直觉不确定语言Frank集结算子及其应用

基于直觉不确定语言变量和Frank算子,提出了直觉不确定语言Frank集结算子的概念,给出了直觉不确定语言Frank集结算子的运算规则、期望函数、大小比较方法;定义了直觉不确定语言Frank加权算术平均算子、加权几何平均算子、有序加权算术平均算子、有序加权几何平均算子、广义加权平均算子以及算子具有的幂等性、单调性、有界性等性质.并基于这些算子提出两种属性权重确知且属性值以直觉不确定语言形式给出的决策方法,最后通过实例验证了方法的可行性.     

基于对偶犹豫模糊语言变量的多属性决策方法

首先定义了对偶犹豫模糊语言变量,然后给出其运算规则、得分值函数、精确值函数、比较规则以及对偶犹豫模糊语言变量的加权算术平均算子、有序加权算术平均算子和混合平均算子。针对属性值为对偶犹豫模糊语言变量的多属性决策问题,提出了一种基于对偶犹豫模糊语言变量集结算子的多属性决策方法。最后,结合国家电网公司合作单位选择问题,验证了该方法的有效性和可行性。     

一种模糊有序加权(FOWA)算子及其应用

针对多个三角模糊数的集结问题，提出一种新的模糊有序加权(FOWA)算子。该算子是对传统OWA算子的扩展，它使三角模糊数可根据其所在排序位置进行集结。分析FOWA算子所具有的性质，给出在群决策中模糊信息集结的一个应用算例。     

大规模混合信息下的交互式群体评价方法及应用

针对目前多阶段交互式群体评价研究大多是基于单一评价信息且多适用于中小规模群体的不足,提出了一种大规模混合信息下的交互式群体评价方法.文章首先选用不同的函数对混合信息进行一致化处理;其次运用语言系统聚类的方法对评价群体进行划分,并在每类中选取一个"委托者"来进行下轮的交互;然后给出了稳定性和一致性指标,以此来判断交互终止;最后在密度加权平均算子和认可度诱导语言算术加权集结(RLOWA)算子的基础上,对评价信息进行单轮和多轮的集结.算例验证了方法的有效性和普适性.     

二维区间密度加权算子及其应用

针对不确定多属性决策中的属性信息分布不均匀,且评价信息多数为二维信息的情况,本文提出了二维区间密度加权算子(TDIDW算子)的属性信息集结方法.依据密度算子的集结过程特点,文章首先定义了二维区间密度加权算子及其合成算子,然后介绍了基于灰色区间聚类法的评价信息分组方法以及基于非线性模型的密度加权向量确定方法,最后进行了算例验证.验证结果表明,该方法可以有效地解决由于属性信息分布不均匀而导致评价结果不准确的问题.     

基于广义WOWA算子的Pythagorean模糊决策方法

针对Pythagorean模糊信息的决策问题,构建广义Pythagorean模糊信息加权有序加权平均(PF-GWOWA)算子。首先,提出PF-GWOWA算子,并证明Pythagorean模糊广义加权平均(PF-GWA)算子、Pythagorean模糊加权有序加权平均(PF-WOWA)算子与Pythagorean模糊加权平均(PF-WA)算子均为PF-GWOWA算子的特例;其次,根据GWOWA算子属性综合权重计算模型,利用PF-GWOWA算子对信息进行集结;最后,通过算例分析和传统方法对比,说明本文提出方法的合理性与有效性。     

空间密度算子及其应用研究

为在信息集结过程中体现空间时序数据的分布特征,提出了一种新的集结方法,即空间密度算子.该算子首先构建了融合灰色关联度和相似度思想的空间贴近度,并在此基础上利用直接聚类法对空间时序数据进行聚类;然后在组内和组间信息基础上,以信息偏差最小为原则确定组内权重,以规模密度及属性密度为基准确定组间密度权重;最后提出空间密度加权算术平均算子(SDWA)和空间密度加权几何平均算子(SDWGA)这两种新算子,对空间时序数据进行集结,得到最终评价结果.通过性质分析,发现该算子具有置换不变性、幂等性、介值性和单调性等特征.进一步,文末用一个算例来验证方法的可行性和有效性.     

