ivnpiv-Neutrosophic soft sets and their decision making based on similarity measure

In recent years, soft sets and neutrosophic sets have become a subject of great interest for researchers and have been widely studied based on decision-making problems. In this paper, we propose a new concept of the soft sets that is called interval-valued neutrosophic parameterized interval-valued neutrosophic soft sets (ivnpivn-soft sets). It is a generalization of the other soft sets such as fuzzy soft sets, intuitionistic fuzzy soft sets, neutrosophic soft sets, fuzzy parameterized soft sets, intuitionistic fuzzy parameterized soft sets, neutrosophic parameterized neutrosophic soft sets. Also, we proposed ivnpivn-soft matrices which are representative of the ivnpivn-soft sets. We then developed a decision-making method on the ivnpivn-soft sets and ivnpivn-soft matrices. Then, we proposed a numerical example to verify validity and feasibility of the developed method. Finally, the proposed method is compared with several different methods to verify its feasibility.

     

软直觉模糊集

直觉模糊集是在模糊集上增加了一个新的属性参数：非隶属度函数,成为描述“非此非彼”的“模糊概念”的工具。为了提高决策的精确性,将软集与直觉模糊集相结合,构造了一种新的数学模型,即直觉模糊软集,对其性质进行了一些讨论。     

Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR

Linguistic hesitant intuitionistic fuzzy set, which allows an element having several linguistic evaluation values and each linguistic argument having several intuitionistic fuzzy memberships, is a power tool to model uncertain information existing in multiple attribute decision-making problems. In this paper, we propose new methods by using TOPSIS and VIKOR for multiple attribute decision-making problems, in which evaluation values are in the form of linguistic hesitant intuitionistic fuzzy elements. Different situations of attribute weight information are considered. If attribute weights are partly known, a linear programming model is set up based on the idea that reasonable weights should make the relative closeness of each alternative evaluation value to the linguistic hesitant intuitionistic fuzzy positive ideal solution as large as possible. If attribute weights are unknown completely, an optimization model is set up based on the maximum deviation method. A numerical example is presented to illustrate feasibility and practical advantages of the proposed method. We compare the alternatives’ rankings derived from the linguistic hesitant intuitionistic fuzzy TOPSIS method with those derived from the hesitant fuzzy linguistic TOPSIS and the hesitant intuitionistic fuzzy TOPSIS approach to further illustrate their advantages.

     

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.     

A logic-based incremental approach to graph repair featuring delta preservation

We introduce a logic-based incremental approach to graph repair, generating a sound and complete (upon termination) overview of least-changing graph repairs from which a user may select a graph repair based on non-formalized further requirements. This incremental approach features delta preservation as it allows to restrict the generation of graph repairs to delta-preserving graph repairs, which do not revert the additions and deletions of the most recent consistency-violating graph update. We specify consistency of graphs using the logic of nested graph conditions, which is equivalent to first-order logic on graphs. Technically, the incremental approach encodes if and how the graph under repair satisfies a graph condition using the novel data structure of satisfaction trees, which are adapted incrementally according to the graph updates applied. In addition to the incremental approach, we also present two state-based graph repair algorithms, which restore consistency of a graph independent of the most recent graph update and which generate additional graph repairs using a global perspective on the graph under repair. We evaluate the developed algorithms using our prototypical implementation in the tool AutoGraph and illustrate our incremental approach using a case study from the graph database domain.

     

Volume-based large dynamic graph analysis supported by evolution provenance

We present an approach for the visualization and interactive analysis of dynamic graphs that contain a large number of time steps. A specific focus is put on the support of analyzing temporal aspects in the data. Central to our approach is a static, volumetric representation of the dynamic graph based on the concept of space-time cubes that we create by stacking the adjacency matrices of all time steps. The use of GPU-accelerated volume rendering techniques allows us to render this representation interactively. We identified four classes of analytics methods as being important for the analysis of large and complex graph data, which we discuss in detail: data views, aggregation and filtering, comparison, and evolution provenance. Implementations of the respective methods are presented in an integrated application, enabling interactive exploration and analysis of large graphs. We demonstrate the applicability, usefulness, and scalability of our approach by presenting two examples for analyzing dynamic graphs. Furthermore, we let visualization experts evaluate our analytics approach.

