直觉模糊多属性决策方法综述

直觉模糊多属性决策是当前决策领域的一个研究热点,在实际决策中有着广泛的应用.按照直觉模糊集的发展形式:直觉模糊集、区间直觉模糊集、直觉三角模糊数和直觉梯形模糊数,分别介绍它们在多属性决策与群决策中的研究现状,并对其未来的发展方向进行了探讨与展望.     

模糊多准则决策方法研究综述

模糊多准则决策是当前决策领域的一个研究热点,在实际决策中有着广泛的应用.为此,介绍了基于模糊数、直觉模糊集和Vague集的多准则决策方法和语言多准则决策方法的研究现状,定义了直觉梯形模糊数和区间直觉梯形模糊数,扩展了模糊数和直觉模糊集.最后探讨了目前模糊多准则决策要解决的问题和发展方向.     

Intuitionistic Fuzzy Filters of the BL-Algebras

结合直觉模糊集和滤子理论,对BL-代数上的直觉模糊滤子进行了研究.首先回顾了BL-代数和直觉模糊集的有关基础知识.然后引入BL-代数上的直觉模糊滤子、直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子的概念,讨论了它们的一系列重要性质,证明了直觉模糊滤子与直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子是等价的,并用实例进行了验证.最后探讨了直觉模糊滤子和模糊滤子的关系.     

基于直觉模糊的满意度计算模型

满意度理论广泛应用于优化、控制、管理、决策、资源分配、任务调度等领域,但大多是针对具体问题背景定义和计算满意度,缺乏一种普遍适用的形式化满意度计算模型。基于直觉模糊集理论建立了一个普适的多级直觉模糊满意度计算模型;利用直觉模糊集算子有效地诱导出直觉模糊满意度,将定性与定量的方法结合起来进行满意度计算,使计算结果信息量更大、更加科学合理且自动化程度高。分析了该模型的计算复杂度,并结合实例计算了商洛旅游的直觉模糊满意度,结果显示该模型高效实用。     

BL-代数上的几种直觉模糊滤子

结合直觉模糊集和滤子理论,对BL-代数上的直觉模糊滤子进行了研究。首先回顾了BL-代数和直觉模糊集的有关基础知识。然后引入BL-代数上的直觉模糊滤子、直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子的概念,讨论了它们的一系列重要性质,证明了直觉模糊滤子与直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子是等价的,并用实例进行了验证。最后探讨了直觉模糊滤子和模糊滤子的关系。     

模糊数直觉模糊几何集成算子及其在决策中的应用

模糊数直觉模糊集是直觉模糊集的拓展.针对模糊数直觉模糊信息的集成问题,定义了模糊数直觉模糊数的一些运算法则,基于这些法则给出了一些新的几何集成算子,即模糊数直觉模糊加权几何(FIFWG)算子、模糊数直觉模糊有序加权几何(FIFOWG)算子和模糊数直觉模糊混合几何(FIFHG)算子.在此基础上,提出一种属性权重确知且属性值以模糊数直觉模糊数形式给出的多属性群决策方法.最后通过实例分析结果证明了该方法的有效性.     

EQ-代数的直觉模糊前滤子

在EQ-代数和直觉模糊集理论的基础上,引入了EQ-代数上直觉模糊前滤子和直觉模糊前素滤子的定义,讨论了它们的有关性质;研究了EQ-代数上直觉模糊前滤子的生成;得到了直觉模糊前滤子的全体构成的集合所具有的代数结构。     

基于ε-修正的直觉模糊信息集成方法及其在决策中的应用

已有的一些直觉模糊集成算子在处理一些特殊直觉模糊数时会出现反直觉现象。首先介绍了两个直觉模糊集成算子和直觉模糊数的比较方法。接着,举例说明了这些集成算子在某些情况下出现的反直觉现象。然后提出了基于ε-修正的直觉模糊集成算子,并讨论了ε取值对此算子结果的影响。之后建立了一种基于ε-修正的直觉模糊集成算子的决策方法。最后通过一个实例比较了原集成算子和本文提出的修正集成算子的集成结果,验证基于ε-修正的直觉模糊集成算子可以修正这些反直觉现象,这也拓宽了原集成算子的使用范围。     

