Vague集的截集及其分解定理

从Fuzzy集的基本理论出发,提出了Fuzzy集的扩展形式—vague集的截集定义和分解定理,进一步表明了Fuzzy集和vague集的相同的本质,丰富了vague集的理论体系,以期拓宽vague集的应用领域.     

直觉Fuzzy集的基本定理

提出直觉Ｆｕｚｚｙ集的截集的概念,并详细讨论其基本性质,在此基础上建立直觉Ｆｕｚｚｙ集的一系列分解定理、表现定理与扩张原理。     

模糊赋范线性空间的紧性与完备性

讨论了Fuzzy赋范线性中准紧集、完备集及有界集间的关系;给出完备Fuzzy赋范空间的闭球套定理与Baire定理;刻画了了有限维Fuzzy赋范空间的特征。     

Vague集的表现定理

在Fuzzy集理论和现有Vague集理论的基础上,引入二元集合套的概念,讨论它的代数性质。在此基础上,结合Vague集的分解定理,建立Vague集的表现定理,同时得到一系列相关结果,进一步揭示Vague集与经典集合之间的联系。     

广义可加Fuzzy测度

本文首先引入Fuzzy集类上（广义）可加Fuzzy测度的有关概念，然后给出Fuzzy集上关于可加Fuzzy测度的Fuaay积分及有关定理，最后在一定条件下给出广义可加Fuzzy测度的一系列分解定理。     

L—Fuzzy集表现定理

简化文[1]引入的L－集合套概念的条件,并借助文[2]的结论给出L－Fuzzy表现定理的几种形式,进一步揭示普通集合簇与L－Fuzzy集之间的良好对应关系。     

L—Fuzzy集分解定理

随着隶属函数真值域的拓广,原来关于Zadch-Fuzzy集的分解定理II和III对于L－Fuzzy集不再成立,尽管已有一些它们的关于L＿Fuzzy集的改进形式,但因条件较强,失去了原来的许多优越性,本文从格论入手,首先引入格中元素的强上集和L－Fuzzy集准截集的两个新概念,并讨论了它们的部分性质,进而借助它们给出了L－Fuzzy集分解定理的两个新形式。     

直觉I-Fuzzy拓扑空间的杨忠道定理

以L~*-格值上Lukasiewicz蕴含算子为工具引入了直觉I-Fuzzy拓扑空间中导集概念,接着给出它的一些性质,最后证明了直觉I-Fuzzy拓扑空间中导集的杨忠道定理.     

基于IGIFS关系与截集的区间灰数直觉模糊粗糙集模型及性质

在论述区间灰数直觉模糊集概念基础上,提出了区间灰数直觉模糊关系(IGIFS关系)与区间灰数直觉模糊等价关系概念,定义了基于区间灰数直觉模糊关系环境下的区间灰数直觉模糊粗糙集模型,并讨论了相关性质.在界定了区间灰数直觉模糊集关于区间灰数直觉模糊数截集概念的基础上,定义了区间灰数直觉模糊粗糙集上、下截集近似,给出了区间灰数直觉模糊粗糙集的截集表现定理.     

L-Fuzzy伴随的若干特征定理照

研究 Frame格上的一类等价关系 ,给出 L - Fuzzy伴随的若干性质定理及其等价刻画 ,体现了L- Fuzzy伴随的层次伴随特点 ,最后引入广义 L-值偏序集的概念 ,得到了类似经典伴随的若干特征定理。     

A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. The interval-valued intuitionistic fuzzy soft set is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The aim of this paper is to investigate the decision making based on interval-valued intuitionistic fuzzy soft sets. By means of level soft sets, we develop an adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making and some numerical examples are provided to illustrate the developed approach. Furthermore, we also define the concept of the weighted interval-valued intuitionistic fuzzy soft set and apply it to decision making.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

An adjustable approach to intuitionistic fuzzy soft sets based decision making

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. There has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. In this paper we generalize the adjustable approach to fuzzy soft sets based decision making. Concretely, we present an adjustable approach to intuitionistic fuzzy soft sets based decision making by using level soft sets of intuitionistic fuzzy soft sets and give some illustrative examples. The properties of level soft sets are presented and discussed. Moreover, we also introduce the weighted intuitionistic fuzzy soft sets and investigate its application to decision making.     

