Redundant fuzzy rules exclusion by genetic algorithms

A genetic-algorithm-based method for exclusion of the potential redundant if-then fuzzy rules that have been extracted from numerical input-output data is proposed. The main idea is the input-space separation into activation rectangles, corresponding to certain output intervals. The generation of fuzzy rules and the membership functions are based on these activation rectangles and appropriate fuzzy rules inference mechanism is proposed. As the method usually produces too many rules, it is necessary to exclude the potential redundant if-then rules. The concept for varying the family of sensitivity parameters, defining the overlapping of the fuzzy regions is proposed. The genetic algorithms are used to resolve the following combinatorial optimization problem: the generation of families of sensitivity parameters. In this way the potential redundant if-then fuzzy rules are excluded.

The method formalizes the synthesis of the fuzzy system and could be used for function approximation, classification and control purposes. An illustrative example for implementation of the method for traffic fuzzy control is given.     

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。     

基于VIKOR和关联系数的犹豫三角模糊语言多属性决策方法

针对属性评价值为犹豫三角模糊语言集的多属性决策问题,提出一种基于VIKOR方法的犹豫三角模糊语言多属性决策方法.首先定义了犹豫三角模糊语言集的相关概念.然后运用VIKOR和关联系数方法,在可接受优势和决策过程稳定的条件下对方案进行择优,在理论分析的基础上,提出了这种新方法的计算步骤.并构建了确定最优属性权重的非线性规划模型,研究了当专家权重和属性权重未知情况下的犹豫三角模糊语言多属性决策方法.最后通过实例说明了该方法的有效性和可行性.     

基于二元语义TAC积分算子的语言型多属性群决策方法

针对属性之间存在模糊关联的语言型多属性群决策问题,给出了二元语义TAC(Two-Additive Choquet)积分算子的定义,分析和证明了算子的有关性质,并提出了相应的决策方法。该方法首先将各专家提供的语言短语形式的属性权重信息、属性关联信息与属性评价信息转化为二元语义形式,然后利用二元语义TAC积分算子将转化后的属性相关信息集结为各专家的方案评价值,并进一步集结专家意见获得方案的综合评价值,从而确定其排序。最后,通过实例分析和方法比较说明了所给方法的有效性和优点。研究结果表明,该方法具有属性关联刻画细致、计算过程简单且无信息损失、决策结果可解释性强等优点,为求解属性之间存在模糊关联的语言型多属性群决策问题提供了一种新的途径。     

一种基于梯形模糊语言变量的多属性决策方法

针对属性权重未知、属性值以梯形模糊语言变量形式给出的多属性决策问题,提出了一种扩展的VIKOR决策方法。首先介绍了梯形模糊语言变量的概念、运算法则,提出了梯形模糊语言变量值之间的距离公式,并进行了证明。在此基础上利用离差最大化方法确定了属性指标权重,并建立了基于梯形模糊语言变量的扩展VIKOR方法,给出了决策步骤。最后,通过一个算例说明该方法的有效性。     

基于语义Choquet积分的知识服务能力测评方法

针对知识服务中考虑模糊语言关联性信息的知识服务能力评价与提升策略问题,提出了一种评价方法。为了解决该问题,首先构建了知识服务能力的评价指标体系和矩阵分析模型;然后,明晰了知识服务能力的语言评价指标会在不同程度上存在关联的问题特征及二元语义信息处理方法的特征,并进行了形式化描述;同时,提出并定义了二元语义Choquet积分算子,给出了一种基于二元语义Choquet积分算子评价知识服务能力的方法;最后,通过算例分析说明了本文给出方法的可行性和实用性。     

广义概率对偶犹豫模糊语言幂集结算子在多属性决策中的应用

在对偶犹豫模糊语言集、概率对偶犹豫模糊集和广义幂集结算子的基础上,研究了在概率对偶犹豫模糊语言环境下的广义幂集结算子问题。首先,给出了概率对偶犹豫模糊语言集的定义、运算规则、得分函数、精确函数、距离测度、熵。然后,定义了广义概率对偶犹豫模糊语言幂集结算子,并研究其具有的性质。其次,提出了一种决策方法来解决集结数据之间存在相互关系的概率对偶犹豫模糊语言多属性决策问题。最后,结合相关案例验证了该方法的有效性和可行性。     

A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment

The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method.     