基于区间直觉模糊集的多准则决策方法

研究基于区间直觉模糊集的多准则决策方法.首先定义了区间直觉模糊点算子,并讨论了其性质;然后对区间直觉模糊集定义了一系列得分函数,并给出两种基于区间直觉模糊集的多准则决策方法.将该方法应用于区间直觉模糊集多准则决策问题,所得结果推广了有关直觉模糊集的相关结果.     

基于熵和改进的协相关度的直觉模糊决策方法

针对决策信息为直觉模糊集且属性权重未知的多属性决策问题,以及关于协相关度的决策方法研究中存在的问题,提出了一种基于直觉模糊熵和改进的协相关度的决策方法。为准确度量直觉模糊集的直觉性和模糊性,给出了一种改进的直觉模糊熵的公式,概括并推广了原有的一类直觉模糊熵的公式,并讨论了其相关性质。然后由概率统计中相关系数的构造思想,改进了直觉模糊集协相关度的定义,构造了直觉模糊集与理想对象之间的相关系数以及得分函数,由此给出了一种改进的基于直觉模糊信息的多属性决策方法,最后通过实例计算验证了该方法的有效性和可行性。     

On intuitionistic fuzzy topologies based on intuitionistic fuzzy reflexive and transitive relations

Topologies and rough set theory are widely used in the research field of machine learning and cybernetics. An intuitionistic fuzzy rough set, which is the result of approximation of an intuitionistic fuzzy set with respect to an intuitionistic fuzzy approximation space, is an extension of fuzzy rough sets. For further studying the theories and applications of intuitionistic fuzzy rough sets, in this paper, we investigate the topological structures of intuitionistic fuzzy rough sets. We show that an intuitionistic fuzzy rough approximation space can induce an intuitionistic fuzzy topological space in the sense of Lowen if and only if the intuitionistic fuzzy relation in the approximation space is reflexive and transitive. We also examine the sufficient and necessary conditions that an intuitionistic fuzzy topological space can be associated with an intuitionistic fuzzy reflexive and transitive relation such that the induced lower and upper intuitionistic fuzzy rough approximation operators are, respectively, the intuitionistic fuzzy interior and closure operators of the given topology.     

二型直觉模糊粗糙集

将二型直觉模糊集和粗糙集理论融合,建立二型直觉模糊粗糙集模型。首先,在二型直觉模糊近似空间中,定义了一对二型直觉模糊上、下近似算子,并讨论了二型直觉模糊关系退化为普通二型模糊关系和一般等价关系时,上、下近似算子的具体变化形式。然后,将普通二型模糊集之间包含关系的定义推广到了二型直觉模糊集,在此基础上研究了二型直觉模糊上、下近似算子的一些性质。最后,定义了自反的、对称的和传递的二型直觉模糊关系,并讨论了这3种特殊的二型直觉模糊关系与近似算子的特征之间的联系。该结论进一步丰富了二型模糊集理论和粗糙集理论,为二型直觉模糊信息系统的应用奠定了良好的理论基础。     

基于最小/最大描述的多粒度覆盖粗糙直觉模糊集模型

覆盖粗糙集和直觉模糊集都是处理不确定性问题的基础理论,它们有着很强的互补性,且覆盖粗糙集和直觉模糊集的融合研究是一个新的热点。对多粒度覆盖粗糙集和直觉模糊集的融合进行深入研究。首先将最小描述、最大描述从单一粒度推广到多个粒度,提出了多粒度的最小描述和最大描述,讨论了多粒度的融合;其次,分别给出了基于最小描述和最大描述的模糊覆盖粗糙隶属度、非隶属度的概念,构建了两种新的模型即基于最小描述的多粒度覆盖粗糙直觉模糊集和基于最大描述的多粒度覆盖粗糙直觉模糊集,并讨论了它们的性质,同时举例说明;最后,分析和研究了两种模型的关系。该研究为多粒度覆盖粗糙集和直觉模糊集的融合提供了一种方法。     

