Design Of Fuzzy Models Research Articles

Application of Gradient Boosting in the Design of Fuzzy Rule-Based Regression Models

Application of Gradient Boosting in the Design of Fuzzy Rule-Based Regression Models

A Design of Fuzzy Rule-Based Models With Data Privacy

One of the currently visible requirement of data analysis is to cope with data privacy requirements. The quest for privacy triggers design challenges in the construction of Machine Learning models. In this study, we propose a novel and systematic design methodology of fuzzy rule-based models completed in the following privacy-driven environment. Multidimensional data are available for model design in two different formats: those attributes that are privacy sensitive are provided at the higher non-numeric level of abstraction represented in the form of information granules while the remaining ones are available directly. It is shown that the granular manifestation of data becomes beneficial in the formation of the conditions of the rules whereas numeric attributes are available for the construction of the conclusions of the rules. The generic development scheme is discussed. Some generalization is introduced to cope with a number of data islands associated with corresponding data owners. It is shown that a formation of the data structure calls for a mechanism of collaborative clustering. A way of handling information granules at different levels of information granularity is discussed. Some illustrative examples are presented.

Design and Development of Granular Fuzzy Rule-Based Models for Knowledge Transfer

As an effective way for knowledge representation and processing, fuzzy rule-based models have been extensively studied and widely used in practice. In many circumstances, a very limited amount of data or insufficient computational resources make the construction of accurate models a genuine challenge. In this study, a granular augmentation of fuzzy rule-based models is proposed with intent to realize knowledge transfer in system modeling. This research mainly focuses on how to effectively exploit the existing fuzzy model, which has been constructed on extensive previously acquired experimental evidence and could be regarded as source of knowledge, in a new environment where only very limited experimental evidence is available. Rather than constructing a new model from scratch, knowledge conveyed by the existing model could be retained and reused in the target domain. The originality and innovation of this study lies in the adaption of the existing model to the new environment through optimal allocation of information granularity to produce granular fuzzy models, which are more abstract and general than the original numeric constructs. The granular fuzzy models yield results in a granular form whose quality is evaluated using the coverage and specificity criteria.

Design of fuzzy rule-based models with fuzzy relational factorization

This study opens an original avenue of designing interpretable fuzzy rule-based models realized in the presence of data characterized by a large number of attributes (input variables). In the presence of such high-dimensional data, the development of rule-based models faces serious challenges both at the design and interpretability level. To address these two problems, we develop a new architecture of the rules and establish a two-step design process. First, the dimensionality reduction is realized with the aid of a fuzzy relational matrix factorization which transforms original fuzzy set-based encoded variables and yields a logic-oriented level of activation of individual rules. The results of relational factorization are logic expressions built over the encoded input variables forming condition parts of the rules. Second, the conclusions of the rules are built by optimizing local functions (both constant and linear functions are considered). A number of experiments are reported along with comparative studies involving a standard Takagi-Sugeno (TS) model.

Designing Distributed Fuzzy Rule-Based Models

In the design of fuzzy rule-based models, in the presence of high-dimensional data, we are faced with conceptual and algorithmic challenges. Conceptually, as the dimensionality of data increases, the notion of distance starts to be questionable, resulting in the well-known concentration effect. This has a direct detrimental effect given the fact that the distance is used in fuzzy clustering, using which the condition parts of the rules are being formed. Computationally, with the increase of dimensionality, the computing overhead becomes significant and has to be carefully addressed. In this article, we advocate a construction of distributed fuzzy rule-based models, where instead of a single monolithic (multivariable) rule-based model, we construct a collection of low-dimensional (in particular, 1- or 2-D) rule-based models and aggregate their results through some linear transformations. A suite of experimental studies realized using publicly available data are reported along with a comparative analysis engaging accuracy criteria and computing overhead. Interestingly, building distributed models exhibits some tangible benefits over the construction of the monolithic rule-based models. In terms of accuracy and computing costs, the gains of 1-D rule-based models with optimal linkage matrix (on average) are around 43.46% and 98.85%, respectively.