犹豫模糊语言Heronian平均算子在多属性决策中的应用

针对输入变量之间的相互影响以及评价值为犹豫模糊语言信息的多属性决策问题,提出一种基于犹豫模糊语言Heronian平均算子的多属性决策方法。由于Heronian平均(HM)算子具有能够反映输入变量之间相互关联的良好特性,在犹豫模糊语言信息环境下,提出了两种新的集成算子,即犹豫模糊语言Heronian平均(HFLHM)算子和犹豫模糊语言几何Heronian平均(HFLGHM)算子,同时研究了它们的一些特性。考虑到输入变量具有不同的重要程度,还定义了犹豫模糊语言加权Heronian平均(HFLWHM)算子和犹豫模糊语言加权几何Heronian平均(HFLWGHM)算子。最后提出了基于HFLWHM算子和HFLWGHM算子的犹豫模糊语言多属性决策方法,并通过实例验证了这些算子的合理性和可行性。     

An architecture of fuzzy neural networks for linguistic processing

Fuzzy sets have been used successfully in order to deal with imprecise data, linguistic terms or not well-defined concepts. Recently, considerable effort has been made in the direction of combining the neural network approach with fuzzy sets. In this paper a fuzzy feed-forward neural network, able to process trapezoidal fuzzy sets, has been investigated. Normalized trapezoidal fuzzy sets have been considered. The fuzzy generalized delta rule with different back-propagation algorithms is discussed. The more interesting and characteristic property of the proposed architecture is the ability of each node to process fuzzy sets or linguistic terms, preserving the simplicity of the back-propagation algorithm. Consequently, the resulting architecture is able to cope with problems in which the input parameters and the desired targets are described by linguistic terms. This methodology has the further interesting characteristic of being able to operate at the linguistic level rather than at the numerical level, that is it can work at a higher data abstraction level. An example in computerized electrocardiography will be illustrated in order to test the proposed approach.     

服务管理目标优化配置的Fuzzy-QFD线性规划模型构建与求解

由于服务管理的复杂性和模糊性,现有方法难以有效解决基于主观语言评价的服务质量改进问题。本文拓展了质量功能展开(QFD)方法在服务业中的应用,通过构建一个模糊线性规划模型,以求解最大化提高顾客需求综合满意度的企业能力优化配置问题。首先基于顾客感知-期望差距的模糊评估确定顾客需求、需求权重和边界约束等模型参数,接着运用模糊线性回归和非对称三角模糊数的隶属函数,将含有模糊变量的模糊线性规划问题转化为经典线性规划问题,进而求得不同模糊条件下的模型解。最后通过网购平台的实例验证了模型的有效性和可行性。     

基于ELECTRE方法的模糊多属性群决策

结合模糊集理论知识,将经典的ELECTRE方法拓展到模糊环境下,用来解决模糊多属性群决策问题.决策问题中涉及到的属性评价值与属性权值是以三角模糊数的形式给出.首先集结各决策者的评价矩阵,构造模糊群决策矩阵,在规范化的基础上,分别对其进行模糊和谐性检验与模糊非和谐性检验,最后通过设定否决门槛值得到一致性比较矩阵,最终评价结果也是以三角模糊数的形式给出.该方法操作方便,计算简单.给出的实例验证了此方法的可行性和有效性.     

Two novel FMCDM methods for alternative-fuel buses selection

In this paper, we consider the problem of alternative-fuel buses selection using two novel fuzzy multiple criteria decision-making (MCDM) methods. Several types of fuels are considered as fuel modes, i.e., electricity, fuel cell (hydrogen), and methanol. For the purpose of determining appropriate fuel buses, many factors including quantitative and qualitative ones such as efficiency, price, and capability must be taken into account. In the first proposed method, linguistic variables are used to assess the ratings and weights for factors. These linguistic ratings can be expressed in trapezoidal or triangular fuzzy numbers. Then, a hierarchical MCDM method based on fuzzy-sets theory is proposed to deal with the fuel buses selection problem. To simultaneously determine the ranking order of all alternatives based on the concept of the TOPSIS by calculating the distances to the both fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS), a closeness coefficient is defined. In the second presented method we extend preference selection index (PSI) method for fuzzy environment. In this method performance ratings of criteria evaluate by linguistic variable which can be expressed in trapezoidal fuzzy numbers. Finally, an example is shown to highlight the procedure of the proposed methods and compare the results of these methods with each other.     

面向电子商务服务水平的变权分析评价方法

针对电子商务服务水平评价问题,提出一种基于变权分析方法的评价方法。首先,建立电子商务服务水平评价指标体系;其次,采用实数、区间数、三角模糊数、语言变量和直觉模糊数5种不同类型表示其评价信息,提出各个电子商务服务水平关于正理想解的相对满意度计算方法,据此确定电子商务服务水平,并具体给出其变权分析评价步骤;最后,通过实例说明该方法的有效性和合理性。     

基于模糊语言评估和联系数的多属性群决策方法

对方案的属性评估信息以模糊语言形式给出的多属性群决策问题,采用集对分析理论进行处理,提出了一种基于模糊语言评估和联系数的多属性群决策方法,实例应用表明了该方法的有效性和实用性.     

