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Fuzzy measures generalize additive measures and probabilities. Their advantage with respect to additive ones is that they permit to model interactions between objects. Mesiar introduced in 1999 k-order Pan-additive fuzzy measures that generalize k-order additive and k-maxitive ones. They are related to the Möbius transform and related generalizations. In this paper we introduce some other transforms that we call (M a x , +) and (M a x , ⊕) that permit to represent fuzzy measures in a convenient way when we use genetic algorithms in fuzzy measure identification problems. We illustrate its use identifying a measure for a subjective evaluation problem using a Choquet integral and a Sugeno integral. [ABSTRACT FROM AUTHOR]

Time series forecasting is an important research topic applied to various areas of human knowledge, such as economics, medicine, meteorology, and engineering. The forecasting results can assist the decision-making process, providing useful projections to specialists. In this paper, a hybrid approach named Parallel Recursive Singular Spectrum Analysis and Evolving Neuro-Fuzzy Network (PRSSA+ENFN) for forecasting univariate and multivariate experimental time series, with learning from data streams composed of time series samples, is presented. The adopted methodology considers an evolving neuro-fuzzy basis, i.e., the PRSSA+ENFN adapts, extends, and evolves the fuzzy rule structure from new incoming data of the time series. The time series is subdivided into unobservable components, which are patterns contained in the data, and the neuro-fuzzy network forecasts these component samples so to reconstruct the original time series considering future values. An alternative to determine the specific parameters of PRSSA+ENFN is the application of a genetic algorithm. Four multi-steps ahead forecasting experiments are outlined with univariate and multivariate time series. Finally, some competitive results in relation to other methods in literature are discussed. [ABSTRACT FROM AUTHOR]

• In this work we propose two metaheuristic algorithms for generating linguistic descriptions of data. • We proposed fuzzy quantified statements involving three well-known quantification models. • We describe extensive experimentation with two real meteorological data sources: observation and forecasting. • We compare both approaches in terms of their performance and quality of the descriptions generated. • We perform tests of statistical significance for assessing the differences between both algorithms. In this paper we experimentally assess, from both algorithmic and pragmatic perspectives, the adequacy of linguistic descriptions of real data generated by two metaheuristics: simulated annealing and genetic algorithm meta-heuristics. The type of descriptions we consider are fuzzy quantified statements (both Zadeh's type-1 and type-2) involving three well-known quantification models (Zadeh's scalar and fuzzy and Delgado's GD). We conducted an empirical validation using real observation and prediction meteorological data, where both automatic (metrics-based) and manual (human experts-based) assessment on the adequacy of the generated descriptions was assessed. Results indicate that, overall, the genetic approach performs better than simulated annealing in terms of quality of the obtained descriptions and time execution. Significance of this outperforming depends on the type of meteorological data and the quantification model selected. Tests of statistical significance point out that for type-1 descriptions no significant differences exist between the two meta-heuristics in the prediction case. For type-2 descriptions, significant differences exist for Delgado's GD model for both types of data. For Zadeh's scalar and fuzzy quantification significance depends on the type of data (observation or prediction). Globally, outperforming of the genetic approach over simulated annealing i) is significant in 4 out of 12 scenarios considered (all of them type-2), and ii) is not significant in the other 8 out 12 scenarios (all type-1 and two type-2). Also human expert assessment on the adequacy of the descriptions was conducted, showing that both meta-heuristics behave similarly for type-1 descriptions, while genetic algorithms produce more suitable type-2 linguistic descriptions. [ABSTRACT FROM AUTHOR]

