A Generalized Maximum Entropy (GME) estimation approach to fuzzy regression model

Fuzzy statistics provides useful techniques for handling real situations which are affected by vagueness and imprecision. Several fuzzy statistical techniques (e.g., fuzzy regression, fuzzy principal component analysis, fuzzy clustering) have been developed over the years. Among these, fuzzy regression can be considered an important tool for modeling the relation between a dependent variable and a set of independent variables in order to evaluate how the independent variables explain the empirical data which are modeled through the regression system. In general, the standard fuzzy least squares method has been used in these situations. However, several applicative contexts, such as for example, analysis with small samples and short and fat matrices, violation of distributional assumptions, matrices affected by multicollinearity (ill-posed problems), may show more complex situations which cannot successfully be solved by the fuzzy least squares. In all these cases, different estimation methods should instead be preferred. In this paper we address the problem of estimating fuzzy regression models characterized by ill-posed features. We introduce a novel fuzzy regression framework based on the Generalized Maximum Entropy (GME) estimation method. Finally, in order to better highlight some characteristics of the proposed method, we perform two Monte Carlo experiments and we analyze a real case study.     

Support vector fuzzy adaptive network in regression analysis

Neural-fuzzy systems have been proved to be very useful and have been applied to modeling many humanistic problems. But these systems also have problems such as those of generalization, dimensionality, and convergence. Support vector machines, which are based on statistical learning theory and kernel transformation, are powerful modeling tools. However, they do not have the ability to represent and to aggregate vague and ill-defined information. In this paper, these two systems are combined. The resulting support vector fuzzy adaptive network (SVFAN) overcomes some of the difficulties of the neural-fuzzy system. To illustrate the proposed approach, a simple nonlinear function is estimated by first generating the training and testing data needed. The results show that the proposed network is a useful modeling tool.     

A new approach for fuzzy information retrieval based on weighted power-mean averaging operators

An information retrieval system can help users to retrieve documents relevant to the users’ queries. In recent years, some researchers used averaging operators (i.e., Infinite–One operators, Waller–Kraft operators, P-Norm operators and GMA operators) to handle “AND” and “OR” operations of users’ fuzzy queries for fuzzy information retrieval, but they still have some drawbacks, e.g., sometimes query results do not coincide with the intuition of the human being. In this paper, we present new averaging operators, called weighted power-mean averaging (WPMA) operators, based on the weighted power mean for dealing with fuzzy information retrieval to overcome the drawbacks of the existing methods. Furthermore, we also extend the proposed WPMA operators into the extended WPMA operators to handle weighted fuzzy queries for fuzzy information retrieval. The proposed WPMA operators are more flexible and more intelligent than the existing averaging operators to handle users’ fuzzy queries for fuzzy information retrieval.     

Forward–backward analysis of RFID-enabled supply chain using fuzzy cognitive map and genetic algorithm

Supply chain is a non-deterministic system in which uncontrollable external states with probabilistic behaviors (e.g., machine failure rate) influence on internal states (e.g., inventory level) significantly through complex causal relationships. Thanks to Radio frequency identification (RFID) technology, real time monitoring of the states is now possible. The current research on processing RFID data is, however, limited to statistical information. The goal of this research is to mine bidirectional cause-effect knowledge from the state data. In detail, fuzzy cognitive map (FCM) model of supply chain is developed. By using genetic algorithm, the weight matrix of the FCM model is discovered with the past state data, and forward (what-if) analysis is performed. Also, when sudden change in a certain state is detected, its cause is sought from the past state data throughout backward analysis. Simulation based experiments are provided to show the performance of the proposed forward–backward analysis methodology.     

Distances between fuzzy sets

Given two fuzzy subsets μ and ν of a metric space S (e.g., the Euclidean plane), we define the ‘shortest distance’ between μ and ν as a density function on the non-negative reals; our definition is applicable both when μ and ν are discrete-valued and when they are ‘smooth’ (i.e., differentiable), and it generalizes the definition of shortest distance for crisp sets in a natural way. We also define the mean distance between μ and ν, and show how it relates to the shortest distance. the relationship to earlier definitions of distance between fuzzy sets [1,3] is also discussed.     

Linear and sigmoidal fuzzy cognitive maps: An analysis of fixed points

Fuzzy cognitive mapping is commonly used as a participatory modelling technique whereby stakeholders create a semi-quantitative model of a system of interest. This model is often turned into an iterative map, which should (ideally) have a unique stable fixed point. Several methods of doing this have been used in the literature but little attention has been paid to differences in output such different approaches produce, or whether there is indeed a unique stable fixed point. In this paper, we seek to highlight and address some of these issues. In particular we state conditions under which the ordering of the variables at stable fixed points of the linear fuzzy cognitive map (iterated to) is unique. Also, we state a condition (and an explicit bound on a parameter) under which a sigmoidal fuzzy cognitive map is guaranteed to have a unique fixed point, which is stable. These generic results suggest ways to refine the methodology of fuzzy cognitive mapping. We highlight how they were used in an ongoing case study of the shift towards a bio-based economy in the Humber region of the UK.     

