一种输入数据为模糊数的模糊支持向量机

支持向量机所处理的数据绝大多数是精确值,但当训练样本中含有模糊信息时,支持向量机将无能为力。基于此,针对输入数据是模糊数的分类问题,提出一种带有去模糊函数的模糊支持向量机（FSVM*）。该算法采用模糊数间的距离作为模糊数去模糊的度量,从而构造去模糊函数将模糊值转化为精确值,同时将去模糊函数与模糊支持向量机相结合完成模糊数据的分类。数值结果表明：相比Forghani提出的FSVDD*算法,该算法更有效。     

The implementation of quality function deployment based on linguistic data

Quality function deployment (QFD) is a customer-driven quality management and product development system for achieving higher customer satisfaction. The QFD process involves various inputs in the form of linguistic data, e.g., human perception, judgment, and evaluation on importance or relationship strength. Such data are usually ambiguous and uncertain. An aim of this paper is to examine the implementation of QFD under a fuzzy environment and to develop corresponding procedures to deal with the fuzzy data. It presented a process model using linguistic variables, fuzzy arithmetic, and defuzzification techniques. Based on an example, this paper further examined the sensitivity of the ranking of technical characteristics to the defuzzification strategy and the degree of fuzziness of fuzzy numbers. Results indicated that selection of the defuzzification strategy and membership function are important. This proposed fuzzy approach allows QFD users to avoid subjective and arbitrary quantification of linguistic data. The paper also presents a scheme to represent and interprete the results.     

Designing an algorithm for evaluating decision-making units based on neural weighted function

Fuzzy systems have gained more and more attention from researchers and practitioners of various fields. In such systems, the output represented by a fuzzy set sometimes needs to be transformed into a scalar value, and this task is known as the defuzzification process. Several analytic methods have been proposed for this problem, but in this paper, firstly the researchers introduce a novel parametric distance between fuzzy numbers and secondly suggest a new approach to the problem of defuzzification, using this distance. This defuzzification can be used as a crisp approximation with respect to fuzzy quantity. By considering this and with benchmark between fuzzy numbers, we can present a method for evaluating. The method can effectively evaluate various fuzzy numbers and their images and overcome the shortcomings of the previous techniques.     

一类基于指数型模糊数的模糊多属性topsis决策

针对指数型模糊数上的模糊多属性决策问题,根据模糊理想点法的思想,给出两种多属性topsis决策方法。通过定义指数型模糊数的期望值,实现属性权重向量的解模糊化处理;定义指数型模糊数之间的距离测度,以计算各方案与理想方案之间的距离。基于期望值和距离测度的定义,从两种不同的角度出发,给出了两种模糊多属性topsis决策方法。实例验证两种方法的可行性和有效性,并对这两种方法进行比较和分析。     

Application of weighting functions to the ranking of fuzzy numbers

This paper proposes a new ranking method for fuzzy numbers, which uses a defuzzification of fuzzy numbers and a weighting function. Following Saeidifar and Pasha (2008), first, we define a weighted distance measure on fuzzy numbers, and then, by minimizing this distance, the weighted interval and point approximations of fuzzy numbers are obtained. These indices are applied to rank the fuzzy numbers. This method is new and interesting for ranking fuzzy numbers, and it can be applied for solving and optimizing engineering and economics problems in a fuzzy environment.     

基于指数型模糊数的多属性决策模型及其应用

针对模糊多属性决策问题,给出一种基于指数型模糊数的多属性决策模型。一方面,通过定义指数型模糊数的期望,以实现属性权重向量的解模糊化处理;另一方面,根据三元区间数理论和指数型模糊数的截集信息,定义指数型模糊数上一种新的距离度量,以计算各备选方案与正、负理想方案之间的距离。根据模糊理想点思想,基于指数型模糊数的期望和距离的定义,给出一种指数型模糊数上的Topsis多属性决策方法。将该模型应用于一个具体实例,其结果证实了该方法的有效性。     

A trainable transparent universal approximator for defuzzificationin Mamdani-type neuro-fuzzy controllers

A novel technique of designing application specific defuzzification strategies with neural learning is presented. The proposed neural architecture considered as a universal defuzzification approximator is validated by showing the convergence when approximating several existing defuzzification strategies. The method is successfully tested with fuzzy controlled reverse driving of a model truck. The transparent structure of the universal defuzzification approximator allows us to analyze the generated customized defuzzification method using the existing theories of defuzzification. The integration of universal defuzzification approximator instead of traditional methods in Mamdani-type fuzzy controllers can also be considered as an addition of trainable nonlinear noise to the output of the fuzzy rule inference before calculating the defuzzified crisp output. Therefore, nonlinear noise trained specifically for a given application shows a grade of confidence on the rule base, providing an additional opportunity to measure the quality of the fuzzy rule base. The possibility of modeling a Mamdani-type fuzzy controller as a feedforward neural network with the ability of gradient descent training of the universal defuzzification approximator and antecedent membership functions fulfil the requirement known from multilayer preceptrons in finding solutions to nonlinear separable problems     