This paper concentrates on the development of precise fuzzy rule-based classification systems for high-dimensional and multi-class problems. The approach begins with the extraction on potential fuzzy if-then rules using fitness sharing based genetic algorithms, this ensures effective searching for productive niches, thereby evolving and maintaining a diverse, cooperative population. Subsequently, for the purpose of combining the obtained fuzzy rules and eliminating their conflicts, an adaboost ensemble method is utilized, enhancing the accuracy of the fuzzy classification systems. Experiments have been conducted on 10 UCI datasets and 3 well-known image classification problems. The features for these image tasks were derived from the activation values of the final convolutional layer in pre-trained convolutional neural networks. These datasets, which were chosen to evaluate the effectiveness of the proposed approach, exhibit significant variation in terms of dimensionality and the number of class labels. Comparative analyses are carried out with conventional fuzzy rule-based classification methods, and the results demonstrate that the classification systems can be developed for complex problems, while maintaining a high-level of prediction accuracy. • Linguistic fuzzy rules are applied for high-dimensional and multi-class problems. • Fitness sharing based genetic search promotes the cooperation among rules. • Adaboosting based ensemble further improves systems accuracy. • Images classification systems are modeled with high-level features of CNNs. [ABSTRACT FROM AUTHOR]

Abstract In recent times, advanced data mining research has been mostly focusing on clustering of categorical data, where a natural ordering in attribute values is missing. To address this fact the Rough Fuzzy K-Modes clustering technique has been recently developed in order to handle imperfect information, i.e. indiscernibility (coarseness) and vagueness within the dataset. However, it has been observed that the said technique suffers from the problem of local optima due to the random choice of initial cluster modes. Hence, in this paper, we have proposed an integrated clustering technique using multi-phase learning. In this regard, first, Simulated Annealing based Rough Fuzzy K-Modes and Genetic Algorithm based Rough Fuzzy K-Modes are proposed in order to perform the clustering better by considering clustering as an underlying optimization problem. These clustering methods individually produce clusters having set of central and peripheral points. Thereafter, for each case, final improved clustering results are obtained by assigning peripheral points to a particular crisp cluster using Random Forest, where central points are used as training set. Second, the varying cardinality of the training and testing sets produced by each clustering method further motivated us to propose a generalized technique called Integrated Rough Fuzzy Clustering using Random Forest, where, results of three aforementioned clustering techniques are used to compute the roughness measure. Based on this measure, three different sets namely best central points , semi-best central points and pure peripheral points are determined. Thereafter, using multi-phase learning, best central points are used to classify the semi-best central points and then using both of them, pure peripheral points are classified by Random Forest. Experimental results are reported quantitatively and visually to demonstrate the effectiveness of the proposed methods in comparison with well-known state-of-the-art methods for six synthetic and five real-life datasets. Finally, statistical significance tests are conducted to establish the superiority of the results produced by the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: In previous papers, we introduced a new reasoning method based on quantifying linguistic domains, established a new fuzzy control algorithm, called hedge-algebras-based controller (HAC), and applied it to solve some fuzzy control problems. The HAC does not require fuzzy sets to provide the semantics of the linguistic terms used in the fuzzy rule system rather the semantics is obtained through the semantically quantifying mappings (SQMs). It was shown that the new method is very effective, i.e. for these problems it is always able to efficiently control the process toward the stable state. In the algebraic approach, the design of an HAC leads to the determination of the parameters of SQMs, which are the fuzziness measure of primary terms and linguistic hedges occurring in the fuzzy model, and the weights of a weighted averaging operator. However, there exists another problem, namely, how one can determine the optimal parameters of the method. In the present paper, we improved the HAC''s design by adding an optimal step that aims to find the optimal parameters of HAC using a genetic algorithm (GA). To show the effectiveness of the proposed method, we apply it to solve again the inverted pendulum problem and the problem of holding an object on a “hill”. The results demonstrate the good performance of the designed HAC. [Copyright &y& Elsevier]

