A new approach to fuzzy modeling

This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm     

A formal approach to fuzzy modeling

A formalism for coding fuzzy models of dynamical systems is presented. It is shown that the formalism is rich enough to capture the performance of arbitrary conventional discrete time dynamical systems whose transition maps are polynomials with rational coefficients. The proof of this fact provides a constructive algorithm for generating fuzzy models to arbitrarily closely approximate an arbitrary map on a compact set. Our modeling formalism highlights the similarities between fuzzy systems and hybrid control systems. We hope to be able to exploit these similarities by extending results from the area of hybrid systems to the fuzzy domain and vice versa     

The fuzzy crystallization algorithm: a new approach to complexsystems modeling

A new identification method for fuzzy modeling is introduced. Since the method has some analogy with the process of material crystallization in nature, the name of fuzzy crystallization algorithm (FCA) is given to this novel approach. This method accomplishes structure identification and parameter identification at the same time, and possesses the properties of simplicity, flexibility, and high calculation speed. Compared with other modeling strategies, it is easier to construct a model with a specific accuracy. Numerical examples are provided to demonstrate the performance of this approach.     

A transformed input-domain approach to fuzzy modeling

This paper presents an explanation of a fuzzy model considering the correlation among components of input data. Generally, fuzzy models have a capability of dividing an input space into several subspaces compared to a linear model. But hitherto suggested fuzzy modeling algorithms have not taken into consideration the correlation among components of sample data and have addressed them independently, which results in an ineffective partition of the input space. In order to solve this problem, this paper proposes a new fuzzy modeling algorithm, which partitions the input space more effectively than conventional fuzzy modeling algorithms by taking into consideration the correlation among components of sample data. As a way to use the correlation and divide the input space, the method of principal component is used. Finally, the results of the computer simulation are given to demonstrate the validity of this algorithm     

A probabilistic fuzzy approach to modeling nonlinear systems

Recently, the study of incorporating probability theory and fuzzy logic has received much interest. To endow the traditional fuzzy rule-based systems (FRBs) with probabilistic features to handle randomness, this paper presents a probabilistic fuzzy neural network (ProFNN) by introducing the probability of input linguistic terms and providing linguistic meaning into the connectionist architecture. ProFNN integrates the probabilistic information of fuzzy rules into the antecedent parts and quantifies the impacts of the rules on the consequent parts using mutual subsethood, which work in conjunction with volume defuzzification in a gradient descent learning frame work. Despite the increase in the number of parameters, ProFNN provides a promising solution to deal with randomness and fuzziness in a single frame. To evaluate the performance and applicability of the proposed approach, ProFNN is carried out on various benchmarking problems and compared with other existing models with a performance better than most of them.     

基于模糊ARMAX模型的模糊建模

提出了一种利用MGS(modified Gram-Schmidt)算法建立模糊ARMAX模型的方法, 给出了基于MGS算法的模型结构和参数辨识的一体化方法. 利用MGS正交变换对通过GK模糊聚类的聚类结果进行变换, 确定对模型贡献大的规则, 删除对模型贡献小的规则, 同时对模型中的参数进行估计. 本文提出的方法能够实现模糊模型的结构和参数的优化. 仿真结果表明, 本文提出的方法能够建立非线性系统的模糊ARMAX模型.     

Fuzzy polynomial neural networks: hybrid architectures of fuzzy modeling

We introduce a concept of fuzzy polynomial neural networks (FPNNs), a hybrid modeling architecture combining polynomial neural networks (PNNs) and fuzzy neural networks (FNNs). The development of the FPNNs dwells on the technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The structure of the FPNN results from a synergistic usage of FNN and PNN. FNNs contribute to the formation of the premise part of the rule-based structure of the FPNN. The consequence part of the FPNN is designed using PNNs. The structure of the PNN is not fixed in advance as it usually takes place in the case of conventional neural networks, but becomes organized dynamically to meet the required approximation error. We exploit a group method of data handling (GMDH) to produce this dynamic topology of the network. The performance of the FPNN is quantified through experimentation that exploits standard data already used in fuzzy modeling. The obtained experimental results reveal that the proposed networks exhibit high accuracy and generalization capabilities in comparison to other similar fuzzy models.     

Mathematical modeling of decision making: a soft and fuzzy approach to capturing hard decisions

This research focuses on a modeling approach and set of mathematical tools that were derived from research on intelligence systems, namely fuzzy system modeling. This study systematically evaluates these tools as an approach for modeling human decision making, contrasting the approach with more traditional methods based on regression. The research was conducted using experts and a simulated task environment related to allocating rewards in the form of merit pay. The results indicate that fuzzy system models generally perform as well as or better than both linear and nonlinear regression methods in terms of model fit. These results are discussed in terms of issues regarding modeling precision versus parsimony, the value of adaptive modeling techniques, empirical versus subjective approaches to model building, and individual differences in judgment strategies. Potential applications of this research include using the modeling approach studied to build higher-fidelity models that yield new insights and a better understanding of decision-making strategies and environments.     

