Intuitionistic fuzzy rough set model based on conflict distance and applications

Due to the complexity and uncertainty of the objective world, as well as the limitation of human ability to understand, it is difficult for one to employ only a single type of uncertainty method to deal with the real-life problem of decision-making, especially problems involving conflicts. On the other hand, by incorporating the advantages of various theories of uncertainty, one is expected to develop a more powerful hybrid method for soft decision making and to solve such problems more effectively. In view of this, in this paper the thought and method of intuitionistic fuzzy set and rough set are used to construct a novel intuitionistic fuzzy rough set model. Corresponding to the fact that the decision-making information system of rough sets is of intuitionistic fuzzy information system, our method defines the conflict distance by using the idea of measuring intuitionistic fuzzy similarity so that it is introduced into the models of rough sets, leading to the development of our intuitionistic fuzzy rough set model. After that, we investigate the properties of the model, introduce a novel tool for conflict analysis based on our hybrid model, and employ this new tool to describe and resolve a real-life conflict problem.     

基于变精度粗糙直觉模糊集的决策规则获取

以直觉模糊目标信息系统为研究对象,以粗糙集和直觉模糊集为工具,以知识发现为目的,给出了从直觉模糊决策表中获取决策规则的一种有效方法。即通过对Pawlak粗糙隶属函数的定义进行推广,给出粗糙直觉模糊隶属函数,利用新的粗糙隶属函数,建立了变精度粗糙直觉模糊集模型。在此模型基础上定义了变精度粗糙直觉模糊集的近似质量和近似约简,由近似约简导出概率决策规则集,从而给出了直觉模糊决策表的概率决策规则获取方法。最后,以实例说明了这一方法的有效性。关键词：     

On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods

In this paper, a kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z-soft rough fuzzy sets. As a novel Z-soft fuzzy rough set, its applications in the corresponding decision making problems are established. It is noteworthy that the underlying concepts keep the features of classical Pawlak rough sets. Moreover, this novel approach will involve fewer calculations when one applies this theory to algebraic structures. In particular, an approach for the method of decision making problem with respect to Z-soft fuzzy rough sets is proposed and the validity of the decision making methods is testified by a given example. At the same time, an overview of techniques based on some types of soft set models is investigated. Finally, the numerical experimentation algorithm is developed, in which the comparisons among three types of hybrid soft set models are analyzed.     

基于包含度的变精度模糊粗糙集

利用模糊集的一个强包含度,在弱模糊划分的基础上建立了基于该包含度的变精度模糊粗糙集模型,对其重要性质进行了深入研究,并给出了对应形式粗糙度的计算方法,进一步利用海明距离和欧几里得距离定义了该模型下模糊粗糙集的两个粗糙性度量。给出的变精度模糊粗糙集模型能够使模糊粗糙集的运算按照模糊集的运算实现,为变精度模糊粗糙集理论的研究和应用莫定了一定的理论基础。     

Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators

The fuzzy rough set model and interval-valued fuzzy rough set model have been introduced to handle databases with real values and interval values, respectively. Variable precision rough set was advanced by Ziarko to overcome the shortcomings of misclassification and/or perturbation in Pawlak rough sets. By combining fuzzy rough set and variable precision rough set, a variety of fuzzy variable precision rough sets were studied, which cannot only handle numerical data, but are also less sensitive to misclassification. However, fuzzy variable precision rough sets cannot effectively handle interval-valued data-sets. Research into interval-valued fuzzy rough sets for interval-valued fuzzy data-sets has commenced; however, variable precision problems have not been considered in interval-valued fuzzy rough sets and generalized interval-valued fuzzy rough sets based on fuzzy logical operators nor have interval-valued fuzzy sets been considered in variable precision rough sets and fuzzy variable precision rough sets. These current models are incapable of wide application, especially on misclassification and/or perturbation and on interval-valued fuzzy data-sets. In this paper, these models are generalized to a more integrative approach that not only considers interval-valued fuzzy sets, but also variable precision. First, we review generalized interval-valued fuzzy rough sets based on two fuzzy logical operators: interval-valued fuzzy triangular norms and interval-valued fuzzy residual implicators. Second, we propose generalized interval-valued fuzzy variable precision rough sets based on the above two fuzzy logical operators. Finally, we confirm that some existing models, including rough sets, fuzzy variable precision rough sets, interval-valued fuzzy rough sets, generalized fuzzy rough sets and generalized interval-valued fuzzy variable precision rough sets based on fuzzy logical operators, are special cases of the proposed models.     

Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge

Abstract: Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets, enriching the latter with extra features to represent uncertainty (on top of vagueness). Unfortunately, the various tentative definitions of the concept of an ‘intuitionistic fuzzy rough set’ that were raised in their wake are a far cry from the original objectives of rough set theory. We intend to fill an obvious gap by introducing a new definition of intuitionistic fuzzy rough sets, as the most natural generalization of Pawlak's original concept of rough sets.     