Logistic scheduling problems are often multi-criteria optimization problems, with many contradictory objectives and constraints, which cannot be properly described by conventional cost functions. The use of fuzzy decision making may improve the performance of this type of systems, since it allows an easier and suitable description of the confluence of the different criteria of the scheduling process. This paper introduces the application of fuzzy weighted aggregation to formulate the logistic system optimization problem. Further, this paper also extends the application of this framework to different types of optimization methodologies: dispatching rules, if it is used as a performance index; or meta-heuristics, such as genetic algorithms (GA) or ant colony optimization (ACO), if it is used as an objective function. Simulation results show that the fuzzy combination of criteria improves the scheduling results whatever optimization methodology is used. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a self-adaptive neural fuzzy network with group-based symbiotic evolution (SANFN-GSE) method. A self-adaptive learning algorithm consists of two major components. First, a self-clustering algorithm (SCA) identifies a parsimonious internal structure. An internal structure is said to be parsimonious in the sense that the number of clusters (fuzzy rules) is equal to the true number of clusters in a given training data set. The proposed SCA is an online method and is a distance-based connectionist clustering method. Unlike the traditional cluster techniques that only consider the total variation to updates the only one mean and deviation. The proposed SCA method considers the variation of each dimension for the input data. Second, a group-based symbiotic evolution learning (GSE) method is used to adjust the parameters for the desired outputs. The GSE method is different from traditional GAs (genetic algorithms), with each chromosome in the GSE method representing a fuzzy system. Moreover, in the GSE method, there are several groups in the population. Each group represents a set of the chromosomes that belong to a cluster computing by the SCA. In this paper we used numerical time series examples (one-step-ahead prediction, Mackey-Glass chaotic time series, and sunspot number forecasting) to evaluate the proposed SANFN-GSE model. The performance of the SANFN-GSE model compares excellently with other existing models in our time series simulations. [Copyright &y& Elsevier]

This paper shows how a small number of simple fuzzy if-then rules can be selected for pattern classification problems with many continuous attributes. Our approach consists of two phases: candidate rule generation by rule evaluation measures in data mining and rule selection by multi-objective evolutionary algorithms. In our approach, first candidate fuzzy if-then rules are generated from numerical data and prescreened using two rule evaluation measures (i.e., confidence and support) in data mining. Then a small number of fuzzy if-then rules are selected from the prescreened candidate rules using multi-objective evolutionary algorithms. In rule selection, we use three objectives: maximization of the classification accuracy, minimization of the number of selected rules, and minimization of the total rule length. Thus the task of multi-objective evolutionary algorithms is to find a number of non-dominated rule sets with respect to these three objectives. The main contribution of this paper is to propose an idea of utilizing the two rule evaluation measures as prescreening criteria of candidate rules for fuzzy rule selection. An arbitrarily specified number of candidate rules can be generated from numerical data for high-dimensional pattern classification problems. Through computer simulations, we demonstrate that such a prescreening procedure improves the efficiency of our approach to fuzzy rule selection. We also extend a multi-objective genetic algorithm (MOGA) in our former studies to a multi-objective genetic local search (MOGLS) algorithm where a local search procedure adjusts the selection (i.e., inclusion or exclusion) of each candidate rule. Furthermore, a learning algorithm of rule weights (i.e., certainty factors) is combined with our MOGLS algorithm. Such extensions to our MOGA for fuzzy rule selection are another contribution of this paper. [Copyright &y& Elsevier]

Fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains. Currently, there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities. Two of the most successful approaches to hybridise fuzzy systems with learning and adaptation methods have been made in the realm of soft computing. Neural fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms.The objective of this paper is to provide an account of genetic fuzzy systems, with special attention to genetic fuzzy rule-based systems. After a brief introduction to models and applications of genetic fuzzy systems, the field is overviewed, new trends are identified, a critical evaluation of genetic fuzzy systems for fuzzy knowledge extraction is elaborated, and open questions that remain to be addressed in the future are raised. The paper also includes some of the key references required to quickly access implementation details of genetic fuzzy systems. [Copyright &y& Elsevier]

Abstract: Fuzzy modeling of complex systems is a challenging task, which involves important problems of dimensionality reduction and calls for various ways of improving the accuracy of modeling. The IG-FRBFNN, a hybrid architecture of the IG-FIS (Fuzzy Inference System) and FRBFNN (Fuzzy Radial Basis Function Neural Networks), is proposed to address these problems. The paper is concerned with the analysis and design of IG-FRBFNNs and their optimization by means of the Hierarchical Fair Competition-based Parallel Genetic Algorithm (HFC-PGA). In the proposed network, the membership functions of the premise part of the fuzzy rules of the IG-based FRBFNN model directly rely on the computation of the relevant distance between data points and the use of four types of polynomials such as constant, linear, quadratic and modified quadratic are considered for the consequent part of fuzzy rules. Moreover, the weighted Least Square (WLS) learning is exploited to estimate the coefficients of the polynomial forming the conclusion part of the rules. Since the performance of the IG-RBFNN model is affected by some key design parameters, such as a specific subset of input variables, the fuzzification coefficient of the FCM, the number of rules, and the order of polynomial of the consequent part of fuzzy rules, it becomes beneficial to carry out both structural as well as parametric optimization of the network. In this study, the HFC-PGA is used as a comprehensive optimization vehicle. The performance of the proposed model is illustrated by means of several representative numerical examples. [Copyright &y& Elsevier]

