基于Vague集的多准则模糊决策方法

基于Vague集的模糊决策方法的提出，为决策系统提供了一个有用的工具．对模糊条件下的多准则决策问题，指出了采用Vague集进行多准则模糊决策的现有计分函数的不足，根据Vague集的性质提出了二种新的方案选择方法：记分函数法和加权记分函数法。对已有的Vgue集记分函数法进行了分析与联系，并通过例子阐明本文方法的有效性和优越性．     

一个新的基于Vague集加权相似度量的双向近似推理方法

提出了一种新的Vague集的加权相似度量方法以解决文献[1]中关于vague集相似度量的某些缺陷，并且提出了Vague集间相似方向的概念，用它来描述两个相似Vague集中哪个所包含的信息更精确，并给出了一个判定方法。在此基础上给出了一种基于Vague集加权相似度量的双向近似推理方法，该方法更好地利用了vague集信息的精确性，从而提高了推理的精确性和适用性．这为智能系统中的近似推理提供了一个十分有用的工具．     

基于一般二元关系下的粗糙Vague集

本文研究了一般关系下Vague集合的近似问题，建立了一般关系下粗糙Vague近似的框架。在分析经典的粗集理论、模糊集理论、Vague集理论三者关系的基础上，提出了一般关系下粗糙Vague集的概念，并定义了粗糙Vague近似算子，讨论了粗糙Vague的性质。本文的结果对进一步开展粗糙集Vague集的研究具有一定的意义。     

二元截集下Vague集的表现定理及扩展原理

在Fuzzy集和Vague集理论的基础上,根据二元截集下集合套的概念和Vague集的分解定理,得出新的Vague集的表现定理、扩展原理,并且讨论了相关的代数性质,清楚地表现了经典集与Vague集之间的联系。     

二元截集下的Vague集的分解定理

为了揭示Vague集和经典集之间的联系,在Vague集二元截集的基础上,提出了两个新的Vague集的分解定理。Vague集的分解定理表明Vague集可以由它分解出的截集簇来表示,而这些截集簇都是普通集。最后实例说明了其有效性。     

基于Vague集加权相似度量的双向近似推理

本文提出了一种新的Vague集的加权相似度量方法，以解决文献中关于Vague集相似度量的某些缺陷以及权向量中各个分量难以确定的问题，并且提出了Vague集间相似方向的概念，用它来描述两个相拟Vague集中哪个所包含的信息更精确，并给出了一个判定方法。在此基础上的给出了一种基于Vague集加权相似度量的双向近似推理方法，该方法更好地利用了Vague集信息的精确性，从而提高了推理的精确性和适用性。这为智能系统中的近似推理提供了一个十分有用的工具。     

Vague的等价聚类分析

聚类分析在现实生活中有着重要的应用.参考模糊集中有关等价聚类分析的方法,在Vague集的等价关系基础上,提出了Vague集的等价聚类分析中如等价矩阵、at,af截矩阵等一些基本理论,给出了Vague集的等价聚类分析一个具体的方法--传递闭包法,最后以一个具体的实例,验证了Vague集理论的等价聚类分析的可行性.     

Vague集及其相似度量

相似度量是Vague集研究中的一个重要内容，具有重要的理论和工程实际意义。本文首先讨论了Vague集的两种扩张原理，并结合Vague集自身的特点及其典型的背景知识，提出了两种Vague集的相似度量方法，同时分析了它们的性质。本文的结果对Vague的研究和工程应用有一定意义。     

基于Vague集的加权多目标模糊决策方法

1 引言在多目标模糊决策支持系统中,通常要在多个目标中依据有关约束条件选择最佳的目标。由于信息的不确定性,许多学者采用Fuzzy集理论来处理这类问题。Chen在文[3]中提出了采用Vague集的方法来处理模糊条件下的多目标决策问题,并讨论了加权情况下的处理方法。然而在Chen的方法中,没有定义加权情况下Vague集的运算,其加权处理是针对目标选择计分函数S的,而非Vague集;并且文[3]中的     

一种基于Vague集间距离的双向近似推理方法

指出现有Vague(值)集间距离公式的一个缺陷.给出Vague(值)集间的一个加权距离公式.提出一种Vague集间距离的双向近似推理方法,实例表明该方法是可行的.     

Interval-valued fuzzy hypergraph and fuzzy partition

This paper extends the work of H. Lee-Kwang and L.M. Lee (1995) to present the concept of the interval-valued fuzzy hypergraph. In the interval-valued fuzzy hypergraph, the concepts of the dual interval-valued fuzzy hypergraph, the crisp-valued alpha-cut hypergraph, and the interval-valued [alpha(1),alpha(2 )]-cut at beta level hypergraph are developed, where alphain [0, 1], 0相似文献   

Applying fuzzy arithmetic to the system dynamics for the customer–producer–employment model

This paper presents a system dynamics analysis based on the application of fuzzy arithmetic. Traditional crisp system dynamics observe that some variables/parameters may belong to the uncertain factors. It is necessary to extend the system dynamics to treat also the vague variables/parameters. The evaluation of fuzzy system dynamics may provide the decision-maker information regarding the system's behavior uncertainties. In this paper, the customer–producer–employment model is examined with the fuzzy system dynamics in two types of fuzzy arithmetic, α-cut fuzzy arithmetic and T_ω weakest t-norm operator. Symmetrical and nonsymmetrical triangular fuzzy number (TFN), varied amount of fuzzy inputs’ fuzziness, and length of the system time delay are examined with useful results provided. Particularly, it is revealed that (1) both types of fuzzy arithmetic can provide the steady-state analysis of the system's variables as their counterpart, the crisp arithmetic analysis. (2) The α-cut arithmetic realizes the fuzziness of the model interactive variables fuzzier than that of the T_ω fuzzy arithmetic due to the accumulating phenomenon of fuzziness of the α-cut arithmetic. The fuzzier the inputs, the higher the level and/or oscillation of the cyclically steady or stable pattern of the stability of these variables exhibit with the α-cut arithmetic. (3) The T_ω arithmetic gives a smaller fuzziness and defuzzified values due to the concept that it takes only the maximal fuzziness encountered and calculated in the operation. In this case, the T_ω arithmetic provides more stable (or conversely less sensitive) results to the amount of fuzziness and nonsymmetricity (fuzziness) of input.     