Granular fuzzy models: Analysis, design, and evaluation

The study is concerned with a design of granular fuzzy models. We exploit a concept of information granularity by developing a model coming as a network of intuitively structured collection of interval information granules described in the output space and a family of induced information granules (in the form of fuzzy sets) formed in the input space. In contrast to most fuzzy models encountered in the literature, the results produced by granular models are information granules rather than plain numeric entities. The design of the model concentrates on a construction of information granules that form a backbone of the overall construct. Interval information granules positioned in the output space are built by considering intervals of equal length, equal probability, and developing an optimized version of the intervals. The induced fuzzy information granules localized in the input space are realized by running a conditional Fuzzy C-Means (FCM). The performance of the model is assessed by considering criteria of coverage and information specificity (information granularity). Further optimization of the model is proposed along the line of an optimal re-distribution of input information granules induced by the individual interval information granules located in the output space. Experimental results involve some synthetic low-dimensional data and publicly available benchmark data sets.

Evolutionary design of efficient type-2 fuzzy models from noisy data using hybrid PSO model

This work presents an efficient framework for designing type-2 fuzzy models from noisy data that represent majority of the real-world databases used for building models. The framework is based on the use of a hybrid particle swarm optimisation (PSO) model that combines the traits of gbest and lbest PSO variants for getting fast results and at the same time avoiding premature convergence. Two major components of the framework, i.e., the encoding mechanism, and the hybrid PSO model have been discussed. Further, two benchmark problems that cover major application domains of type-2 FLSs viz. forecasting and classification, have been presented to demonstrate the effectiveness of the proposed methodology. For each noisy benchmark data, type-1 fuzzy model is also designed and its performance is compared with the designed type-2 fuzzy model with an objective to exhibit better noise handling capability of type-2 models.

개선된 미분 진화 알고리즘에 의한 퍼지 모델의 설계

Evolutionary algorithms such as genetic algorithm (GA) have been proven their effectiveness when applying to the design of fuzzy models. However, it tends to suffer from computationally expensWive due to the slow convergence speed. In this study, we propose an approach to develop fuzzy models by means of an improved differential evolution (IDE) to overcome this limitation. The improved differential evolution (IDE) is realized by means of an orthogonal approach and differential evolution. With the invoking orthogonal method, the IDE can search the solution space more efficiently. In the design of fuzzy models, we concern two mechanisms, namely structure identification and parameter estimation. The structure identification is supported by the IDE and C-Means while the parameter estimation is realized via IDE and a standard least square error method. Experimental studies demonstrate that the proposed model leads to improved performance. The proposed model is also contrasted with the quality of some fuzzy models already reported in the literature.

Granular fuzzy models: a study in knowledge management in fuzzy modeling

In system modeling, knowledge management comes vividly into the picture when dealing with a collection of individual models. These models being considered as sources of knowledge, are engaged in some collective pursuits of a collaborative development to establish modeling outcomes of global character. The result comes in the form of a so-called granular fuzzy model, which directly reflects upon and quantifies the diversity of the available sources of knowledge (local models) involved in knowledge management. In this study, several detailed algorithmic schemes are presented along with related computational aspects associated with Granular Computing. It is also shown how the construction of information granules completed through the use of the principle of justifiable granularity becomes advantageous in the realization of granular fuzzy models and a quantification of the quality (specificity) of the results of modeling. We focus on the design of granular fuzzy models considering that the locally available models are those fuzzy rule-based. It is shown that the model quantified in terms of two conflicting criteria, that is (a) a coverage criterion expressing to which extent the resulting information granules “cover” include data and (b) specificity criterion articulating how detailed (specific) the obtained information granules are. The overall quality of the granular model is also assessed by determining an area under curve (AUC) where the curve is formed in the coverage-specificity coordinates. Numeric results are discussed with intent of displaying the most essential features of the proposed methodology and algorithmic developments.