Abstract: This paper presents a new procedure that extends genetic algorithms from their traditional domain of optimization to fuzzy ranking strategy for selecting efficient portfolios of restricted cardinality. The uncertainty of the returns on a given portfolio is modeled using fuzzy quantities and a downside risk function is used to describe the investor''s aversion to risk. The fitness functions are based both on the value and the ambiguity of the trapezoidal fuzzy number which represents the uncertainty on the return. The soft-computing approach allows us to consider uncertainty and vagueness in databases and also to incorporate subjective characteristics into the portfolio selection problem. We use a data set from the Spanish stock market to illustrate the performance of our approach to the portfolio selection problem. [Copyright &y& Elsevier]

Abstract: In this paper, an efficient method is proposed to design fuzzy wavelet neural network (FWNN) for function learning and identification by tuning fuzzy membership functions and wavelet neural networks. The structure of FWNN is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules. In order to improve the function approximation accuracy and general capability of the FWNN system, an efficient genetic algorithm (GA) approach is used to adjust the parameters of dilation, translation, weights, and membership functions. By minimizing a quadratic measure of the error derived from the output of the system, the design problem can be characterized by the proposed GA formulation. Moreover, the solution is directly obtained without any need for complicated computations. The performance of our approximation is superior to that of existing methods. Several numerical design examples are likewise presented to demonstrate the design flexibility and usefulness of this presented approach. [Copyright &y& Elsevier]

Abstract: The analysis of data complexity is a proper framework to characterize the tackled classification problem and to identify domains of competence of classifiers. As a practical outcome of this framework, the proposed data complexity measures may facilitate the choice of a classifier for a given problem. The aim of this paper is to study the behaviour of a fuzzy rule based classification system and its relationship to data complexity. We use as a case of study the fuzzy hybrid genetic based machine learning method presented in [H. Ishibuchi, T. Yamamoto, T. Nakashima, Hybridization of fuzzy GBML approaches for pattern classification problems, IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics 35 (2) (2005) 359–365]. We examine several metrics of data complexity over a wide range of data sets built from real data and try to extract behaviour patterns from the results. We obtain rules which describe both good or bad behaviours of the fuzzy rule based classification system. These rules use values of data complexity metrics in their antecedents, so we try to predict the behaviour of the method from the data set complexity metrics prior to its application. Therefore, we can establish the domains of competence of this fuzzy rule based classification system. [Copyright &y& Elsevier]

Abstract: Genetic fuzzy systems (GFS) are based on the use of genetic algorithms for designing fuzzy systems, and for providing them with learning and adaptation capabilities. In this context, fuzzy sets represent linguistic granules of information, contained in the antecedents and consequents of the rules, whereas the data used in the genetic learning is assumed to be crisp. GFS seldom deal with fuzzy-valued data. In this paper we address this problem, and propose a set of techniques that can be incorporated to different GFS in order to learn a knowledge base (KB) from interval and fuzzy data for regression problems. Details will be given about the representation of non-standard data with fuzzy sets, about the needed changes in the reasoning method of the fuzzy rule-based system, and also about a new generalization of the mean squared error to vague data. In addition, we will show that the learning process requires a genetic algorithm that must be capable of optimizing a multicriteria fitness function, containing both crisp and interval-valued criteria. Lastly, we benchmark our procedures with some machine learning related datasets and a real-world problem of marketing, and the techniques proposed here are shown to improve the generalization properties of other KBs obtained from crisp training data. [Copyright &y& Elsevier]