连续模糊数OWA算子在物流选址中的运用

物流中心的分布对现代物流活动有很大的影响,物流中心合理的选址能够减少货物运输费用,大大降低运营成本,从而提高企业竞争力.本文在连续模糊有序加权算子的基础上,提出一种新的处理模糊数据信息方法,同时在专家权重无法确定的情况下,建立了一种新的基于离差最小的目标规划模型来集结专家群体的不同偏好,并将其运用在物流选址中,该方法避...     

基于区间二元语义偏好关系一致性偏差的群决策方法

为了避免群决策过程中信息的损失和集结结果的不精确性,将诱导有序加权平均(IOWA)算子和连续区间有序加权平均(C-OWA)算子拓展至区间二元语义环境中,提出一种诱导连续区间二元语义有序加权平均(IC2TLOWA)算子。针对区间二元语义偏好关系提出连续二元语义偏好关系的概念,定义基于连续二元语义偏好关系一致性偏差的诱导连续区间二元语义有序加权平均(CI-IC2TLOWA)算子,并提出一种基于该算子的区间二元语义群决策方法.最后通过算例说明该方法的可行性和有效性。     

区间数Heronian平均算子

定义了区间数Heronian平均算子以及区间数加权Heronian平均算子,并探讨了它们的性质.然后,提出了区间数几何Heronian平均算子以及区间数几何加权Heronian平均算子,并研究了它们的性质.最后,将区间数加权Heronian平均算子和区间数几何加权Heronian平均算子应用于多属性决策,说明了它们的有效性.     

Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations

In [R.R. Yager, D.P. Filev, Operations for granular computing: Mixing words and numbers, in: Proceedings of the FUZZ-IEEE World Congress on Computational Intelligence, Anchorage, 1998, pp. 123–128] Yager and Filev introduced the Induced Ordered Weighted Averaging (IOWA) operator. In this paper, we provide some IOWA operators to aggregate fuzzy preference relations in group decision-making (GDM) problems. These IOWA operators when guided by fuzzy linguistic quantifiers allow the introduction of some semantics or meaning in the aggregation, and therefore allow for a better control over the aggregation stage developed in the resolution process of the GDM problems. In particular, we present the Importance IOWA (I-IOWA) operator, which applies the ordering of the argument values based upon the importance of the information sources; the Consistency IOWA (C-IOWA) operator, which applies the ordering of the argument values based upon the consistency of the information sources; and the Preference IOWA (P-IOWA) operator, which applies the ordering of the argument values based upon the relative preference values associated to each one of them. We provide a procedure to deal with ‘ties’ in respect to the ordering induced by the application of one of these IOWA operators; it consists of a sequential application of the above IOWA operators. We also present a selection process for GDM problems based on the concept of fuzzy majority and the above three IOWA operators. Finally, we analyse the reciprocity and consistency properties of the collective fuzzy preference relations obtained using IOWA operators.     

On the Parameterized OWA Operators for Fuzzy MCDM Based on Vague Set Theory

The family of Ordered Weighted Averaging (OWA) operators, as introduced by Yager, appears to be very useful in multi-criteria decision-making (MCDM). In this paper, we extend a family of parameterized OWA operators to fuzzy MCDM based on vague set theory, where the characteristics of the alternatives are presented by vague sets. These families are specified by a few parameters to aggregate vague values instead of the intersection and union operators proposed by Chen. The proposed method provides a “soft” and expansive way to help the decision maker to make his decisions. Examples are shown to illustrate the procedure of the proposed method at the end of this paper.     