粗糙直觉模糊集的近似表示

在粗糙直觉模糊集的基础上,从新的角度提出了不确定目标概念的近似表示和处理的方法(通过近似模糊集和近似精确集刻画).首先将已有的直觉模糊集相似概念和均值直觉模糊集概念引入到该模型,定义了Pawlak近似空间U/R下的阶梯直觉模糊集、0.5-精确集的概念,然后得到了均值直觉模糊集(0.5-精确集)是所有直觉模糊集中与目标直觉模糊集最接近的直觉模糊集(近似精确集),接着分析了均值直觉模糊集、0.5-精确集分别与目标直觉模糊集的相似度随着知识粒度变化的变化规律.     

Some aspects of intuitionistic fuzzy sets

We first discuss the significant role that duality plays in many aggregation operations involving intuitionistic fuzzy subsets. We then consider the extension to intuitionistic fuzzy subsets of a number of ideas from standard fuzzy subsets. In particular we look at the measure of specificity. We also look at the problem of alternative selection when decision criteria satisfaction is expressed using intuitionistic fuzzy subsets. We introduce a decision paradigm called the method of least commitment. We briefly look at the problem of defuzzification of intuitionistic fuzzy subsets.     

基于直觉模糊集的突发事件应急预案评估

提出了一种基于直觉模糊集理论的突发事件应急预案评价的新方法.首先,定义了直觉模糊集和两个直觉模糊集之间的距离;然后,建立了应急预案评价指标体系,给出了直觉模糊正理想点和负理想点的概念,提出了基于直觉模糊集和TOPS IS法的应急预案评估方法.最后通过实例说明了该方法的有效性.     

Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets

Two basic inference models of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). The Triple I method is a very important method to solve the problems of FMP and FMT. The aim of this paper is to extend the Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets. In the paper, we first investigate the algebra operators' properties on the lattice structure of intuitionistic fuzzy information and provide the unified form of residual implications which indicates the relationship between intuitionistic fuzzy implications and fuzzy implications. Then we present the intuitionistic fuzzy reasoning version of the Triple I principles based on the models of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) and give the Triple I method of intuitionistic fuzzy reasoning for residual implications. Moreover, we discuss the reductivity of the Triple I methods for IFMP and IFMT. Finally, we propose α-Triple I method of intuitionistic fuzzy reasoning.     

Multi-criteria decision-making methods based on intuitionistic fuzzy sets

In this paper we present new methods for solving multi-criteria decision-making problem in an intuitionistic fuzzy environment. First, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker’s requirement. Then, we introduce and discuss the concept of intuitionistic fuzzy point operators. By using the intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an intuitionistic fuzzy set. Furthermore, a series of new score functions are defined for multi-criteria decision-making problem based on the intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.     

直观模糊集的熵、距离测度、相似测度及它们的关系

熵、距离测度和相似测度是模糊集理论中的三个重要概念.首先系统地给出了直观模糊集的熵、距离测度和相似测度的公理化定义,并讨论了它们之间的一些基本关系.然后在距离测度公理化定义的基础上产生了一些新的直观模糊集的熵公式.     

Study on divergence measures for intuitionistic fuzzy sets and its application in medical diagnosis

As far as medical diagnosis problem is concerned, predicting the actual disease in complex situations has been a concerning matter for the doctors/experts. The divergence measure for intuitionistic fuzzy sets is an effective and potent tool in addressing the medical decision making problems. We define a new divergence measure for intuitionistic fuzzy sets (IFS) and its interesting properties are studied. The existing divergence measures under intuitionistic fuzzy environment are reviewed and their counter-intuitive cases has been explored. The parameter $\alpha $ is incorporated in the proposed divergence measure and it is defined as parametric intuitionistic fuzzy divergence measure (PIFDM). The different choices of the parameter $\alpha$ provide different decisions about the disease. As we increase the value of $\alpha $, the information about the disease increases and move towards the optimal solution with the reduced in the uncertainty. Finally, we compare our results with the already existing results, which illustrate the role of the parameter $\alpha $ in obtaining the optimal solution in the medical decision making application. The results demonstrate that the parametric intuitionistic fuzzy divergence measure (PIFDM) is more comprehensive and effective than the proposed intuitionistic fuzzy divergence measure and the existing intuitionistic fuzzy divergence measures for decision making in medical investigations.