可变直觉模糊多粒度粗糙集模型及其近似分布约简算法

为了在多粒度粗糙集模型中对目标概念达到更好的近似逼近效果,首先将直觉模糊粗糙集与多粒度粗糙集结合,提出直觉模糊多粒度粗糙集模型。由于该模型的目标近似存在过于宽松的缺陷,因此通过引入参数的方式对所提模型进行改进,提出一种可变直觉模糊多粒度粗糙集模型,并证明了该模型的有效性,同时基于该模型提出了相应的近似分布约简算法。在仿真实验结果中,所提出的下近似分布约简结果比已提出的模糊多粒度决策理论粗糙集约简和多粒度双量化决策理论粗糙集多了2~4个属性,所提出的上近似分布约简算法比这些算法少了1~5个属性,同时约简结果的近似精度拥有了更为合理且优越的表现。因此,理论和实验结果均验证了所提的可变直觉模糊多粒度粗糙集模型在近似逼近和数据降维方面均具有更高的优越性。     

变精度粗糙模糊集模型研究

介绍了Ziarko’s变精度粗糙集模型和粗糙模糊集模型,找出了它们的不足。基于支集相对错误分类率及误差参数β（0≤β<0.5）,提出了变精度粗糙模糊集模型,讨论了模型中β上、下近似算子的性质;分析了该模型与Ziarko’s变精度粗糙集模型和粗糙模糊集模型的关系;最后给出了该模型中近似约简的定义和方法,并通过实例分析说明了约简算法的有效性。     

多粒度覆盖粗糙模糊集模型不确定性研究

针对覆盖粗糙模糊集中存在的上下近似不一致问题.引入一种更为合理的覆盖粗糙模糊集模型,讨论了该模型的结构与相关性质,定义了基于此模型的粗糙度度量方法.基于覆盖粗糙模糊集中粗糙度相等的情形,提出模糊集中极大模糊集的概念,并利用模糊集与极大模糊集的距离问题定义了模糊集的优劣次序,从而有效解决了模糊集在覆盖粗糙模糊集中粗糙度的度量问题.通过引入粗糙熵等相关概念,证明了此模型中仍然存在随最简覆盖变细,两种度量单调减少的规律,并通过实例进行了验证.从而为进一步揭示粗糙集、粗糙模糊集及覆盖粗糙模糊集之间的不确定性度量规律提供了理论依据.     

Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision‐making

Probabilistic approaches to rough sets are still an important issue in rough set theory. Although many studies have been written on this topic, they focus on approximating a crisp concept in the universe of discourse, with less effort on approximating a fuzzy concept in the universe of discourse. This article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space over two universes. We first present the definition of a lower and upper approximation of a fuzzy set with respect to a probabilistic approximation space over two universes by defining the conditional probability of a fuzzy event. That is, we define the rough fuzzy set on a probabilistic approximation space over two universes. We then define the fuzzy probabilistic approximation over two universes by introducing a probability measure to the approximation space over two universes. Then, we establish the fuzzy rough set model on the probabilistic approximation space over two universes. Meanwhile, we study some properties of both rough fuzzy sets and fuzzy rough sets on the probabilistic approximation space over two universes. Also, we compare the proposed model with the existing models to show the superiority of the model given in this paper. Furthermore, we apply the fuzzy rough set on the probabilistic approximation over two universes to emergency decision‐making in unconventional emergency management. We establish an approach to online emergency decision‐making by using the fuzzy rough set model on the probabilistic approximation over two universes. Finally, we apply our approach to a numerical example of emergency decision‐making in order to illustrate the validity of the proposed method.     

直觉模糊数决策粗糙集

决策粗糙集模型的代价函数不包含模糊概念,不能够细腻地描述包含模糊信息的决策。针对上述不足,首先将模型中精确值的代价函数拓展为直觉模糊数,构建直觉模糊数决策粗糙集模型。然后,通过分析基于直觉模糊数下、上理想的决策预期代价函数,形成保守、激进、可变的决策策略和相应的决策规则,并分析其相关数学性质。最后,通过对战略目标防空部署策略的风险分析来说明模型的具体应用过程。     

基于直觉模糊粗糙集的属性约简研究

本文针对传统的离散化技术所造成的信息丢失问题,提出了利用直觉模糊粗糙集合理论来进行属性约简的方法。文中描述了直觉模糊等价关系下粗糙集的模型,并在此基础之上定义了正域、依赖度与非依赖度概念,然后详细分析了直觉模糊粗糙集属性约简算法。最后,用实例证明了该算法的可行性,并对算法的优缺点进行了阐述。     

广义优势多粒度直觉模糊粗糙集及规则获取

优势关系粗糙集模型是研究序信息系统中数据挖掘的主要方法。为了丰富现有优势关系粗糙集模型,使其更加有效地应用于实际问题,本文首先在直觉模糊决策信息系统中利用三角模和三角余模定义了3种优势关系,得到了3种优势类;其次构造了广义优势关系多粒度直觉模糊粗糙集模型,讨论了该模型的主要性质;随后给出如何从直觉模糊决策信息系统中获取逻辑连接词为“或”的决策规则;最后通过实例说明该模型在处理直觉模糊决策序关系信息系统时是有效的。     

模糊相似关系下变精度模糊粗糙集

经典变精度模糊粗糙集模型是基于模糊等价关系建立的.在实际应用中,模糊等价关系很难直接构造,需要通过求模糊相似关系的传递闭包生成.对模糊关系的这种改造会丢失较多有价值的信息,而且还增大了模糊粗糙集应用的计算复杂度.基于模糊逻辑算子构造2个模糊集的相对错误包含度,构造性地提出基于模糊相似关系的变精度模糊粗糙集模型,研究了该模型的性质.该模型一方面具有变精度粗糙集的优点,对噪声数据具有很好的容错能力,另一方面是基于模糊相似关系建立的,其应用范围更为广泛.     