A genetic reduction of feature space in the design of fuzzy models

The two fundamental conflicting requirements of fuzzy modeling, namely accuracy and transparency (interpretability) have resulted in a plethora of design methodologies and ensuing architectures of fuzzy models. This study contributes to the ongoing approaches to the enhancement of interpretability of fuzzy models by focusing on the reduction of input space in which such models are constructed. Fuzzy clustering realized through Fuzzy C-Means (FCM) is carried out in the input space of reduced dimensionality and the information granules obtained in such space are used to form a series of local models of the rule-based fuzzy model. The reduction of the input space is a problem of combinatorial nature and to solve this task, considered is the optimization scheme of genetic algorithms. In this sense, the feature (input) space reduction is realized by a wrapper algorithm, where the objective function guiding its development of the input space expresses the performance of the resulting fuzzy model. The design utilizes two commonly encountered concepts and functional constructs of fuzzy models, viz. information granules built in the reduced input space and a collection of local linear models forming the conclusion parts of the rules. Considering the well-established architecture of fuzzy models, the main objective of this study is to present a way of an efficient reduction of the input space leading to the enhanced interpretability of the fuzzy models and investigate and quantify possibilities of optimization of fuzzy models with regard. The underlying design issues being of particular practical interest in this modeling context deal with the dependencies between the level of reduction of the input space versus the granularity of the fuzzy model (viz. the number of its rules) and a quantification of an impact of the parameters of the granules (fuzzification coefficient) on the performance of the obtained model. The experimental studies highlighting the numerical aspects of the design comprise experimentation with synthetic data and those publicly available at several data sites.

개선된 공간 탐색 알고리즘을 이용한 정보입자 기반 퍼지모델 설계

This study is concerned with the identification of fuzzy models. To address the optimization of fuzzy model, we proposed an improved space search evolutionary algorithm (ISSA) which is realized with the combination of space search algorithm and Gaussian mutation. The proposed ISSA is exploited here as the optimization vehicle for the design of fuzzy models. Considering the design of fuzzy models, we developed a hybrid identification method using information granulation and the ISSA. Information granules are treated as collections of objects (e.g. data) brought together by the criteria of proximity, similarity, or functionality. The overall hybrid identification comes in the form of two optimization mechanisms: structure identification and parameter identification. The structure identification is supported by the ISSA and C-Means while the parameter estimation is realized via the ISSA and weighted least square error method. A suite of comparative studies show that the proposed model leads to better performance in comparison with some existing models.

Design of interval type-2 fuzzy models through optimal granularity allocation

In this paper, we offer a new design methodology of type-2 fuzzy models whose intent is to effectively exploit the uncertainty of non-numeric membership functions. A new performance index, which guides the development of the fuzzy model, is used to navigate the construction of the fuzzy model. The underlying idea is that an optimal granularity allocation throughout the membership functions used in the fuzzy model leads to the best design. In contrast to the commonly utilized criterion where one strives for the highest accuracy of the model, the proposed index is formed in such a way so that the type-2 fuzzy model produced intervals, which “cover” the experimental data and at the same time are made as narrow (viz. specific) as possible. Genetic algorithm is proposed to automate the design process and further improve the results by carefully exploiting the search space. Experimental results show the efficiency of the proposed design methodology.

A Comparative Study of Space Search Algorithm and Particle Swarm Optimization in the Design of ANFIS-based Fuzzy Models

In this study, we propose a space search algorithm (SSA) and then introduce a hybrid optimization of ANFIS-based fuzzy models based on SSA and information granulation (IG). In comparison with “conventional” evolutionary algorithms (such as PSO), SSA leads not only to better search performance to find global optimization but is also more computationally effective. In the hybrid optimization of ANFIS-based fuzzy inference system, SSA is exploited to carry out the parametric optimization of the fuzzy model as well as to realize its structural optimization. IG realized with the aid of C-Means clustering helps determine the initial values of the apex parameters of the membership function of fuzzy model. The overall hybrid identification of ANFIS-based fuzzy models comes in the form of two optimization mechanisms: structure identification (such as the number of input variables to be used, a specific subset of input variables, the number of membership functions, and polynomial type) and parameter identification (viz. the apexes of membership function). The structure identification is developed by SSA and C-Means while the parameter estimation is realized via SSA and a standard least square method. The evaluation of the performance of the proposed model was carried out by using three representative numerical examples such as Non-linear function, gas furnace, and Mackey-Glass time series. A comparative study of SSA and PSO demonstrates that SSA leads to improved performance both in terms of the quality of the model and the computing time required. The proposed model is also contrasted with the quality of some “conventional” fuzzy models already encountered in the literature.