Influence of Defuzzification Methods on the Rate of Tuning a Fuzzy Model

The results of computer experiments performed to determine the influence of defuzzification methods on the rate of tuning fuzzy models are presented. The experiments were conducted for the defuzzification methods of the center of gravity and center of maxima and for the median method. The defuzzification method of the center of gravity was found to be the best method providing the highest tuning rate and exactness.     

Simulation-based evaluation of defuzzification-based approaches to fuzzy multiattribute decision making

This paper presents a simulation-based study to evaluate the performance of 12 defuzzification-based approaches for solving the general fuzzy multiattribute decision-making (MADM) problem requiring cardinal ranking of decision alternatives. These approaches are generated based on six defuzzification methods in conjunction with the simple additive weighting (SAW) method and the technique for order preference by similarity to the ideal solution method. The consistency and effectiveness of these approaches are examined in terms of four new objective performance measures, which are based on five evaluation indexes. The simulation result shows that the approaches, which are capable of using all the available information on fuzzy numbers effectively in the defuzzification process, produce more consistent ranking outcomes. In particular, the SAW method with the degree of dominance defuzzification is proved to be the overall best performed approach, which is followed by the SAW method with the area center defuzzification. These findings are of practical significance in real-world settings where the selection of the defuzzification-based approaches is required in solving the general fuzzy MADM problems under specific decision contexts.     

Analytical structures and analysis of the simplest fuzzy PI controllers

This paper deals with simplest fuzzy PI controllers which employ two fuzzy numbers on the universe of discourse (UOD) of each input variable, and three fuzzy numbers on the UOD of output variable. Analytical structures of such controllers are derived using triangular membership functions for fuzzification, different combinations of T-norms and T-conorms, different inference methods, and center of area (COA) method for defuzzification. Properties of these controllers are investigated. A comparative study is made on (i) the fuzzy PI controllers derived, and (ii) on the fuzzy PI controllers and their counterpart—conventional PI controller. Moreover, sufficient conditions for bounded-input bounded-output (BIBO) stability of fuzzy PI control systems are established using the well-known small gain theorem.     

Fuzzy inventory models for items with imperfect quality and shortage backordering under crisp and fuzzy decision variables

This paper considers inventory models for items with imperfect quality and shortage backordering in fuzzy environments by employing two types of fuzzy numbers, which are trapezoidal and triangular. Two fuzzy models are developed. In the first model the input parameters are fuzzified, while the decision variables are treated as crisp variables. In the second model, not only the input parameters but also the decision variables are fuzzified. For each fuzzy model, a method of defuzzification, namely the graded mean integration method, is employed to find the estimate of the profit function in the fuzzy sense, and then the optimal policy for the each model is determined. The optimal policy for the second model is determined by using the Kuhn–Tucker conditions after the defuzzification of the profit function. Numerical examples are provided in order to ascertain the sensitiveness in the decision variables with respect to fuzziness in the components.     

A Fuzzy Quantity Mean‐Variance View and Its Application to a Client Financial Risk Tolerance Model

In this paper, we associate a probability distribution to a fuzzy variable represented by a continuous fuzzy quantity, where a fuzzy quantity is a fuzzy set that may be nonnormal and/or nonconvex. Our proposal is quite general and contains as particular cases other transformations presented in the literature. Furthermore, we define the variance of a fuzzy quantity as the variance of the probability distribution associated with it. The proposed variance agrees in the case of fuzzy numbers with the possibilistic one introduced by Irina Georgescu. We also apply our transformation to the evaluation of fuzzy quantities. The expected value of such probability distribution agrees with those introduced for fuzzy numbers by other authors; moreover, it matches the defuzzification value of a fuzzy quantity proposed by the same authors in other papers. To capture more information contained in a fuzzy quantity, or for ranking problems, we suggest to evaluate it by means of the pair mean variance, using the probability distribution associated with it. To illustrate how our method works, we apply it to evaluate the financial risk tolerance of a bank client using a fuzzy inference system.     

