A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making

In this paper, we investigate the relationships among rough sets, soft sets and hemirings. The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring. It is pointed out that in this paper, we first apply soft rough sets to algebraic structure-hemirings. Further, we first put forward the concepts of C-soft sets and CC-soft sets, which provide a new research idea for soft rough algebraic research. Moreover, we study roughness in hemirings with respect to MSR-approximation spaces. Some new soft rough operations over hemirings are explored. In particular, lower and upper MSR-hemirings (k-ideal and h-ideal) are investigated. Finally, we put forth an approach for multicriteria group decision making problem based on modified soft rough sets and offer an actual example.     

一种改进的模糊软集多参数决策方法

模糊软集多参数决策方法中经常将Zadeh交与代数积使用在数据融合方法中,在一些实际应用中会产生信息缺失,导致决策者无法做出准确的选择。针对这一问题,结合Einstein运算法则提出一种新的数据融合方法,用于解决信息缺失和对象无法排序的问题。所提出的基于模糊软集的多参数决策方法是通过Einstein积运算进行多个参数集合的整合,从而得到一个合成模糊软集,再由合成模糊软集计算得到对照矩阵与得分表,最终得到对象的全排序,为决策者提供判断依据。通过实例结果,可以验证新方法在决策问题中的正确性和有效性。     

多粒化模糊软粗糙集模型

为了扩大粗糙集理论的应用,特别是在模糊环境中的应用,基于模糊软集和模糊蕴涵算子,主要研究基于软模糊近似空间的乐观多粒化模糊软粗糙集模型。该模型将参数集根据客户的不同要求或目标进行重组,只选择若干相关参数集参与计算上、下近似,这样定义的上、下近似不再由整个属性集决定,而是根据重组后的多个属性集一并生成,从而使结果更加符合实际需求。另外,还定义了乐观多粒化模糊软粗糙集模型的截集并讨论了其相关性质。最后给出了算例。     

基于软区分矩阵的模糊软集决策方法及其应用

通过在模糊软集中引入水平软集,用软区分矩阵来处理决策问题。首先,利用模糊软集的水平软集,将模糊软集转化为经典软集。其次,在软集中引入软区分矩阵的概念,提出了一种基于软区分矩阵解决模糊软集的新算法来处理决策问题。最后,通过实例说明了该算法的可行性。     

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。     

Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.     

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。     

Group decision making in medical system: An intuitionistic fuzzy soft set approach

In medical system, there may be many critical diseases, where experts do not have sufficient knowledge to handle those problems. For these cases, experts may provide their opinion only about certain aspects of the disease and remain silent for those unknown features. Feeling the need of prioritizing different experts based on their given information, this article uses a novel concept for assigning confident weights to different experts which are mainly based on their provided information. Experts provide their opinions about various symptoms using intuitionistic fuzzy soft matrix (IFSM). In this article, we propose an algorithmic approach based on intuitionistic fuzzy soft set (IFSS) which explores a particular disease reflecting the agreement of all experts. This approach is guided by the group decision making (GDM) model and uses cardinals of IFSS as novel concept. We have used choice matrix (CM) as an important parameter which is based on choice parameters of individual expert. This article has also validated the proposed approach using distance measurements and consents of the majority of experts. The effectiveness of the proposed approach is demonstrated using a suitable case study.     

基于Vague软集的模糊群决策方法研究

运用传统的模糊集进行模糊型群决策时存在一定的困难,而Vague软集是一种处理不确定信息的重要工具。为此,给出了一种加权的Vague软集间相似度定义,并运用Vague软集对备选方案进行评判;在此基础上运用正态云模型进行群体一致性评判,将基于Vague软集的模糊群决策方法应用于供应商选择问题中,结果表明,Vague软集能极大地提高模糊群决策的科学性和有效性。     

软模糊粗糙集

软集理论是1999年Molodtsov为了克服传统数学在处理不确定性问题时所遇到的困难而提出的一种新的数学工具。将软集理论与Z.Pawlak粗糙集结合起来,提出了软模糊粗糙集和软模糊粗糙群及它们的同态的概念,讨论了它们相关的性质。     

一种应用软粗糙模糊集的多属性决策方法

将软粗糙模糊集应用于多属性决策问题,用软粗糙模糊集分析模糊知识表达系统,定义了软模糊决策系统、决策分类模糊软集依赖度、条件双射软集对决策分类模糊软集的重要性、软模糊决策系统的约简、软模糊决策系统的决策规则等概念,借助这些概念给出了一种基于软粗糙模糊集的多属性决策算法,通过实例分析说明了该算法的可行性。     

基于直觉模糊粗糙集的属性约简

针对Jensen下近似定义的局限性,提出一种新的等价类形式的近似算子表示,并将其推广到直觉模糊环境.在此基础上,将相对正域、相对约简、相对核等粗糙集的知识约简概念推广到直觉模糊环境,提出一种直觉模糊信息系统的启发式属性约筒算法.实例计算表明.该方法比Jensen的属性约简方法更为合理有效.     