Fuzzy systems are universal approximators for a smooth function and its derivatives

One of the reasons why fuzzy methodology is successful is that fuzzy systems are universal approximators, i.e., we can approximate an arbitrary continuous function within any given accuracy by a fuzzy system. In some practical applications (e.g., in control), it is desirable to approximate not only the original function, but also its derivatives (so that, e.g., a fuzzy control approximating a smooth control will also be smooth). In our paper, we show that for any given accuracy, we can approximate an arbitrary smooth function by a fuzzy system so that not only the function is approximated within this accuracy, but its derivatives are approximated as well. In other words, we prove that fuzzy systems are universal approximators for smooth functions and their derivatives. ©2000 John Wiley & Sons, Inc.     

基于移动率的T-S模糊模型的结构辨识方法

为了提高现行模糊辨识方法的有效性,提出了基于移动率的T-S模糊模型的结构辫识方法。主要工作如下: 首先,定义I=S模糊模型的S型、Z型和梯形隶属函数的移动率,将此移动率与现行的隶属度相比较可以看出,提出的 方法比较有效;然后,定义基于移动率的T-S模糊推理方法,并且提出基于移动率的前提和结论部分的子S模型的辫 识方法;最后,将提出的识别方法应用于降水量和安全形势的预测模糊建模。测试结果表明,与现行方法和模糊神经 网络算法相比,该方法明显提高了模糊辨识的有效性,减少了规则数目,并降低了辫识误差。     

Optimization of fuzzy partitions for inductive reasoning using genetic algorithms

Fuzzy Inductive Reasoning (FIR) is a data-driven methodology that uses fuzzy and pattern recognition techniques to infer system models and to predict their future behavior. It is well known that variations on fuzzy partitions have a direct effect on the performance of the fuzzy-rule-based systems. The FIR methodology is not an exception. The performance of the model identification and prediction processes of FIR is highly influenced by the discretization parameters of the system variables, i.e. the number of classes of each variable and the membership functions that define its semantics. In this work, we design two new genetic fuzzy systems (GFSs) that improve this modeling and simulation technique. The main goal of the GFSs is to learn the fuzzification parameters of the FIR methodology. The new approaches are applied to two real modeling problems, the human central nervous system and an electrical distribution problem.     

Usability Ratings for Everyday Products Measured With the System Usability Scale

This article characterizes the usability of 14 common, everyday products using the System Usability Scale (SUS). More than 1,000 users were queried about the usability of these products using an online survey methodology. The study employed two novel applications of the SUS. First, participants were not asked to perform specific tasks on these products before rating their usability but were rather asked to assess usability based on their overall integrated experience with a given product. Second, some of the evaluated products were assessed as a class of products (e.g., “microwaves”) rather than a specific make and model, as is typically done. The results show clear distinctions among different products and will provide practitioners and researchers with important known benchmarks as they seek to characterize and describe results from their own usability studies.     

模糊属性Petri网建模方法及学习模型研究

定性映射易于表达模糊不确定性知识,但其在表达人类认知思维活动动态特征上存在不足;模糊Petri网比较符合人类思维方式,但相关参数不易获得且其自学习能力存在较大局限性。为此,提出一种模糊属性Petri网(FAPN)形式定义及建模方法。在FAPN结构中构建定性基准参数学习方法,通过定性映射定义4类变迁发生的模糊定性判断规则和相应变迁发生后的结果运算公式,给出FAPN模型的推理算法和学习机制,并模拟系统的动态运行过程。分析结果表明,该方法能有效提高FAPN的学习能力,可适用于以定性判断为特点的诊断系统。     

Control of three degrees-of-freedom underactuated manipulator using fuzzy based switching

A novel concept for designing a fuzzy logic-based switching controller to control underactuated manipulators is presented. The proposed controller employs elemental controllers, which are designed in advance. Parameters of both antecedent and consequent parts of a fuzzy indexer are optimized by using evolutionary computation. Design parameters of the fuzzy indexer are encoded into chromosomes, i.e., the shapes of the Gaussian membership functions and corresponding switching laws of the consequent part are evolved to minimize the angular position errors. Then, these trained fuzzy rules can be brought into the online operation of underactuated manipulators. Simulation results show that the new methodology is effective in designing controllers for underactuated robot manipulators.This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24–26, 2003     

Formal approach for reengineering fuzzy XML in fuzzy object-oriented databases

Since semi-structured documents (e.g., XML) could benefit greatly from database support and more specifically from object-oriented (OO) database management systems, we study the methodology of reengineering XML to object-oriented databases when database migration occurs in this paper. In particular, considering the need of processing the imprecise and uncertain information existing in practical applications, we investigate the problem of migrating fuzzy XML to fuzzy object-oriented databases. To find the object-oriented schema that best describes the existing fuzzy XML schema (DTD), we devise a comprehensive approach centering on a set of mapping rules. Such reengineering practices could not only provide a significant consolidation of the interoperability between fuzzy OO and fuzzy XML modeling techniques, but also develop the practical design methodology for fuzzy OO databases.     