Modeling uncertain variables of the weighted average operation by fuzzy vectors

The paper deals with the fuzzy extension of the weighted average operation. First, we study the convenient ways how uncertain weights and weighted values can be modeled by fuzzy vectors. We show that, in comparison to a tuple of fuzzy numbers that have been used for modeling uncertain values of particular weights and weighted values up to now, fuzzy vectors extend the possibilities of utilizing the vague expert information concerning the weights and weighted values. Next, we focus on computation of a fuzzy weighted average of a fuzzy vector of weighted values with a fuzzy vector of weights. We derive a general formula and we study its special forms. The advantage of the approach presented in the paper is that the resulting fuzzy weighted average is not overly imprecise since every available information about its variables is involved in computation. This fact is illustrated by several examples. Finally, we briefly discuss the problem of defuzzification of the resulting fuzzy weighted average.     

模糊神经网络在非线性短期负荷预测中的应用

为提高负荷预测精度,提出了一种新的4层模糊神经网络短期负荷预测模型.该模型将模糊逻辑和神经网络的长处融合在一起,使模糊推理和解模糊均通过神经网络来实现.选取的隶属函数使神经网络权值有一定的知识表示意义,并通过模糊化层将输入特征量转化为模糊量.在模糊推理层提出了两种不同的算法来完成模糊推理,然后从中确定出模糊取小算法预测效果更好.最后在输出层通过适当的解模糊得到确切的预测输出值.仿真结果表明了该方法的有效性.     

基于DEMATEL和VIKOR的服务外包风险评估

服务外包风险评估是企业供应商管理的重要依据。传统风险评估方法FMEA没有考虑风险模式间的相互影响关系,模糊DEMATEL方法用来分析风险模式的净影响度,进而修正其初始评估的严重度。针对传统FMEA方法将风险因子简单相乘的缺陷,采用模糊VIKOR方法对风险模式的严重度、发生频率和难检度进行综合评估。传统模糊VIKOR计算过程中需要进行模糊数的反模糊化处理,造成信息的损失,相对偏好关系分析引入模糊VIKOR计算解决这一问题。以某公司服务外包风险评估为例,验证了所提方法的有效性。     

Two nonparametric models for fusing heterogeneous fuzzy data

Two models are discussed that integrate heterogeneous fuzzy data of three types: real numbers, real intervals, and real fuzzy sets. The architecture comprises three modules: 1) an encoder that converts the mixed data into a uniform internal representation; 2) a numerical processing core that uses the internal representation to solve a specified task; and 3) a decoder that transforms the internal representation back to an interpretable output format. The core used in this study is fuzzy clustering, but there are many other operations that are facilitated by the models. Two schemes for encoding the data and decoding it after clustering are presented. One method uses possibility and necessity measures for encoding and several variants of a center of gravity defuzzification method for decoding. The second approach uses piecewise linear splines to encode the data and decode the clustering results. Both procedures are illustrated using two small sets of heterogeneous fuzzy data     

模糊控制器输出值不变的两个充分条件

模糊控制器通常由模糊化、模糊推理以及清晰化三部分构成, 而模糊推理决定了一个由输入论域到输出论域的模糊映射. 当模糊映射为常值映射时, 任意选择模糊化和去模糊化方式, 模糊控制器的输出值不因输入信号变化而改变. 本文给出了模糊映射为常值映射的两个充分条件, 并将结论从单入单出模糊系统推广到多入单出模糊系统.     

基于模糊逻辑应用于反馈结构的多传感器航迹融合的研究

在分布式多传感器信息融合系统中,反馈结构可用来提高局部节点的跟踪性能,进而提高全局航迹的融合精度.模糊逻辑应用于对多个航迹的位置偏差、速度偏差和加速度偏差进行模糊化、模糊逻辑推理及去模糊等,提出了关于模糊逻辑应用于反馈结构的多传感器航迹融合的方法.     

基于模糊逻辑应用于反馈结构的多传感器航迹融合的研究

在分布式多传感器信息融合系统中,反馈结构可用来提高局部节点的跟踪性能,进而提高全局航迹的融合精度.模糊逻辑应用于对多个航迹的位置偏差、速度偏差和加速度偏差进行模糊化、模糊逻辑推理及去模糊等,提出了关于模糊逻辑应用于反馈结构的多传感器航迹融合的方法.     

A survey of defuzzification strategies

Defuzzification is an important operation in the theory of fuzzy sets. It transforms a fuzzy set information into a numeric data information. This operation along with the operation of fuzzification is critical to the design of fuzzy systems as both of these operations provide nexus between the fuzzy set domain and the real-valued scalar domain. We need the synergy of both of these domains to solve many of our ill-posed problems effectively. In this paper, we address the problem of defuzzification, we present merits and demerits of various defuzzification strategies that are used in the theory and practice, and in design and implementation of applications involving fuzzy theory, fuzzy control, and fuzzy rule base, and fuzzy inference-based systems. We also present in this paper a simple and yet a novel defuzzification mechanism. © 2001 John Wiley & Sons, Inc.