Cooperative Evolutionary Learning of Linguistic Fuzzy Rules and Parametric Aggregation Connectors for Mamdani Fuzzy Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> There are two tasks in the design of linguistic fuzzy models for a concrete application: The derivation of the linguistic rule base and the setup of the inference system and the defuzzification method. Traditionally, the derivation of the linguistic rule base has been considered the most important task, but the use of the appropriate aggregation connectors in the inference system and the defuzzification interface can improve the fuzzy system behavior. In this paper, we take in consideration this idea, we propose an evolutionary learning method to learn a linguistic rule base and the parametric aggregation connectors of the inference and defuzzification in a single step. The aim of this methodology is to make possible a high level of positive synergy between the linguistic rule base and the aggregation connectors, improving the accuracy of the linguistic Mamdani fuzzy systems. Our proposal has shown good results solving three different applications. We introduce a statistical analysis of results for validating the model behavior on the applications used in the experimental study. We must remark that we present an experimental study with a double intention: a) to compare the behavior of the new approach in comparison with those ones that first learn the rule base and then adapt the connectors, and b) to analyze the rule bases obtained with fixed aggregation connectors and with the adaptive ones for showing the changes on the consequent rules, changes on labels that produce a better behavior of the linguistic model than the classic ones. </para>

Improving the design of clustered neural fuzzy models for optimization

This article discusses the application of hierarchical clustering techniques in the design of clustered neural fuzzy approximations for optimization problems. Different clustering techniques are investigated for addressing the function approximation problem from data samples. The hierarchical clustering process has the advantage of providing a rational manner to determine the adequate number of clusters. We present a methodology for the iterative design of the neural fuzzy network model using the clustering scheme. Experiments with some analytical functions are performed to confirm the methodology discussed. Finally, we investigate the design of a superconducting magnetic energy storage device with two solenoids and three design parameters. The results indicate that the employment of hierarchical clustering techniques for generating neural fuzzy approximations is a valuable technique to solve and to reduce the computational cost of practical optimization problems.

Distinguishability quantification of fuzzy sets

Distinguishability is a semantic property of fuzzy sets that has a great relevance in the design of interpretable fuzzy models. Distinguishability has been mathematically defined through different measures, which are addressed in this paper. Special emphasis is given to similarity, which exhibits sound theoretical properties but its calculation is usually computationally intensive, and possibility, whose calculation can be very efficient but it does not exhibit the same properties of similarity. It is shown that under mild conditions – usually met in interpretable fuzzy modeling – possibility can be used as a valid measure for assessing distinguishability, thus overcoming the computational inefficiencies of similarity measures. Moreover, procedures that minimize possibility also minimize similarity and, consequently, improve distinguishability. In this sense, the use of possibility is fully justified in interpretable fuzzy modeling.

A robust design criterion for interpretable fuzzy models with uncertain data

We believe that nonlinear fuzzy filtering techniques may be turned out to give better robustness performance than the existing linear methods of estimation (H/sup 2/ and H/sup /spl infin// filtering techniques), because of the fact that not only linear parameters (consequents), but also the nonlinear parameters (membership functions) attempt to identify the uncertain behavior of the unknown system. However, the fuzzy identification methods must be robust to data uncertainties and modeling errors to ensure that the fuzzy approximation of unknown system's behavior is optimal in some sense. This study presents a deterministic approach to the robust design of fuzzy models in the presence of unknown but finite uncertainties in the identification data. We consider online identification of an interpretable fuzzy model, based on the robust solution of a regularized least-squares fuzzy parameters estimation problem. The aim is to resolve the difficulties associated with the robust fuzzy identification method due to lack of a priori knowledge about upper bounds on the data uncertainties. The study derives an optimal level of regularization that should be provided to ensure the robustness of fuzzy identification strategy by achieving an upper bound on the value of energy gain from data uncertainties and modeling errors to the estimation errors. A time-domain feedback analysis of the proposed identification approach is carried out with emphasis on stability, robustness, and steady-state issues. The simulation studies are provided to show the superiority of the proposed fuzzy estimation over the classical estimation methods.

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