     

Formal testing of timed graph transformation systems using metric temporal graph logic

Embedded real-time systems generate state sequences where time elapses between state changes. Ensuring that such systems adhere to a provided specification of admissible or desired behavior is essential. Formal model-based testing is often a suitable cost-effective approach. We introduce an extended version of the formalism of symbolic graphs, which encompasses types as well as attributes, for representing states of dynamic systems. Relying on this extension of symbolic graphs, we present a novel formalism of timed graph transformation systems (TGTSs) that supports the model-based development of dynamic real-time systems at an abstract level where possible state changes and delays are specified by graph transformation rules. We then introduce an extended form of the metric temporal graph logic (MTGL) with increased expressiveness to improve the applicability of MTGL for the specification of timed graph sequences generated by a TGTS. Based on the metric temporal operators of MTGL and its built-in graph binding mechanics, we express properties on the structure and attributes of graphs as well as on the occurrence of graphs over time that are related by their inner structure. We provide formal support for checking whether a single generated timed graph sequence adheres to a provided MTGL specification. Relying on this logical foundation, we develop a testing framework for TGTSs that are specified using MTGL. Lastly, we apply this testing framework to a running example by using our prototypical implementation in the tool AutoGraph.

     

Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

The notion of intuitionistic fuzzy soft sets (IFSSs) provides an effective tool for solving multiple attribute decision making with intuitionistic fuzzy information. The most crucial issue in decision making based on IFSSs is how to derive the ranking of alternatives from the information quantified in terms of intuitionistic fuzzy values. In this study, we propose a new extension of the preference ranking organization method for enrichment evaluation (PROMETHEE), by taking advantage of IFSSs. In addition to presenting a myriad of new notions, such as intuitionistic fuzzy membership (or nonmembership) deviation matrices, intuitionistic fuzzy membership (or nonmembership) preference matrices, and aggregated intuitionistic fuzzy preference matrices, we put more emphasis on the construction of three distinct preference structures and related utility functions on the corresponding weakly ordered sets by considering the positive, negative, and net flows of the alternatives based on the aggregated intuitionistic fuzzy preference matrix. We present a new algorithm for solving multiple attribute decision-making problems with the extended PROMETHEE method based on IFSSs. Moreover, a benchmark problem concerning risk investment is investigated to give a comparative analysis and show the feasibility of our approach.     

基于IFN 输入的复杂系统关联MCGDM方法

考虑现有直觉模糊熵公理化定义存在的不足,提出改进直觉模糊熵的公理化定义及其计算公式;同时,定义广义幂均算子,验证其相关性质,给出确定幂方参数的方法,并将其推广至广义直觉模糊幂均算子;在以直觉模糊数(IFN)为信息输入的复杂系统框架内,针对决策者及准则之间均存在交互关联关系且权重信息完全未知的多准则群决策(MCGDM)问题,提出基于直觉模糊熵与广义直觉模糊幂均算子的关联MCGDM方法。案例分析表明,所提出的方法是可行且有效的。     

Intuitionistic fuzzy MST clustering algorithms

In this paper, we investigate graph theory-based clustering techniques for Atanassov’s intuitionistic fuzzy sets (A-IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs). We start by introducing the concepts of graph, minimum spanning tree (MST), A-IFS, and intuitionistic fuzzy distance, and develop two intuitionistic fuzzy MST clustering algorithms ( and ). Then we extend Algorithm II for clustering IVIFSs, and show the effectiveness of our algorithms through some numerical experiments.     

区间直觉模糊动态规划方法

基于直觉模糊集理论的思想与方法,探讨多阶段决策问题．运用分析技巧,构建直觉模糊集比较可能度公式及区间直觉模糊集比较可能度公式．在普通动态规划的基础上,提出区间直觉模糊动态规划及其最优解的概念,建立相应的数学模型及其最优解的算法,并指出直觉模糊动态规划是区间直觉模糊动态规划的特例．通过算例分析,说明了算法的合理性和可行性．为不确定动态规划和直觉模糊集理论的应用研究提供了新的思路．     

基于直觉模糊熵的直觉语言多准则决策方法

针对现有直觉模糊熵方法中存在的一些问题,提出一种新的直觉模糊熵,并将其与现有的几种直觉模糊熵计算结果进行比较.针对准则权重信息不完全且准则值为直觉语言数的多准则决策问题,通过建立基于模糊熵的决策模型来求解准则的最优权系数,并利用直觉语言加权算数平均算子(IL-WAA)求出方案的综合准则值,进而由直觉语言数的记分函数确定方案的排序.最后,通过算例分析验证了该方法的有效性和合理性.     