On Ordered Weighted Averaging Social Optima

In this paper, we look at the classical problem of aggregating individual utilities and study social orderings which are based on the concept of Ordered Weighted Averaging Aggregation Operator. In these social orderings, called Ordered Weighted Averaging Social Welfare Functions, weights are assigned a priori to the positions in the social ranking and, for every possible alternative, the total welfare is calculated as a weighted sum in which the weight corresponding to the kth position multiplies the utility in the kth position. In the α-Ordered Weighted Averaging Social Welfare Function, the utility in the kth position is the kth smallest value assumed by the utility functions, whereas in the β-Ordered Weighted Averaging Social Welfare Function it is the utility of the kth poorest individual. We emphasize the differences between the two concepts, analyze the continuity issue, and provide results on the existence of maximum points.     

Bottleneck combinatorial optimization problems with uncertain costs and the OWA criterion

In this paper a class of bottleneck combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing a finite number of cost vectors, called scenarios. In order to choose a solution the Ordered Weighted Averaging aggregation operator (OWA for short) is applied. The OWA operator generalizes traditional criteria in decision making under uncertainty such as the maximum, minimum, average, median, or Hurwicz criterion. New complexity and approximation results in this area are provided. These results are general and remain valid for many problems, in particular for a wide class of network problems.     

Possibilistic analysis of arity-monotonic aggregation operators and its relation to bibliometric impact assessment of individuals

A class of arity-monotonic aggregation operators, called impact functions, is proposed. This family of operators forms a theoretical framework for the so-called Producer Assessment Problem, which includes the scientometric task of fair and objective assessment of scientists using the number of citations received by their publications.The impact function output values are analyzed under right-censored and dynamically changing input data. The qualitative possibilistic approach is used to describe this kind of uncertainty. It leads to intuitive graphical interpretations and may be easily applied for practical purposes.The discourse is illustrated by a family of aggregation operators generalizing the well-known Ordered Weighted Maximum (OWMax) and the Hirsch h-index.     

WRAO and OWA learning using Levenberg–Marquardt and genetic algorithms

The generalized Weighted Relevance Aggregation Operator (WRAO) is a non-additive aggregation function. The Ordered Weighted Aggregation Operator (OWA) (or its generalized form: Generalized Ordered Weighted Aggregation Operator (GOWA)) is more restricted with the additivity constraint in its weights. In addition, it has an extra weights reordering step making it hard to learn automatically from data. Our intension here is to compare the efficiency (or effectiveness) of learning these two types of aggregation functions from empirical data. We employed two methods to learn WRAO and GOWA: Levenberg–Marquardt (LM) and a Genetic Algorithm (GA) based method. We use UCI (University of California Irvine) benchmark data to compare the aggregation performance of non-additive WRAO and additive GOWA. We found that the non-constrained aggregation function WRAO was learnt well automatically and produced consistent results, while GOWA was learnt less well and quite inconsistently.     

Fuzzy set approach to the utility,preference relations,and aggregation operators

Score x = (x₁, … , x_n) describing an alternative α is modelled by means of a continuous quasi-convex fuzzy quantity μ_α = μ_x, thus allowing to compare alternatives (scores) by means of fuzzy ordering (comparison) methods. Applying some defuzzification method leads to the introduction of operators acting on scores. A special stress is put on the Mean of Maxima defuzzification method allowing to introduce several averaging aggregation operators. Moreover, our approach allows to introduce weights into above mentioned aggregation, even in the non-anonymous (non-symmetric) case. Finally, Ordered Weighted Aggregation Operators (OWAO) are introduced, generalizing the standard OWA operators.     

A Learning Algorithm for Level Sets Weights in Weighted Level-based Averaging Method

The method which we call the Weighted Averaging Based on Levels (WABL) can be used to calculate the average representative of a fuzzy number. It utilizes weight coefficients for the level sets as well as the sides of a fuzzy number. We have developed an algorithm to obtain these coefficients. The most remarkable feature of this algorithm is that it makes use of the decision maker’s (DM) aggregation strategy.