直觉I-fuzzy拓扑空间的基与子基

给出了直觉I-fuzzy拓扑空间的基与子基,并利用它研究了模糊连续和模糊开函数.我们还给出了直觉I-fuzzy拓扑空间的乘积空间的定义,并研究了乘积空间与因子空间的关系.     

直觉I-fuzzy拓扑空间中的(r,s)直觉模糊紧

介绍了直觉I-fuzzy拓扑空间中(r,s)直觉模糊半正规的定义,研究了直觉I-fuzzy拓扑空间中直觉弱连续、直觉弱开和直觉弱闭映射的等价定理及(r,s)直觉模糊紧,(r,s)直觉模糊殆紧、(r,s)直觉模糊几乎紧的相关定理.     

I-Fuzzy拓扑空间中的可数性

引入I-fuzzy拓扑空间中的I—fuzzy第一可数性,I—fuzzy第二可数性,I—fuzzy稠密性,I—fuzzy可分性,I-fuzzyLindelbf性等概念。界定了它们的本质性质,并讨论了它们之间的关系,还给出了第一可数I-fuzzy拓扑空间中的映射连续性的序列刻画。     

诱导的I-fuzzy拓扑生成序空间

本文研究了模糊拓扑生成序空间与其诱导的I-fuzzy拓扑生成序空间之间的关系.利用三种Lowen映射内在关联的方法,引入了三种I-fuzzy拓扑生成序空间,建立了诱导的I-fuzzy拓扑生成序空间理论.获得了诱导的I-fuzzy拓扑与诱导的I-fuzzy拓扑生成序之间的从属关系.     

基于k阶二元关系的直觉模糊粗糙集

利用k阶二元关系定义直觉模糊粗糙集,讨论了分别为串行、自反、对称、传递关系时所对应的上、下近似算子的性质。在有限论域U中,研究了任一自反二元关系所诱导的直觉模糊拓扑空间中直觉模糊闭包、内部算子与相对应的上、下近似算子的关系。     

I-fuzzy拓扑中的正则开集

在I-fuzzy拓扑空间框架下引入了I-fuzzy正则开集和某个模糊点的I-fuzzy正则R-邻域系的概念,进一步,又给出了I-fuzzyδ-闭包、I-fuzzyδ-开集等概念,且分别研究了它们的基本性质.     

I-fuzzy拓扑空间中的pre-重域结构

首先在I-fuzzy拓扑空间框架下引入了I-fuzzy pre-开集,I-fuzzy pre-重域,及I-fuzzy pre-闭包等概念,进而分别研究了它们的性质,最后在I-fuzzy拓扑空间中讨论了I-fuzzy pre-网收敛.     

I-Fuzzy拓扑空间中的θ-连续函数

利用R-邻域系在I-fuzzy拓扑空间中定义θ-闭包、θ-内部、Rθ-邻域系和θ-连续函数,并且研究它们的一些性质。     

I-fuzzy拓扑空间中的Moore-Smith收敛

用方进明提出的I-fuzzy拟重邻域系研究I-fuzzy拓扑空间中的Moore-Smith收敛性，给出它的应用，并获得了很多重要结论。     

I-fuzzy拓扑中的几乎连续与δ-连续

在I-fuzzy拓扑空间框架下引入了I-fuzzy正则开集、I-fuzzyδ-开集等基本概念,进一步,在此基础上又给出了I-fuzzy几乎连续、I-fuzzyδ-连续的概念,且分别研究了I-fuzzy几乎连续、I-fuzzyδ-连续的基本性质.     

由子基生成的内部算子和闭包算子

本文研究粗糙集与拓扑空间的关系,统一地使用拓扑空间中的集合关于子基的内部和闭包来研究粗糙集理论和覆盖广义粗糙集理论中的下近似集和上近似集,以及由它们导出的关于子基的开集,导集,闭集,边界．研究这两个概念及由它们导出的相关概念的性质不仅对于粗糙集理论,而且对于拓扑学本身都有重要的理论和实际应用意义．     

I-Fuzzy拓扑空间中的基与子基

本文给出了I-fuzzy拓扑空间中基与子基的合理定义,对连续映射和开映射进行了刻画。此外,文中界定了乘积空间中基与子基并研究了乘积空间与因子空间的关系。     

Some results on generalized topological spaces and generalized systems

Summary We characterize some properties of generalized topological spaces and (g,g’)-continuity by using an interior operator defined on a generalized topological space. Also, we introduce the notions of (ψ, ψ’)-open map, gn-continuity, gn-open map and investigate their properties by using new interior (or closure) operators defined on generalized neighborhood systems of a nonempty set.     

Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator

On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval‐valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval‐valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval‐valued intuitionistic fuzzy generalized weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. © 2015 Wiley Periodicals, Inc. Complexity 21: 277–290, 2016     

Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems

In this paper, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFN), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then we use the obtained attribute weights and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator to fuse the interval-valued intuitionistic fuzzy information in the collective interval-valued intuitionistic fuzzy decision matrix to get the overall interval-valued intuitionistic fuzzy values of alternatives, and then rank the alternatives according to the correlation coefficients between IVIFNs and select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.     

I-FTOP同构于I-FRN

首先引入了I-fuzzy远域系和I-fuzzy远域空间的概念,然后构造了I-fuzzy远域空间和它们的连续映射的范畴,将此记作I-FRN.并进一步证明了I-FRN同构于I-FTOP.     

梯形模糊数直觉模糊Bonferroni平均算子及其应用

本文研究决策信息为梯形模糊数直觉模糊数(TFNIFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出一种基于梯形模糊数直觉模糊加权Bonferroni平均(TFNIFWBM)算子的决策方法.首先,介绍了TFNIFN的概念和运算法则,基于这些运算法则和Bonferroni平均(Bonferroni mean,BM)算子,定义了梯形模糊数直觉模糊Bonferroni平均算子和TFNIFWBM算子.然后,研究了这些算子的一些性质,建立基于TFNIFWBM算子的多属性群决策模型,结合排序方法进行决策.最后,将该方法应用在MAGDM中,算例结果表明了该方法的有效性与可行性.     

三角模糊数直觉模糊PA算子及其应用

针对决策信息为三角模糊数直觉模糊数（TFNIFN）且属性间存在相互关联的多属性群决策（MAGDM）问题,提出了一种基于三角模糊数直觉模糊PA （TFNIFPA）算子的决策方法.首先,基于TFNIFN的运算法则和PA （Power Average）算子,定义了TFNIFPA算子.然后,研究了该算子的一些性质,建立基于TFNIFPA算子的MAGDM模型,结合排序方法进行决策.最后通过MAGDM算例验证了该算子的有效性与可行性.     

Intuitionistic supra fuzzy topological spaces

In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space.