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.     

一种应用Rough集的多属性决策方法

将Rough集应用于多属性决策问题,通过引入属性的综合客观权重给出一种依据已有决策案例进行决策的新算法。其基本思想是： 首先根据已有决策案例建立决策表;然后应用条件属性关于决策属性的重要度、决策案例的局部权重和全局权重等概念确定各属性的综合客观权重; 再通过经验因子来调整综合客观权重和主观权重的比例,得到各属性的最终权重; 最后利用所得权重计算待决策对象的决策属性值,以此进行决策。文中通过对实例的分析,说明了该算法的实用性。     

On Pythagorean fuzzy decision making using soft likelihood functions

Multicriteria decision making (MCDM) is to select the optimal candidate which has the best quality from a finite set of alternatives with multiple criteria. One important component of MCDM is to express the evaluation information, and the other one is to aggregate the evaluation results associated with different criteria. For the former, Pythagorean fuzzy set (PFS) is employed to represent uncertain information in this paper, and for the latter, the soft likelihood function developed by Yager is used. To address MCDM issues from a new perspective, the likelihood function of PFS is first proposed in this study and, to improve some of its limitations, the ordered weighted averaging (OWA)-based soft likelihood function is defined, which introduces the attitudinal characteristic to identify decision makers' subjective preferences. In addition, the defined soft likelihood function of PFS is extended by weighted OWA operator considering the importance weight of the argument. Several illustrative cases are provided based on the presented (weighted) OWA-based soft likelihood functions in Pythagorean fuzzy environment for MCDM problem.     

两个论域上的覆盖粗糙模糊集模型

粗糙集模型的扩展是粗糙集研究的主要内容之一,目前已经存在许多有关粗糙集模型的扩展形式。其中基于覆盖而建立的粗糙集模型得到了很大的发展,然而学者们主要是针对单个论域进行研究的,但是实际生活中的问题却往往是在多个论域上的,如在医疗诊断中的应用等。同时考虑到在实际生活中,研究的对象往往是不确定的,即带有模糊的。基于以上考虑,提出了在两个论域上的覆盖粗糙模糊集模型,并对近似算子的性质进行了研究。     

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。     

单向S-区间值模糊粗糙集及应用

以Z.Pawlak粗集理论为基础,将动态区间值模糊近似概念引入区间值模糊粗糙集中。由此提出了单向S-区间值模糊粗糙集概念,给出了单向S-区间值模糊粗糙集的结构与性质。定义了单向S-区间值模糊粗糙集的粗相等、截集、粗糙度等概念,并对一些相关性质进行讨论和证明;给出了单向S-区间值模糊粗糙集的应用及存在价值。     

基于软直觉multiplicative集的决策方法

针对软直觉模糊集在决策中出现的部分反直觉的现象,结合直觉multiplicative集,首先提出了一种新的软集模型——软直觉multiplicative集,推广了软集和直觉multiplicative集;然后,研究了软直觉multiplicative集的基本运算和性质,同时,给出了基于软直觉multiplicative集理论的决策算法;最后,给出软直觉multiplicative集在决策中的一个应用实例,通过实例说明了该方法的正确性和有效性。     

Variable precision intuitionistic fuzzy rough set model and applications based on conflict distance

Due to the complexity and uncertainty of the physical world, as well as the limitation of human ability to comprehend, it is very difficult for any single method of uncertainty to effectively deal with the decision‐making problem that exists in real life. So, it is natural for us to think about incorporating the advantages of various theories of uncertainty to develop a more powerful hybrid method of soft decision‐making. In view of this recognition, the thought and method of intuitionistic fuzzy sets and variable precision rough sets are used to construct a novel intuitionistic fuzzy rough set model. With respect to the fact that the information system is intuitionistic fuzzy, the idea of measuring intuitionistic fuzzy similarity is used to define conflict distance. After that, this concept is combined with the variable precision rough sets so that a variable precision intuitionistic fuzzy rough set model is established, and its properties are investigated. After proposing an attribute reduction algorithm based on variable precision intuitionistic fuzzy rough sets, a case study is used to verify the feasibility and effectiveness of our novel model. The results show that our model indeed improves the classification ability of earlier models and possesses some ability to tolerate faults through adjusting the parameter λ and the confidence threshold β; it realizes the correct classification and extracts the decision rules.