一种改进的直觉模糊信息系统的决策规则及其约简

直觉模糊集是基于模糊概念研究而建立的,表达模糊度更为细腻,处理不精确信息更为准确。论文是以直觉模糊信息系统为研究对象,以直觉模糊集为工具,给出了一种改进的直觉模糊信息系统的决策规则及约简方法。论文首先给出直觉模糊信息系统的预备知识,然后构造了一种改进的直觉模糊集并研究其性质及规则提取,最后通过实例验证该方法的有效性和可行性。     

Belief and Plausibility Functions on Intuitionistic Fuzzy Sets

Belief and plausibility functions based on Dempster–Shafer theory have been used to measure uncertainty. They are also widely studied and applied in diverse areas. Numerous studies in the literature have presented various generalizations of belief and plausibility functions to fuzzy sets. However, there are still less generalizations of belief and plausibility functions to intuitionistic fuzzy sets. Because intuitionistic fuzzy sets can present the degrees of both membership and nonmembership with a degree of hesitancy, the knowledge and semantic representation becomes more general and applicable than fuzzy sets. In this paper, we propose a generalization of belief and plausibility functions to intuitionistic fuzzy sets based on fuzzy integral. Some numerical examples show the effectiveness of the proposed generalization. Furthermore, this generalization of belief and plausibility functions to intuitionistic fuzzy sets is able to catch more information about the change of intuitionistic fuzzy focal elements.     

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.     

二型直觉模糊集

二型模糊集和直觉模糊集都具有很强的实际应用背景.二型模糊集增强了系统处理不确定性的能力,直觉模糊集为解决人们判断问题所出现的犹豫信息提供了理论依据.本文在二型模糊集和直觉模糊集的基础上,给出了二型直觉模糊集的概念,证明了二型直觉模糊集是一型模糊集、直觉模糊集、区间值模糊集、区间值直觉模糊集的广义形式,讨论了二型直觉模糊集的基本运算和二型直觉模糊关系.最后,研究了基于二型直觉模糊理论的近似推理,并实例说明了二型直觉模糊集的实际应用背景.     

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.     

An evolving recurrent interval type-2 intuitionistic fuzzy neural network for online learning and time series prediction

The prediction of time series has both the theoretical value and practical significance in reality. However, since the high nonlinear and noises in the time series, it is still an open problem to tackle with the uncertainties and fuzziness in the forecasting process. In this article, an evolving recurrent interval type-2 intuitionistic fuzzy neural network (eRIT2IFNN) is proposed for time series prediction and regression problems. The eRIT2IFNN employs interval type-2 intuitionistic fuzzy sets to enhance the modeling of uncertainties by intuitionistic evaluation and noise tolerance of the system. In the eRIT2IFNN, the antecedent part of each fuzzy rule is defined using intuitionistic interval type-2 fuzzy sets, and the consequent realizes the Takagi–Sugeno–Kang type fuzzy inference mechanism. In order to utilize the prior knowledge including intuitionistic information, a local internal feedback is established by feeding the rule firing strength of each rule to itself eRIT2IFNN is fully adaptive to the evolving of sequence data by online learning of structure and parameters. A modified density-based clustering is implemented for the structure learning, where both densities and membership degrees are involved to determine the fuzzy rules. Performance of eRIT2IFNN is evaluated using a set of benchmark problems and compared with existing fuzzy inference systems. Moreover, the eRIT2IFNN is tested for identification of dynamics under both noise-free and noisy environments. Finally, a group of practical financial price-tracking problems including high-frequency data of financial future, commodity future and precious metal are used for the evaluation of the proposed inference system.