Abstract: This paper presents a design method for fuzzy rule-based systems that performs data modeling consistently according to the symbolic relations expressed by the rules. The focus of the model is the interpretability of the rules and the model''s accuracy, such that it can be used as tool for data understanding. The number of rules is defined by the eigenstructure analysis of the similarity matrix, which is computed from data. The rule induction algorithm runs a clustering algorithm on the dataset and associates one rule to each cluster. Each rule is selected among all possible combinations of one-dimensional fuzzy sets, as the one nearest to a cluster''s center. The rules are weighted in order to improve the classifier performance and the weights are computed by a bounded quadratic optimization problem. The model complexity is minimized in a structure selection search, performed by a genetic algorithm that selects simultaneously the most representative subset of variables and also the number of fuzzy sets in the fuzzy partition of the selected variables. The resulting model is evaluated on a set of benchmark datasets for classification problems. The results show that the proposed approach produces accurate and yet compact fuzzy classifiers. The resulting model is also evaluated from an interpretability point of view, showing how the rule weights provide additional information to help data understanding and model exploitation. [Copyright &y& Elsevier]

Abstract: Different studies have proposed methods for mining fuzzy association rules from quantitative data, where the membership functions were assumed to be known in advance. However, it is not an easy task to know a priori the most appropriate fuzzy sets that cover the domains of quantitative attributes for mining fuzzy association rules. This paper thus presents a new fuzzy data-mining algorithm for extracting both fuzzy association rules and membership functions by means of a genetic learning of the membership functions and a basic method for mining fuzzy association rules. It is based on the 2-tuples linguistic representation model allowing us to adjust the context associated to the linguistic term membership functions. Experimental results show the effectiveness of the framework. [Copyright &y& Elsevier]

Abstract: The paper develops a hybrid intelligent approach to path planning for high mobility robots operating in rough environments. Path planning consists of characterization of the environment using a fuzzy logic framework, and a two-stage genetic algorithm planner. A global planner determines the path that optimizes a combination of terrain roughness and path curvature. A local planner uses sensory information, and in case of detection of previously unknown and unaccounted for obstacles, performs an on-line replanning to get around the newly discovered obstacle. Fuzzy adaptation of the genetic operators is achieved by adjusting the probabilities of the operators based on a diversity measure of the paths population and traversability measure of the paths. Path planning for an articulated rover in a rugged Mars terrain is presented to demonstrate the effectiveness of the proposed path planner. [Copyright &y& Elsevier]

Abstract: This paper proposes a framework which consists of a novel fuzzy inference algorithm to generate fuzzy decision trees from induced crisp decision trees. Fuzzy theoretical techniques are used to fuzzify crisp decision trees in order to soften sharp decision boundaries at decision nodes inherent in this type of trees. A framework for the investigation of various types of membership functions and fuzzy inference techniques is proposed. Once the decision tree has been fuzzified, all branches throughout the tree will fire, resulting in a membership grade being generated at each branch. Five different fuzzy inference mechanisms are used to investigate the degree of interaction between membership grades on each path in the decision tree, which ultimately leads to a final crisp classification. A genetic algorithm is used to optimize and automatically determine the set of fuzzy regions for all branches and simultaneously the degree in which the inference parameters will be applied. Comparisons between crisp trees and the fuzzified trees suggest that the later fuzzy tree is significantly more robust and produces a more balanced classification. In addition, the results obtained from five real-world data sets show that there is a significant improvement in the accuracy of the fuzzy trees when compared with crisp trees. [Copyright &y& Elsevier]

Abstract: In this paper, a new fuzzy logic based decision support system for parallel machine scheduling/rescheduling in the presence of uncertain disruptions is presented. It is applied to a real-life problem identified in a pottery company. The uncertain disruption considered is glaze shortage, defined by two parameters: number of glaze shortage occurrences and glaze shortage duration. Both parameters are specified imprecisely. They are modelled and combined using standard fuzzy sets and level 2 fuzzy sets, respectively. In order to deal with the glaze shortage disruption, a predictive–reactive scheduling approach is proposed and implemented. It is defined as a two-step procedure. In the first step, a predictive schedule is generated in such a way as to being capable of absorbing the impact of the glaze shortage disruption. In the second step, rescheduling is applied when the impact of the glaze shortage disruption is too high. Two sets of Sugeno type rules are proposed to support rescheduling decision making. One set of the fuzzy rules determines when to reschedule, whilst the other one determines which rescheduling method to use. Various tests are carried out that show that (1) the predictive schedules have good performance in the presence of uncertain disruptions and (2) the fuzzy inference generates appropriate rescheduling decisions. [Copyright &y& Elsevier]