MEASUREMENT OF POSSIBILISTIC HISTOGRAMS FROM INTERVAL DATA

Abstract

Measurement methods are a central requirement for the semantic grounding of any mathematical systems theory. Therefore possibility theory, as a branch of General Information Theory (git), requires objective measurement methods to extend its agenda and applications beyond the fuzzy theory from which it emerged. General measuring devices, when defined on intervals of R, yield empirical random intervals which, when consistent, yield possibility distributions as their plausibilistic traces. These empirical possibility distributions are called possibilistic histograms, and are fuzzy intervals. Their continuous approximations, even for very small sample sizes, yield the the standard fuzzy interval forms commonly used in fuzzy system applications.     

半直觉模糊图与应用

将对象作顶点集,用直觉模糊数刻画对象间的相关性和不相关性表示成直觉模糊边;建立了半直觉模糊图模型。定义了半直觉模糊图的生成子图、度、路径、相关截图、序关系、最大生成树等概念。给出基于半直觉模糊图的聚类分析算法,分析了算法的复杂度。结合经典实例作了基于半直觉模糊图的聚类分析,结果显示基于半直觉模糊图的聚类分析算法复杂度低于一般直觉模糊聚类算法。高效实用且自动化程度高。     

基于模糊结构元的模糊数直觉模糊多准则决策方法

针对准则权重信息不完全确定的模糊数直觉模糊多准则决策问题,采用模糊结构元方法进行处理.基于模糊数直觉模糊集的模糊结构元表示、模糊数比较和排序的模糊结构元方法以及直觉模糊数的记分函数和距离测度,定义了模糊数直觉模糊数的记分函数和距离测度,进而提出两种准则权重信息不完全确定而准则值为模糊数直觉模糊数的多准则决策方法:记分函数法和逼近理想解排序(TOPSIS)法.实例分析表明了这两种方法的可行性和有效性.     

基于群广义直觉模糊软集的空袭目标威胁评估方法

空袭目标威胁评估是提高防空武器系统应对多目标的基础. 针对威胁评估的实时性、多因素和信息不确定性问题, 构建一种基于群广义直觉模糊软集的多属性威胁评估模型. 在选择合适的威胁评估指标和量化方法的基础上, 引入多专家参量集来弥补传统广义直觉模糊软集中单个专家的评估不准确性和知识局限性等缺陷. 通过应用实例分析并与其他最新决策评估方法进行比较, 验证了该方法的可行性和有效性.

     

直觉模糊集的结构化分析

直觉模糊集理论采用隶属度函数和非隶属度函数刻画不确定性信息,具有一定程度的主观性。为了研究直觉模糊集的本质特征,提出一种直觉模糊集的结构化分析方法,定义了直觉模糊相容关系,给出了直觉模糊集的同构原理,讨论了直觉模糊集的结构化特征。所得结果表明,直觉模糊集也具有客观性的一面。     

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.     

基于新直觉模糊相似度的聚类方法

针对现有直觉模糊聚类方法大都未考虑属性(指标)权重,计算过于复杂且计算结果为实数的问题,提出一种基于新直觉模糊相似度的聚类方法,计算结果为直觉模糊数,运用直觉模糊熵得到属性权重,构造了一种考虑属性权重的直觉模糊相似度公式,得到直觉模糊相似矩阵,设计了风险参数,决策者根据自己风险偏好选择风险参数进行聚类.最后通过算例验证了所提出方法的可行性和合理性.     

核空间直觉模糊局部C-均值聚类分割算法研究

针对现有直觉模糊C-均值聚类仅适合呈团状数据的不足,采用非线性函数将数据样本从欧式空间映射至再生希尔伯特高维特征空间,得到核空间直觉模糊聚类算法;同时考虑相邻像素的相互影响,将邻域像素融入核空间直觉模糊聚类的最优化目标函数中,经数学推导便得到嵌入像素局部信息的核空间直觉模糊聚类分割算法。图像分割测试结果表明,核直觉模糊C-均值聚类分割法相比现有直觉模糊C-均值聚类分割法能获得更满意的分割效果;同时,嵌入局部信息的核直觉模糊C-均值聚类分割法表现出良好的抗噪鲁棒性。