一种基于FPGA的改进粗糙集属性约简方法

粗糙集理论是一种新型的数学工具,主要用于分析处理模糊和不确定知识。属性约简是其中的一个重要环节。本文结合遗传算法,提出了一种基于FPGA改进的粗糙集属性约简方法,在原研究的基础上,先利用属性重要度求解决策表的核属性,再运用于属性约简,从而减少遗传操作的迭代次数,加快属性约简速度。     

基于粗糙集理论的水质模糊综合评价

针对水质评价中存在指标选取主观和赋权计算繁琐等问题,提出了利用粗糙集做属性约简,消除不相关和不重要的指标;运用属性重要度对约简后的指标赋权,并应用模糊综合评价进行水质评价。结果表明,粗糙集理论应用于模糊综合评价和传统模糊综合评价的结果基本一致,而且粗糙集属性约简和属性重要度赋权能够达到客观选取指标、简化水质评价过程等目的。     

基于相似矩阵的折半属性约简算法

针对大多数属性约简算法时间复杂度比较高的问题,利用粗糙集理论提出了一种新的解决办法,该方法基于相似矩阵概念,利用属性在相似矩阵中出现的频率给出了属性重要性的计算公式,以此作为启发式知识来约间决策表中的冗余属性,并将折半查询的思想运用到算法中以加快约简的速度。实验表明该算法是简单有效的.     

基于分治的属性约简相对核计算

针对信息表中相对核的计算采用分治策略提出了一个新的属性约简方法，将在计算整个全域上的属性约简问题转化为计算在相应划分的子区域上属性约简问题．将原有计算POS X0(y)的算法复杂度O(|A||U|^2)，降为O(|A|(|Y1|^2 |Y2|^2 … |Yn|^2))，对于一般比较大的|U|说，效率提高非常明显，提高了属性约简的可计算性.     

集值信息系统的属性约简

属性约简是粗糙集理论研究中的重要内容之一。本文主要研究集值信息系统的属性约简问题。在集值信息系统中基于拟序关系引入了信息量的概念,给出了属性特征的判定方法,以及信息量与属性约简之间的关系。根据信息量定义了属性重要性,研究了属性重要性与属性约简之间的关系。进而得到了基于信息量和属性重要性的属性约简算法,给出了该算法的时间复杂度。通过实例说明,该算法是有效的。     

一种基于属性划分的序信息系统并行约简算法

在粗糙集理论中,序信息系统的属性约简是一个重要的问题.目前已取得一些初步的研究成果,但仍缺乏有效的计算方法,主要表现为求解约简耗时过长.本文采用"分而治之"的策略,利用递减划分对属性进行分组,从而将原系统分解为规模相近的若干子系统,并在互不影响的情况下同步计算各子系统的核与约简,然后将子系统的核与约简合并得到原系统的核与约简.算例分析验证了本文提出的属性约简方法的可行性和有效性.     

基于形式概念分析的多光谱遥感影像波段选择

针对遥感图像特征选择和提取的波段选择,利用形式概念分析中属性约简的思想设计了波段约简选择算法。该方法利用遥感影像的信息量作为指标,将多光谱影像作为形式背景,各波段作为形式属性,通过属性约简得到核心属性即最优波段,这样不仅避免了多光谱遥感数据波段之间的相关性对波段选择的影响,还提高了选取训练样本的效率。最后采用了美国地球观测卫星Landsat拍摄的TM遥感影像数据进行实验,与常用的波段选择方法相比,本文的方法更为简便和高效。     

基于粗糙集约简的生产成本决策

成本决策是成本管理的重要环节,为了将先进的人工智能方法融入生产成本决策过程中,并使得决策因素最小化,在深入研究粗糙集理论的基础上,提出了一种新的基于区分矩阵的最小属性约简方法,并详细阐述了该方法的含义和性质,以及算法的搜索策略与执行过程,有效解决了任意相容决策表的最小属性约简问题,并结合现有改进的值约简算法,达到了决策...     

模糊粗糙集在轴承故障模式识别中的应用

提出一种基于模糊粗糙集理论的模式识别方法,将动态聚类法和方差分析法引入连续属性模糊化,获取模糊隶属函数,避开了粗糙集理论属性离散化过程带来的信息丢失;利用F检验判断分类的合理性,克服了人为确定分类数目的缺点;应用模糊化得到的模糊决策表进行条件属性约简,通过属性值约简,提取了清晰、简明的故障模式规则。轴承故障模式识别结果表明,该方法对比一般粗糙集理论,有效地提高了模式识别精度,在实际模式识别中具有很好的应用价值。     

MMAS与粗糙集在齿轮箱故障诊断中的应用

粗糙集理论是一种新的处理含糊和不确定性知识的数学工具,属性约简是粗集理论研究的重要内容,属性约简算法有很多种,而计算一个最佳约简是NP难问题。为了能够有效地获取信息系统的约简,提出了一种新的约简算法。该算法选择最大-最小蚂蚁系统(MMAS),以Fisher准则作为启发式信息来提高搜索效率,将蚁群优化算法引入属性约简中,利用粗糙集理论对故障诊断决策表进行约简,形成清晰、简明的故障诊断规则,为下一步的故障诊断打下了坚实的基础。     

A Comparative Study of Using Grey Relational Analysis in Multiple Attribute Decision Making Problems

This paper uses grey relational analysis (GRA) method in multiple attribute decision making (MADM) problems. The advantages of using the GRA method include the followings: The results are based upon the original data, and the calculations are simple and easy to understand. It is one of the best methods to help management make decisions under business environment. Finally, an example is provided to show how this GRA method works in dealing with MADM problems. Moreover, the results from other methods are compared including the technique for order preference by similarity to ideal solution and operational competitiveness rating method.     