The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making

QUALIFLEX, a generalization of Jacquet-Lagreze’s permutation method, is a useful outranking method in decision analysis because of its flexibility with respect to cardinal and ordinal information. This paper develops an extended QUALIFLEX method for handling multiple criteria decision-making problems in the context of interval type-2 fuzzy sets. Interval type-2 fuzzy sets contain membership values that are crisp intervals, which are the most widely used of the higher order fuzzy sets because of their relative simplicity. Using the linguistic rating system converted into interval type-2 trapezoidal fuzzy numbers, the extended QUALIFLEX method investigates all possible permutations of the alternatives with respect to the level of concordance of the complete preference order. Based on a signed distance-based approach, this paper proposes the concordance/discordance index, the weighted concordance/discordance index, and the comprehensive concordance/discordance index as evaluative criteria of the chosen hypothesis for ranking the alternatives. The feasibility and applicability of the proposed methods are illustrated by a medical decision-making problem concerning acute inflammatory demyelinating disease, and a comparative analysis with another outranking approach is conducted to validate the effectiveness of the proposed methodology.     

Fuzzy pricing,marketing and service planning in a fuzzy inventory model: A geometric programming approach

In the real world markets, demand is influenced by different parameters. Recently, many researchers have been interested in integrated production and marketing planning strategies in inventory models where demand depends on different parameters such as price and/or marketing expenditure. The quality of services that are offered to customers of a product is one of the most important parameters that affects demand in the real markets and has not been considered in development of inventory models. On the other hand, the cost parameters in real inventory systems and other parameters such as price, marketing and service elasticity to demand are imprecise and uncertain in nature. So, the notion of fuzziness can be applied to cope with this uncertainty. In this paper, a new fuzzy profit maximization inventory model with shortages is proposed. The demand is considered as a power function of price, marketing expenditure and service expenditure. Furthermore, unit cost is determined as a power function of order quantity. Since the proposed model is in a fuzzy environment, a fuzzy decision should be made to meet the decision criteria, and the results should be fuzzy. Therefore, the proposed model is formulated and solved using geometric programming and fuzzy optimization techniques to derive an approximation of the results’ membership functions. The model is illustrated with a numerical example and finally a case study is provided for evaluation and validation of the results of model.     

Fuzzy-valued linguistic soft set theory and multi-attribute decision-making application

In this work, we propose the theory of fuzzy linguistic soft set (FLSS) to represent the uncertainty and multi-angle of view when decision makers evaluate an object during decision-making. FLSS integrates fuzzy set theory, linguistic variable and soft set theory. It allows decision makers to utilize linguistic variables to evaluate an object and utilize fuzzy values to describe the corresponding grade of their support of their decisions. Meanwhile, because of the flexibility of soft set, decision makers can use more than one pair of fuzzy-linguistic evaluations to express their opinions from multiple perspectives directly, if necessary. Therefore, it is more flexible and practical than traditional fuzzy set or 2-dimension uncertainty linguistic variable. We also develop a generalized weighted aggregation operator for FLSSs to solve corresponding decision-making issues. Finally, we give a numerical example to verify the practicality and effectiveness of the proposed method.     

基于模糊语言的多属性联系数决策方法

针对属性权重已知,属性值以模糊语言给出的多属性决策问题,提出了一种基于模糊语言标度的区间数表示形式,并利用集对分析方法将区间数进行转化为联系数的表示方式,通过联系数中同、异、反的关系,给出相应集势值,由集势值的大小进行择优排序.最后,通过实例分析,验证了该方法的可行性和有效性.     

基于犹豫模糊语言环境的投资组合优化研究

跟传统模糊投资组合相比,基于犹豫模糊语言环境的投资组合不仅可以使用自然语言对金融资产及其不确定程度进行评价,还可以避免评价过程中信息的丢失。本文根据犹豫模糊语言投资组合综合评价系统,对不同金融产品计算得分。通过设置不同的语言尺度函数的参数值及犹豫模糊语言优化模型的临界值,针对激进型、稳健型和保守型三类投资者分别提出了收益最大化和风险最小化犹豫模糊语言投资组合模型,对建立的非线性模型进行求解,得到犹豫模糊语言投资组合的最优解。最后,用数值仿真验证了模型的合理性和有效性。