means聚类中,数据被分成许多簇,其中数据元素恰好属于一个簇。当数据元素可以很好地分离时,k-means聚类效果很好。为了克服不可分性问题,提出了FCM和IFCM聚类算法。在这里,我们回顾了FCM/IFCM在市场波动问题上的应用。
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引用次数: 1
How to represent uncertainty via qudits: Probability distributions, regular, intuitionistic and picture fuzzy sets, F-transforms, etc. 如何用量词表示不确定性:概率分布、正则、直觉和图像模糊集、f变换等。
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.203-210
O. Kosheleva, V. Kreinovich
While modern computers are fast, there are still many important practical situations in which we need even faster computations. It turns out that, due to the fact that the speed of all communications is limited by the speed of light, the only way to make computers drastically faster is to drastically decrease the size of computer’s components. When we decrease their size to sizes comparable with micro-sizes of individual molecules, it becomes necessary to take into account specific physics of the micro-world – known as quantum physics. Traditional approach to designing quantum computers – i.e., computers that take effect of quantum physics into account – was based on using quantum analogies of bits (2-state systems). However, it has recently been shown that the use of multi-state quantum systems – called qudits – can make quantum computers even more efficient. When processing data, it is important to take into account that in practice, data always comes with uncertainty. In this paper, we analyze how to represent different types of uncertainty by qudits.
虽然现代计算机速度很快,但在许多重要的实际情况下,我们仍然需要更快的计算。事实证明,由于所有通信的速度都受到光速的限制,使计算机速度大幅提高的唯一方法就是大幅减小计算机组件的尺寸。当我们将它们的大小缩小到与单个分子的微观大小相当时,就有必要考虑微观世界的特定物理学——即量子物理学。设计量子计算机的传统方法——即考虑到量子物理效应的计算机——是基于使用比特的量子类比(二态系统)。然而,最近有研究表明,使用多态量子系统(称为qudits)可以使量子计算机更加高效。在处理数据时,重要的是要考虑到在实践中,数据总是带有不确定性。本文分析了如何用量词来表示不同类型的不确定性。
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引用次数: 0
Some notes on intuitionistic fuzzy equivalence relations and their use on real data 直觉模糊等价关系的几个注意事项及其在实际数据中的应用
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.306-318
A. Michalíková
The research presented in this paper is motivated by possibilities of using fuzzy equivalence relations to classify the data into the specific classes. We try to improve these results with the use of intuitionistic fuzzy equivalence relations. We define the basic structures and their properties, which are used in the paper. Then we present the data which we decided to classify and the methods of processing these data. At the end of the paper we discus obtained results and problems which occurred during the processing of the selected data.
本文研究的动机是利用模糊等价关系将数据分类为特定类的可能性。我们尝试使用直觉模糊等价关系来改进这些结果。我们定义了在本文中用到的基本结构及其性质。然后介绍了我们决定分类的数据和处理这些数据的方法。最后讨论了所得结果以及在对所选数据进行处理过程中出现的问题。
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引用次数: 0
An application of the InterCriteria Analysis and clusterization approach over a burnout dataset 标准间分析和聚类方法在倦怠数据集上的应用
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.353-360
S. Sotirov, Valentin Stoyanov, M. Krawczak, E. Sotirova, S. Ribagin
In this investigation the level of burnout among the medical employees was analyzed. Тhe InterCriteria Analysis (ICA) approach is used to find the dependences between different parameters characterizing the 139 medical employees from 6 medical centers. The aim is to analyze the correlations between the health indicators, by surveying with a developed questionnaire. The obtained data from the InterCriteria Analysis were clustered using an adaptive neural network.
本调查对医务人员的职业倦怠水平进行了分析。Тhe采用标准间分析(ICA)方法,对6家医疗中心139名医务人员的不同参数特征进行相关性分析。目的是通过编制一份调查表进行调查,分析各项健康指标之间的相关性。从标准间分析中获得的数据使用自适应神经网络聚类。
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引用次数: 0
Convergence in measure of intuitionistic fuzzy observables 直觉模糊观测量测度的收敛性
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.228-237
K. Čunderlíková, Dušana Babicová
The aim of this paper is to define a convergence in measure m, where m is an intuitionistic fuzzy state. We prove a version of weak law of large numbers for a sequence of independent intuitionistic fuzzy observables, too.
本文的目的是定义测度m中的收敛性,其中m是一个直觉模糊状态。我们也证明了一组独立直觉模糊可观测序列的弱大数定律的一个版本。
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引用次数: 0
The Hauber's law with intuitionistic fuzzy implications 带有直觉模糊含义的豪伯定律
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.271-279
Nora A. Angelova, J. Kacprzyk, A. Michalíková, K. Atanassov
25 years ago, in [7], it was proved that the Hauber's law is an intuitionistic fuzzy tautology. In this case, the used implication was the standard intuitionistic fuzzy one. In the present paper, we check which intuitionistic fuzzy implications, defined during these 25 years, satisfy the Hauber's law as a tautology and which if them – as an intuitionistic fuzzy tautology.
25年前,在[7]中证明了豪伯定律是一个直觉的模糊重言式。在这种情况下,使用的暗示是标准的直觉模糊暗示。在本文中,我们检查了在这25年中定义的直觉模糊含义,哪些是作为重言式满足豪伯定律,哪些是作为直觉模糊重言式满足豪伯定律。
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引用次数: 0
On the intuitionistic fuzzy modal feeble topological structures 直觉模糊模态弱拓扑结构
Pub Date : 2022-09-08 DOI: 10.7546/nifs.2022.28.3.211-222
K. Atanassov
In the paper, for the first time, ideas for intuitionistic fuzzy modal feeble topological structures (of two types) are introduced, and some of their properties are discussed. These topologies are based on the intuitionistic fuzzy operation @, intuitionistic fuzzy operator W, on the two intuitionistic fuzzy modal operators □, ◊ and of simplest intuitionistic fuzzy extended Dα.
本文首次引入了直觉模糊模态弱拓扑结构(两类)的思想,并讨论了它们的一些性质。这些拓扑是基于直觉模糊运算@,直觉模糊算子W,两个直觉模糊模态算子□,最简单的直觉模糊扩展Dα。
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引用次数: 4
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Notes on Intuitionistic Fuzzy Sets
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