A subjective and objective integrated multiple attribute decision making method for material selection

The selection of an optimal material for an engineering design from among two or more alternative materials on the basis of two or more attributes is a multiple attribute decision making (MADM) problem. The selection decisions are complex, as material selection is more challenging today. There is a need for simple, systematic, and logical methods or mathematical tools to guide decision makers in considering a number of selection attributes and their interrelations and in making right decisions. This paper proposes a novel MADM method for material selection for a considered design problem. The method considers the objective weights of importance of the attributes as well as the subjective preferences of the decision maker to decide the integrated weights of importance of the attributes. Furthermore, the method uses fuzzy logic to convert the qualitative attributes into the quantitative attributes. Three examples are presented to illustrate the potential of the proposed method.     

Multiple attribute decision-making solution to material selection problem based on modified fuzzy axiomatic design-model selection interface algorithm

Material selection, one of the mostly encountered decision problems in material science literature, is still an onerous task for manufacturing organisations. Achieving accurate solution to this issue, the paper developed a model selection interface to enable analytical solutions to different problem concepts in material selection under multiple attribute decision-making (MADM) environments. Specifically, the generic framework of the fuzzy axiomatic design-model selection interface (FAD-MSI) is modified and successfully applied to the different material selection problem concepts. Consequently, the derived problem-model sets can be referred to accomplish further proposals on this era.     

A reference framework for the application of MADM fuzzy techniques to selecting AMTS

In the last decade, there has been growing interest in the assessment and selection of investments in advanced manufacturing technologies (AMTs). Several authors have pointed out the shortcomings of traditional financial techniques, proposing alternative approaches usually referred to as 'non-conventional' approaches. Among them, some authors have recently proposed fuzzy multi-attribute decision making (MADM) techniques, which seem to be particularly suitable for dealing with the intangible effects of AMTs. However, no attempt has so far been made to analyse and compare the various MADM techniques included in the fuzzy theory with respect to their applicability to the assessment and selection of AMTs. The objective of this article is to give a reference framework for the application of a MADM fuzzy approach to AMT selection. In particular, the paper describes three major categories of fuzzy MADM approach and compares their results using a case study.     

On the equivalence of operational performance measurement and multiple attribute decision making

Measurement of operational performance and decision making under multiple attributes are shown to be essentially the same process. A recent operational performance measurement (OPM) procedure called OCRA (operational competitiveness rating) and a multiple attribute decision making (MADM) method called TOPSIS (technique for order preference by similarity to ideal solution) are shown to produce ratings that are identical up to a linear transformation. Further investigations into OPM and MADM lead to their equivalence. The equivalence of the two methods can open up new research and application possibilities in both productivity analysis and MADM. Reviews of both the non-parametric approach that leads to the OC RA procedure and the TOPSIS method are provided, new perspectives on these methods are introduced and examples offered.     

Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

In real life, incomplete information, inaccurate data, and the preferences of decision-makers during qualitative judgment would impact the process of decision-making. As a technical instrument that can successfully handle uncertain information, Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making (MADM) problems. This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership, non-membership, and priority are considered simultaneously. Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators, this paper proposes the Fermatean hesitant fuzzy Heronian mean (FHFHM) operator and the Fermatean hesitant fuzzy weighted Heronian mean (FHFWHM) operator. Then, considering the priority relationship between attributes is often easier to obtain than the weight of attributes, this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator (FHFPHM), and discusses its elegant properties such as idempotency, boundedness and monotonicity in detail. Later, for problems with unknown weights and the Fermatean hesitant fuzzy information, a MADM approach based on prioritized attributes is proposed, which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results. Finally, a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.     

SVD-based complexity reduction of rule-bases with nonlinearantecedent fuzzy sets

With the help of the singular value decomposition (SVD) based complexity reduction method, not only can the redundancy of fuzzy rule-bases be eliminated, but further reduction can also be made, considering the allowable error. Namely, in the case of higher allowable error, the result may be a less complex fuzzy inference system, with a smaller rule-base. This property of the SVD-based reduction method makes possible the usage of fuzzy systems, even in cases when the available time and resources are limited. The original SVD-based reduction method was proposed for rule-bases with linear antecedent fuzzy sets. This limitation remained valid in the later extensions, as well. The purpose of this paper is to give a formal mathematical proof for the original formulas with nonlinear antecedent fuzzy sets and thus to end this limitation     

Selection of an optimal refinement condition to achieve maximum tensile properties of Al–15%Mg2Si composite based on TOPSIS method

Recently, in situ Al–Mg₂Si composites have been introduced as a new group of particulate metal matrix composites which contain hard particles of Mg₂Si in Al-matrix. Unfortunately, coarsening of Mg₂Si particles deteriorates the mechanical properties so that it is an important obstacle for the wide application of this type of composites. Our previous investigations depicted that the addition of Na and Mn as alloying elements and solution treatment in the different range of temperature can refine Al–Mg₂Si composite structure and improve tensile properties. Selection of the optimal refinement condition to achieve maximum tensile properties of Al–15%Mg₂Si composite is a multiple attribute decision making (MADM) problem where some criteria must be considered in decision making. In present research, technique for order preference by similarity to ideal solution (TOPSIS) and fuzzy TOPSIS methods were employed in solving the case study problem. Weights of each criterion were determined by using an analytic hierarchy process (AHP) method in both TOPSIS and fuzzy TOPSIS methods. The obtained results showed that the employed methods were suitable approaches in solving case study problem. Empirical findings in this study represented that TOPSIS and fuzzy TOPSIS methods might lead to the choice of refined Al–15%Mg₂Si via solution treatment at 450 °C as the preferred alternative.