Development and optimization of unrestricted LR-type intuitionistic fuzzy mathematical programming problems

To the best of our knowledge, there is no method to find the product of unrestricted LR-type intuitionistic fuzzy numbers (IFNs) as well as the optimal solutions of LR-type intuitionistic fuzzy linear programming problems (IFLPPs) in which some or all the decision variables are unrestricted. Therefore it is necessary to pay attention to this issue and there is need to find the product of unrestricted LR-type IFNs as well as the optimal solutions of such programming problems. In this paper, the product of unrestricted LR-type IFNs based on the α-cut, β-cut and (α, β)-cut is proposed. Then with the help of proposed product, a new method is proposed to find the optimal solutions of unrestricted LR-type IFLPPs. Finally, an illustrative example is given to support the proposed method and investigated the applicability of existing approaches exist in the literature.     

一类Vague集间的相似度量

研究了Vague值的（α,β） 扩展的性质,提出一类基于这种扩展的Vague集间的相似度量。在模式识别中的应用实例表明这类公式是实用的。     

Atanassov’s intuitionistic fuzzy submodules with respect to a t-norm

In this paper, t-norm based intuitionistic fuzzy submodules are defined, and their various properties are investigated. We also show that if an intuitionistic fuzzy set of a module is an intuitionistic fuzzy submodule with respect to a t-norm, then it is also an intuitionistic fuzzy submodule with respect to the annihilation t-norm. We investigate the nature of intuitionistic fuzzy submodules of a module with the help of their respective cut sets. We obtain some results based on (α, β)-level sets and t-norm based α-cut sets of an intuitionistic fuzzy submodule with respect to a t-norm T.     

A fuzzy group data envelopment analysis model for high-technology project selection: A case study at NASA

The assessment and selection of high-technology projects is a difficult decision making process at the National Aeronautic and Space Administration (NASA). This difficulty is due to the multiple and often conflicting objectives in addition to the inherent technical complexities and valuation uncertainties involved in the assessment process. As such, a systematic and transparent decision making process is needed to guide the assessment process, shape the decision outcomes and enable confident choices to be made. Various methods have been proposed to assess and select high-technology projects. However, applying these methods has become increasingly difficult in the space industry because there are many emerging risks implying that decisions are subject to significant uncertainty. The source of uncertainty can be vagueness or ambiguity. While vague data are uncertain because they lack detail or precision, ambiguous data are uncertain because they are subject to multiple interpretations. We propose a data envelopment analysis (DEA) model with ambiguity and vagueness. The vagueness of the objective functions is modeled by means of multi-objective fuzzy linear programming. The ambiguity of the input and output data is modeled with fuzzy sets and a new α-cut based method. The proposed models are linear, independent of α-cut variables, and capable of maximizing the satisfaction level of the fuzzy objectives and efficiency scores, simultaneously. Moreover, these models are capable of generating a common set of multipliers for all projects in a single run. A case study involving high-technology project selection at NASA is used to demonstrate the applicability of the proposed models and the efficacy of the procedures and algorithms.     

Fuzzy data envelopment analysis: A discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on α-cut. One drawback of the α-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the α-cut approach. We introduce the concept of “local α-level” to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.     

A novel general approach to evaluating the PCBA for components with different membership function

The logistic support of high tech industry all emphasize that reliability design start, one must fully considers its life cycle. The reliability analysis and prediction are the main work objectives. The purpose is to ensure that the system (product) can achieve its designed functions under specific operating conditions. However, the incomplete failure data and different fault probability density function of the system elementary event also increase the difficulty of reliability design and calculation. It cannot be fully solved by traditional probability reliability. Therefore, a more general and efficient algorithm to assess the system reliability is needed. This paper proposed speculation by experts’ opinions according to incomplete information condition. It reasonably gives different fault membership function of possibility of failure distribution under different bottom event. It also applies fault-tree analysis, α-cut of vague set, and interval arithmetic operations of vague set to obtain fault interval and reliability interval of the system. Moreover, this paper also modifies Tanaka et al.’s fuzzy fault-tree definition and extended the new usage to fit different membership function of vague fault-tree. Then, find out the critical elementary event that affects the reliability of the system, which could be used for managerial decision-making, and as the bases to future system maintenance strategy. In numerical verification, a malfunction of printed circuit board assembly (PCBA) is presented as a numerical example. The result of the proposed method is compared with the listing approaches of reliability analysis methods.     

An alternative approach to fuzzy control charts: Direct fuzzy approach

The major contribution of fuzzy set theory lies in its capability of representing vague data. Fuzzy logic offers a systematic base to deal with situations, which are ambiguous or not well defined. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. In this paper, some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of α-cut to provide the ability of determining the tightness of the inspection: the higher the value of α the tighter inspection. A new alternative approach “Direct Fuzzy Approach (DFA)” is also developed in this paper. In contrast to the existing fuzzy control charts, the proposed approach is quite different in the sense it does not require the use of the defuzziffication. This prevents the loss of information included by the samples. It directly compares the linguistic data in fuzzy space without making any transformation. We use some numeric examples to illustrate the performance of the method and interpret its results.