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.

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.

Intuitionistic Fuzzy Rough Sets Based on Two Intuitionistic Fuzzy Implicators

This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.

The Approach to Probabilistic Decision-Theoretic Rough Set in Intuitionistic Fuzzy Information Systems

For the moment, the representative and hot research is decision-theoretic rough set (DTRS) which provides a new viewpoint to deal with decision-making problems under risk and uncertainty, and has been applied in many fields. Based on rough set theory, Yao proposed the three-way decision theory which is a prolongation of the classical two-way decision approach. This paper investigates the probabilistic DTRS in the framework of intuitionistic fuzzy information system (IFIS). Firstly, based on IFIS, this paper constructs fuzzy approximate spaces and intuitionistic fuzzy (IF) approximate spaces by defining fuzzy equivalence relation and IF equivalence relation, respectively. And the fuzzy probabilistic spaces and IF probabilistic spaces are based on fuzzy approximate spaces and IF approximate spaces, respectively. Thus, the fuzzy probabilistic approximate spaces and the IF probabilistic approximate spaces are constructed, respectively. Then, based on the three-way decision theory, this paper structures DTRS approach model on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. So, the fuzzy decision-theoretic rough set (FDTRS) model and the intuitionistic fuzzy decision-theoretic rough set (IFDTRS) model are constructed on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. Finally, based on the above DTRS model, some illustrative examples about the risk investment of projects are introduced to make decision analysis. Furthermore, the effectiveness of this method is verified.

Intuitionistic fuzzy C-means clustering algorithms

Intuitionistic fuzzy sets(IFSs) are useful means to describe and deal with vague and uncertain data.An intuitionistic fuzzy C-means algorithm to cluster IFSs is developed.In each stage of the intuitionistic fuzzy C-means method the seeds are modified,and for each IFS a membership degree to each of the clusters is estimated.In the end of the algorithm,all the given IFSs are clustered according to the estimated membership degrees.Furthermore,the algorithm is extended for clustering interval-valued intuitionistic fuzzy sets(IVIFSs).Finally,the developed algorithms are illustrated through conducting experiments on both the real-world and simulated data sets.

Intuitionistic fuzzy hierarchical clustering algorithms

Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set （IVIFS）, whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clustering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs： the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.

Target Priority Determination Methods by Interval-Valued Intuitionistic Fuzzy Sets with Unknown Attribute Weights

The paper aims at the problem of multi-targets threat degree being hard to be evaluated accurately in complex air defense battlefield environments. Combined with multi-sensors information fusion and interval-valued intuitionistic fuzzy sets(IVIFS) theories, the target priority determination is studied. The score and accuracy functions of IVIFS are improved with thinking about the hesitating information in order to increase the rationality.Then, the influence factors of target priority and the nonlinear relationship between the influence factors and target priority are analyzed. Next, the algorithms for calculating the factor weights and sensor weights are given. Based on the theory of IVIFS and technique for order preference by similarity to an ideal solution(TOPSIS), two methods of target priority determination based on the IVIFS and TOPSIS are proposed. At last, an application example verifies the effectiveness and flexibility of the proposed algorithms.

粗糙support-intuitionistic模糊集及其聚类分析应用

粗糙集和模糊集理论已经被用于各种类型的不确定性建模中。Dubois和Prade研究了将模糊集和粗糙集结合的问题。提出了粗糙support-intuitionistic模糊集。介绍了粗糙集、粗糙直觉模糊集和support-intuitionistic模糊集等的概念;定义了在Pawlak近似空间中的support-intuitionistic模糊集的上下近似,讨论了一些粗糙support-intuitionistic模糊集近似算子的性质,给出了其相似度表达式;将其应用到聚类分析问题中,并通过一个实例验证其合理性。

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.

Knowledge modeling based on interval-valued fuzzy rough set and similarity inference: prediction of welding distortion

Knowledge-based modeling is a trend in complex system modeling technology. To extract the process knowledge from an information system, an approach of knowledge modeling based on interval-valued fuzzy rough set is presented in this paper, in which attribute reduction is a key to obtain the simplified knowledge model. Through defining dependency and inclusion functions, algorithms for attribute reduction and rule extraction are obtained. The approximation inference plays an important role in the development of the fuzzy system. To improve the inference mechanism, we provide a method of similaritybased inference in an interval-valued fuzzy environment. Combining the conventional compositional rule of inference with similarity based approximate reasoning, an inference result is deduced via rule translation, similarity matching, relation modification, and projection operation. This approach is applied to the problem of predicting welding distortion in marine structures, and the experimental results validate the effectiveness of the proposed methods of knowledge modeling and similarity-based inference.

NOTES ON “MULTICRITERIA FUZZY DECISION-MAKING METHOD BASED ON A NOVEL ACCURACY FUNCTION UNDER INTERVAL-VALUED INTUITIONISTIC FUZZY ENVIRONMENT”

This note points outs the inappropriateness of an accuracy function introduced by Ye [Ye, J. （2009）. Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Systems with Applications, 36 （3）： 6899-6902] and its misleading use for comparing two interval-valued intuitionistic fuzzy numbers.