A fuzzy approach for performance modeling in a batch plant:application to semiconductor manufacturing

In the current literature dealing with job shop scheduling, most of the approaches have developed models based on the assumption that the problem domain does not contain any imprecision. However, this hypothesis is strongly challenged in the implementation phase of such models-imprecision is inherent to production systems involving human intervention. The aim of this paper is to demonstrate the advantages of possibilistic production data modeling in a real-world application, i.e., semiconductor manufacturing. In this work, a discrete-event simulation model (MELISSA) for performance evaluation of a batch-manufacturing facility previously developed in our laboratory has been extended to treat uncertainties modeled by fuzzy numbers. Due to the confidential nature of industrial data, an illustrative example, presenting the same typical features as a real problem, is treated and analyzed using fuzzy concepts. Inclusion of fuzzy techniques provides the decision-maker with a range of possible values for completion times, average storage times, and operator workload instead of a unique value (which has little significance due to the variety of human operators). In addition, the negative portion of average waiting times yields useful information for the manager to detect deficient resources in the production system     

Support vector learning mechanism for fuzzy rule-based modeling: a new approach

This paper describes a fuzzy modeling framework based on support vector machine, a rule-based framework that explicitly characterizes the representation in fuzzy inference procedure. The support vector learning mechanism provides an architecture to extract support vectors for generating fuzzy IF-THEN rules from the training data set, and a method to describe the fuzzy system in terms of kernel functions. Thus, it has the inherent advantage that the model does not have to determine the number of rules in advance, and the overall fuzzy inference system can be represented as series expansion of fuzzy basis functions. The performance of the proposed approach is compared to other fuzzy rule-based modeling methods using four data sets.     

Least-squares approach to regression modeling in full interval-valued fuzzy environment

A regression procedure is introduced when the observations of the response and the independent variables, as well as the coefficients that are to be estimated, are triangular interval-valued fuzzy numbers (IVFNs). The coefficients of the model are obtained by least square method, using a distance that we define on the space of IVFNs. Three real data sets, on soil sciences and hydrology engineering are used to test the applicability of the proposed method. The predictive performance of the models thus obtained are examined by cross-validation. To check the overall performance of the proposed method, two measures of goodness of fit are introduced and employed.     

Multimodal processes optimization subject to fuzzy operation time constraints: declarative modeling approach

We present an extension of the resource-constrained multi-product scheduling problem for an automated guided vehicle (AGV) served flow shop, where multiple material handling transport modes provide movement of work pieces between machining centers in the multimodal transportation network (MTN). The multimodal processes behind the multi-product production flow executed in an MTN can be seen as processes realized by using various local periodically functioning processes. The considered network of repetitively acting local transportation modes encompassing MTN’s structure provides a framework for multimodal processes scheduling treated in terms of optimization of the AGVs fleet scheduling problem subject to fuzzy operation time constraints. In the considered case, both production takt and operation execution time are described by imprecise data. The aim of the paper is to present a constraint propagation (CP) driven approach to multi-robot task allocation providing a prompt service to a set of routine queries stated in both direct and reverse way. Illustrative examples taking into account an uncertain specification of robots and workers operation time are provided.     

An alternative approach to fuzzy control charts: Direct fuzzy approach

The major contribution of fuzzy set theory lies in its capability of representing vague data. Fuzzy logic offers a systematic base to deal with situations, which are ambiguous or not well defined. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. In this paper, some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of α-cut to provide the ability of determining the tightness of the inspection: the higher the value of α the tighter inspection. A new alternative approach “Direct Fuzzy Approach (DFA)” is also developed in this paper. In contrast to the existing fuzzy control charts, the proposed approach is quite different in the sense it does not require the use of the defuzziffication. This prevents the loss of information included by the samples. It directly compares the linguistic data in fuzzy space without making any transformation. We use some numeric examples to illustrate the performance of the method and interpret its results.     

Combining fuzzy cognitive maps with agent-based modeling: Frameworks and pitfalls of a powerful hybrid modeling approach to understand human-environment interactions

Agent-based modeling (ABM) is an established technique to capture human-environment interactions in socio-ecological systems. As a micro-model, it explicitly represents each agent, such that heterogeneous decision-making processes (e.g. based on the beliefs and experiences of stakeholders) can anticipate the socio-environmental consequences of aggregated individual behaviors. In contrast to ABM, Fuzzy Cognitive Mapping takes a macro-level view of the world that represents causal connections between concepts rather than individual entities. Researchers have expressed interest in reconciling the two, i.e. taking a hybrid approach and drawing of the strengths of each to more accurately model socio-ecological interactions. The intuition is to take FCMs, which can be quickly developed using participatory modeling tools and use them to create a virtual population of agents with sophisticated decision-making processes. In this paper, we detail two ways in which this combination can be done, and highlight the key questions that modelers need to be mindful of.     