变精度粗糙集推广模型及其性质研究

数据挖掘的主要目标之一是进行有效分类,粗糙集的上下近似空间正是为了对信息系统进行分类。变精度粗糙集作为经典粗糙集的推广模型,目前研究仅局限于有限集。针对变精度粗糙集模型无法处理无限集合的问题,在变精度粗糙集和测度的理论基础上,提出了基于Lebesgue测度的变精度粗糙集模型。首先,引入Lebesgue测度的概念,构造了一种基于Lebesgue测度的变精度粗糙集模型,将变精度粗糙集理论推广到无限集;其次,定义了该模型的上、下近似空间;最后,证明了其相关性质。通过理论研究表明,该模型能有效处理无限集合问题,对变精度粗糙集的理论研究形成突破,也将极大的扩充其应用范围。     

区间直觉模糊粗糙集

将模糊粗糙集推广到区间直觉模糊粗糙集,基于区间直觉模糊等价关系和两个论域之间的一般区间直觉模糊关系,给出了区间直觉模糊粗糙集模型的不同形式,并讨论了一些相关性质。     

多重粗糙模糊集模型

为了充分揭示知识颗粒间的重叠性、对象的重要度差别及其多态性,基于多重集合,对Dubois粗糙模糊集意义下的粗糙模糊集模型的论域进行了扩展,提出了基于多重集的粗糙模糊集模型,给出了该模型的完整定义、相关定理和重要性质,其中包括多重粗糙模糊近似集、近似精度和可定义集的定义及其各种性质的证明、多重集意义下的粗糙模糊近似算子之间的关系及其与Dubois意义下的粗糙模糊近似算子之间的关系等。多重粗糙模糊集可用于从具有一对多依赖性关系的且具有模糊特性的数据中挖掘知识。     

改进的直觉模糊粗糙集相似性度量方法

针对现有的直觉模糊粗糙集相似性度量的问题,提出了一种改进的基于海明距离的直觉模糊粗糙集相似性度量方法。该方法考虑了犹豫度并引入加权参数,解决了相似性度量不精确的问题。首先给出了直觉模糊粗糙值间的相似性度量定义,并揭示其若干重要性质。在此基础上,提出了直觉模糊粗糙集间的相似性度量方法,并证明其具有同样性质。最后通过数值算例分析说明了该方法更合理、更有效。     

Decision‐theoretic rough sets under Pythagorean fuzzy information

Decision‐theoretic rough sets (DTRSs), which provide a classical model of three‐way decisions (3WDs), play an important role in risk decision‐making problems. The risk is associated with the loss function of DTRSs, which is evaluated by the decision makers. As a new extension of fuzzy sets, Pythagorean fuzzy sets can handle uncertain information more flexibly than intuitionistic fuzzy sets in the process of decision making and it gives a new measure for the determination of loss functions of DTRSs. More specifically, we take into account the loss functions of DTRSs with Pythagorean fuzzy numbers and propose a Pythagorean fuzzy decision‐theoretic rough set (PFDTRS) model. Some properties of the expected losses are carefully investigated. Then we further design three approaches for deriving 3WDs with the PFDTRS model. The group decision making (GDM) based on the PFDTRS model is also discussed. It provides a novel interpretation for the determination of loss functions. With the aid of the Pythagorean fuzz weighted averaging operator, we aggregate the loss functions, as suggested by the all experts, which support a coherent way of designing information granules in the presence of numerics. An algorithm for 3WDs in GDM based on the PFDTRS model is designed. Then, an example is presented to elaborate on 3WDs with the PFDTRS model.     

基于双论域粗糙集的快捷货物运输方案选择

针对多种不确定因素下的快捷货物运输方案决策问题,提出一种基于双论域直觉模糊粗糙集的快捷货物运输方案决策模型与决策规则。依据双论域直觉模糊粗糙集理论来确定快捷货物运输方案决策的双论域模糊近似空间。将固定成本、运输成本、转运成本、碳排放、转运时间等评价指标的消耗程度视为直觉模糊数,利用评价指标与运输方案之间的直觉模糊关系计算求得下近似集与上近似集,并引入最大直觉性指标及海明贴近度得出运输方案决策规则。以兰州至北京的一条快捷货物运输线路为例,依据决策规则从公路、普铁、航空组合出的9种运输方式中选择出最优运输方案。对运输成本、转运成本进行灵敏度分析以验证结果的准确性。最终选择出的两种最优运输方案表明了双论域直觉模糊粗糙集在此类问题上的适用性。