双论域区间值直觉模糊vague粗糙集及其应用

区间值直觉模糊集可诱导出vague集和粗糙集,而后两者的结合具有不确定性深入分析的优势.立足双论域区间值直觉模糊粗糙集,引入vague集进行融合扩张,研究双论域区间值直觉模糊vague粗糙集.首先,定义区间值直觉模糊vague相容类,构建双论域区间值直觉模糊vague粗糙集模型,提出关于双逼近近似和三支决策区域的计算算法,并确立该模型的精确度、粗糙度、依赖度.然后,研究该模型的近似算子与不确定性度量的性质.最后,采用医疗例子进行模型计算、度量测量、性质验证,并得到关于患者临床诊断的患病分析与治疗决策.

覆盖粗糙直觉Fuzzy集模型的一点注记

通过对一类覆盖粗糙直觉模糊集模型中粗糙度定义的分析,对其所存在疏漏进行了改进;再将粗糙熵的概念引入到该模型,研究直觉模糊集的不确定度量;通过例子说明该度量的有效性。

基于双量化的双论域多粒度直觉模糊粗糙集

双论域多粒度直觉模糊粗糙集有利于不确定性分析,但其乐观与悲观模型具有极端性.引入相对概率与绝对基数进行双量化集成,获取双论域多粒度直觉模糊粗糙集的均衡模型及性质.首先,采用双量化技术,构建双论域多粒度直觉模糊粗糙集“下近似绝对量化-上近似相对量化”模型和“下近似相对量化-上近似绝对量化”模型,设计优化算法.其次,研究2类模型近似算子相关性质,包括集合运算与阈值单调等.最后,采用实例来验证模型有效性与性质正确性,并提供三支决策制定方案.所得结果具有模型改进性、性质扩张性,具有不确定性应用前景.

加权变精度直觉模糊序信息决策表的近似约简

以直觉模糊信息表为背景,利用粗糙集和模糊集,旨在筛除信息表中冗余的属性,提出获取决策规则的近似约简方法.首先,通过在直觉模糊集中引入带权重评分函数来定义加权直觉模糊序关系;进一步,为了提高模型分类的容错率,结合变精度粗糙集模型构建加权变精度直觉模糊序决策信息表;接着,在该决策表中提出上、下近似约简的判定定理和可辨识矩阵,进而生成两种求解上、下近似约简的方法;最后,通过具体案例和数值实验分析验证了该方法的有效性.

直觉模糊粗糙集理论在电网灾害评估中的应用

该文从应对突发事件和灾害造成电网大停电事故的角度,分析自然灾害对电网的影响因素。在此基础上针对电网灾害中影响因素的模糊性、不确定性,建立了应用于电网灾害的评价指标体系。采用基于直觉模糊粗糙集的方法对电网灾害做出及时准确的评估,确定灾害级别,并随着事态的发展调整更新,从而为应急决策提供科学依据。该文利用属性约简,降低灾害属性的冗余度;利用值约简,提取评价规则。以对辽宁省雪灾的评价为例,验证了该评价指标及评价方法的有效性与实用性,并实现了可视化灾害评估系统的设计与开发。该研究对提高电力系统应对自然灾害的应急响应和抗风险能力具有重要意义。

基于自适应邻域空间粗糙集模型的直觉模糊熵特征选择

特征选择是数据预处理中一项很重要的技术,主要从原始数据集的特征中选出一些最有效的特征以降低数据集的维度,从而提高学习算法性能.目前基于邻域粗糙集模型的特征选择算法中,由于没有考虑数据分布不均的问题,对象的邻域存在一定的缺陷.为了解决这个问题,采用方差来度量数据的分布情况,重新定义二元邻域空间,基于此提出自适应二元邻域空间的粗糙集模型,并将该模型与邻域直觉模糊熵结合作为特征评估的方式,进而构造相应的特征选择算法.UCI实验结果表明:所提出的算法能够选出更小且具有更高分类精度的特征子集,同时算法拥有更少的时间消耗.因此所提的特征选择算法具有更强的优越性.

覆盖粗糙直觉模糊集模型的研究

粗糙集和直觉模糊集的融合是一个研究热点。在粗糙集、直觉模糊集和覆盖理论基础上,给出了模糊覆盖粗糙隶属度和非隶属度的定义。考虑到元素自身与最小描述元素的隶属度和非隶属度之间的关系,构建了两种新的模型——覆盖粗糙直觉模糊集和覆盖粗糙区间值直觉模糊集,证明了这两种模型的一些重要性质,与此同时定义了一种新的直觉模糊集的相似性度量公式,并用实例说明其应用。

多粒度粗糙直觉模糊截集的研究

直觉模糊集和多粒度粗糙集的融合是一个研究热点.针对多粒度粗糙直觉模糊集的表示问题,根据直觉模糊集的分解定理和截集理论,构造了乐观和悲观多粒度粗糙直觉模糊集模型,定义了乐观和悲观多粒度粗糙直觉模糊集上下近似集,并证明了多粒度粗糙直觉模糊集的一些性质,同时提出了一个新的直觉模糊集的相似度公式.最后通过小麦长势评估实例,分析讨论了乐观和悲观多粒度粗糙直觉模糊集模型的有效性.