A new approach to fuzzy modeling and control of discrete-time systems

We present a new approach to fuzzy modeling and control of discrete-time systems which is based on the formulation of a novel state-space representation using the hyperbolic tangent function. The new representation, designated the hyperbolic model, combines the advantages of fuzzy system theory and classical control theory. On the one hand, the hyperbolic model is easily derived from a set of Mamdani-type fuzzy rules. On the other hand, classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of Mamdani-type fuzzy rules. Thus, this new approach combines the best of two worlds. It enables linguistic interpretability of both the model and the controller, and guarantees closed-loop stability and robustness.     

基于F-SVMs的多模型建模方法

针对全局模型难以精确描述复杂工业过程的问题,提出一种基于模糊支持向量机(F-SVMs)的多模型(F-SVMs MM)建模方法。用模糊支持向量分类算法(F-SVC)对输入数据进行预处理,得到多模型模糊隶属度;用模糊支持回归算法(F-SVR)建立多模型(MM)估计器。应用该方法对pH中和滴定过程进行建模,仿真结果表明,F-SVMs MM跟踪性能好、泛化能力强,比USOCPN方法和标准支持向量机(SVMs)方法具有更好的性能和推广能力。     

Working memory modeling using inverse fuzzy relational approach

The paper proposes a novel approach to fuzzy modeling of human working memory (WM) using electroencephalographic (EEG) signals, acquired during human face encoding and recall experiments in connection with a face recognition problem. The EEG signals acquired from the short term memory (STM) during memory encoding instances are considered as the input of the proposed working memory model. On the other hand, the EEG response of the WM to visual stimuli acquired during WM recall instances are considered as the output of the proposed working memory model. The entire experiment is primarily divided into two phases. In the first phase, the WM of a human subject is modeled by a fuzzy implication relation, describing a mapping from the STM response (during encoding) to the WM responses (during recall) to visual stimuli. During STM encoding, the subject is visually presented with the full face stimulus of a person. During WM recall, four partial face stimuli of the same person (made familiar during encoding) are used for the subject to recall the respective full face.The second phase is undertaken to validate the WM model by visually stimulating the subject again with randomly selected partial faces of people, being familiar in the first phase and the WM EEG responses are recorded. The WM responses along with the WM model, developed in the first phase, are used to retrieve the STM information by using an inverse fuzzy (implication) relation. Besides WM modeling, another important contribution of the paper lies in devising a solution to the inverse fuzzy relation computation in the settings of an optimization problem. An error metric is then defined to measure the discrepancy between the model-predicted STM encoding pattern and the actual pattern encoded by the STM (as captured by the EEG signal during encoding in the first phase). Apparently, smaller the error magnitude better is the accuracy of the proposed model to effectively differentiate people with memory failures. Experimentally it is observed that the proposed model yields a very small error, in the order of 10⁻⁴, thus showing a high level of similarity between actual and model predicted STM response for all the healthy subjects. An experiment undertaken using eLORETA software confirms that the orbito-frontal cortex of prefrontal lobe is responsible for STM encoding whereas dorsolateral prefrontal region is responsible for WM recall. An analysis undertaken reveals that the proposed WM model produces the best response in the theta frequency band of EEG spectra, thus assuring the association of the theta frequency range in the face recognition task. Comparative analysis performed also substantiates that the proposed technique of computing max–min inverse fuzzy relation outperforms the existing techniques for inverse fuzzy computation, with a successful retrieval accuracy of 87.92%. The proposed study would find interesting applications to diagnose memory failures for people with Pre-frontal lobe amnesia.     

Fuzzy multi-criteria acceptability analysis: A new approach to multi-criteria decision analysis under fuzzy environment

Uncertainty is one of the main difficulties that increases the complexity of multi-criteria decision analysis (MCDA) problems, and often uncertainty cannot be managed by probabilistic models. In such cases, the use of fuzzy methods has been successfully applied to multi-criteria decision methods in which the ranking of fuzzy quantities is crucial for the decision analysis. This paper aims to introduce a new approach to MCDA problems defined under fuzzy contexts that implements the concept of acceptability analysis, Fuzzy Multi-Criteria Acceptability Analysis (FMAA), based on the Fuzzy Rank Acceptability Analysis (FRAA), that provides a ranking and a confidence degree about the ranking of fuzzy quantities. Based on the fuzzy extension of MAVT method, the FMAA is implemented and then applied to a case study, and its results are compared with other well-known MCDA methods in order to show its validity, interpretability and consistency.     

基于特征选择和协同模糊聚类的模糊建模研究

为了提高模糊模型辨识效率,提出了一种新的模糊模型建摸方法,该方法由两步组成：（1）采用基于特征相似性的特征选择方法,去除原始数据的冗余;（2）利用协同模糊聚类与G-K相结合的算法初始化模糊模型,使其前件和后件参数得到优化。采用该算法对有效的特征进行协同模糊聚类,模型参数得到改善,提高了模糊模型辨识的效率。模糊建模的实验结果表明了该方法的有效性。