Stable adaptive fuzzy control of nonlinear systems using small-gain theorem and LMI approach

A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper. The T-S fuzzy model is employed to represent the systems. First, the concept of the so-called parallel distributed compensation (PDC) and linear matrix inequality (LMI) approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling. Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability. Finally, the error caused by fuzzy modeling is considered and the input-tostate stable (ISS) method is used to design the adaptive compensation term to reduce the effect of the modeling error. By the small-gain theorem, the resulting closed-loop system is proved to be input-to-state stable. Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded. The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.     

Fuzzy cognitive map architectures for medical decision support systems

Medical decision support systems can provide assistance in crucial clinical judgments, particularly for inexperienced medical professionals. Fuzzy cognitive maps (FCMs) is a soft computing technique for modeling complex systems, which follows an approach similar to human reasoning and the human decision-making process. FCMs can successfully represent knowledge and human experience, introducing concepts to represent the essential elements and the cause and effect relationships among the concepts to model the behavior of any system. Medical decision systems are complex systems that can be decomposed to non-related and related subsystems and elements, where many factors have to be taken into consideration that may be complementary, contradictory, and competitive; these factors influence each other and determine the overall clinical decision with a different degree. Thus, FCMs are suitable for medical decision support systems and appropriate FCM architectures are proposed and developed as well as the corresponding examples from two medical disciplines, i.e. speech and language pathology and obstetrics, are described.     

Complementary case-based reasoning and competitive fuzzy cognitive maps for advanced medical decisions

This paper presents a new hybrid modeling methodology suitable for complex decision making processes. It extends previous work on competitive fuzzy cognitive maps for medical decision support systems by complementing them with case based reasoning methods. The synergy of these methodologies is accomplished by a new proposed algorithm that leads to more dependable advanced medical decision support systems that are suitable to handle situations where the decisions are not clearly distinct. The methodology developed here is applied successfully to model and test two decision support systems, one a differential diagnosis problem from the speech pathology area for the diagnosis of language impairments and the other for decision making choices in external beam radiation therapy.     

Non-convex fuzzy data and fuzzy statistics: a first descriptive approach to data analysis

LR-fuzzy numbers are widely used in Fuzzy Set Theory applications based on the standard definition of convex fuzzy sets. However, in some empirical contexts such as, for example, human decision making and ratings, convex representations might not be capable to capture more complex structures in the data. Moreover, non-convexity seems to arise as a natural property in many applications based on fuzzy systems (e.g., fuzzy scales of measurement). In these contexts, the usage of standard fuzzy statistical techniques could be questionable. A possible way out consists in adopting ad-hoc data manipulation procedures to transform non-convex data into standard convex representations. However, these procedures can artificially mask relevant information carried out by the non-convexity property. To overcome this problem, in this article we introduce a novel computational definition of non-convex fuzzy number which extends the traditional definition of LR-fuzzy number. Moreover, we also present a new fuzzy regression model for crisp input/non-convex fuzzy output data based on the fuzzy least squares approach. In order to better highlight some important characteristics of the model, we applied the fuzzy regression model to some datasets characterized by convex as well as non-convex features. Finally, some critical points are outlined in the final section of the article together with suggestions about future extensions of this work.     

Spatial dependence-based fuzzy regression clustering

Fuzzy clustering based regression analysis is a novel hybrid approach to capture the linear structure while considering the classification structure of the measurement. Using the concept that weights provided via the fuzzy degree of clustering, some regression models have been proposed in literature. In these models, membership values derived from clustering or some weights obtained from geometrical functions are employed as the weights of regression system. This paper addresses a weighted fuzzy regression analysis based on spatial dependence measure of the memberships. By the methodology presented in this paper, the relative weights are used in fuzzy regression models instead of direct membership values or their geometrical transforms. The experimental studies indicate that the spatial dependence based analyses yield more reliable results to show the correlation of the independent variables into the dependent variable. In addition, it has been observed that spatial dependence based models have high estimation and generalization capacities.     

The effect of set size on the interpretation of quantifiers used in rating scales

Two studies are reported which investigated how people interpret quantifiers of amount such as are commonly used in questionnaires and rating scales. The results indicated that the interpretation of certain quantifiers and rating scales. The results indicated that the interpretation of certain quantifiers varied depending on the context in which they occurred. Low-magnitude quantifiers (e g, 'few', 'several') seemed to signify a much greater proportion when they described small set sizes than when they described relatively large ones. This means that it will be virtually impossible to find quantifiers for use in rating scales which achieve the desirable property of interval scaling. Despite this, some quantifiers are clearly more consistent in their interpretation and more appropriate to use than others, and recommendations are made as to the best ones to use in different situations.