Abstract: The paper gives an overview of applying fuzzy measures and relevant nonlinear integrals in data mining, discussed in five application areas: set function identification, nonlinear multiregression, nonlinear classification, networks, and fuzzy data analysis. In these areas, fuzzy measures allow us to describe interactions among feature attributes towards a certain target (objective attribute), while nonlinear integrals serve as aggregation tools to combine information from feature attributes. Values of fuzzy measures in these applications are unknown and are optimally determined via a soft computing technique based on given data. [Copyright &y& Elsevier]

Abstract: We propose an evolutionary method for the design of beta basis function neural networks (BBFNN) and of beta fuzzy systems (BFS). Classical training algorithms start with a predetermined network structure for neural networks and with a predetermined number of fuzzy rules for fuzzy systems. Generally speaking both the neural network and the fuzzy systems are either insufficient or overcomplicated. This paper describes a hierarchical genetic learning model of the BBFNN and the BFS. In order to examine the performance of the proposed algorithm, it is used for functional approximation problem for the case of BBFNN and for the identification of an induction machine fuzzy plant model for the case of BFS. The results obtained have been encouraging. [Copyright &y& Elsevier]

Abstract: Fuzzy cognitive maps (FCMs) are a very convenient, simple, and powerful tool for simulation and analysis of dynamic systems. They were originally developed in 1980 by Kosko, and since then successfully applied to numerous domains, such as engineering, medicine, control, and political affairs. Their popularity stems from simplicity and transparency of the underlying model. At the same time FCMs are hindered by necessity of involving domain experts to develop the model. Since human experts are subjective and can handle only relatively simple networks (maps), there is an urgent need to develop methods for automated generation of FCM models. This study proposes a novel learning method that is able to generate FCM models from input historical data, and without human intervention. The proposed method is based on genetic algorithms, and requires only a single state vector sequence as an input. The paper proposes and experimentally compares several different design alternatives of genetic optimization and thoroughly tests and discusses the best design. Extensive benchmarking tests, which involve 200 FCMs with varying size and density of connections, performed on both synthetic and real-life data quantifies the performance of the development method and emphasizes its suitability. [Copyright &y& Elsevier]

Abstract: To deal with linguistic attributes in databases, the integrand of the Choquet integral should be allowed to assume fuzzy numbers. This paper provides a detailed discussion on one fuzzification of Choquet integral, in which the integrand as well as the integration result is fuzzy numbers, based on the extension principle. It is a generalized Choquet integral for fuzzy-valued integrand, interval-valued integrand, as well as the crisp-valued integrand. Two numerical methods are provided to calculate the membership function of the integration value of this generalized Choquet integral with respect to the fuzzy measure and the signed fuzzy measure, respectively. The presented generalized Choquet integral with respect to signed fuzzy measure can act as an aggregation tool which is especially useful in many information fusing and data mining problems (such as regression and classification) where not only crisp data but also heterogeneous fuzzy data are involved. [Copyright &y& Elsevier]

Abstract: Logic rules and membership functions are two key components of a fuzzy logic controller (FLC). If only one component is learned, the other one is often set subjectively thus can reduce the applicability of FLC. If both components are learned simultaneously, a very long chromosome is often needed thus may deteriorate the learning performance. To avoid these shortcomings, this paper employs genetic algorithms to learn both logic rules and membership functions sequentially. We propose a bi-level iterative evolution algorithm in selecting the logic rules and tuning the membership functions for a genetic fuzzy logic controller (GFLC). The upper level is to solve the composition of logic rules using the membership functions tuned by the lower level. The lower level is to determine the shape of membership functions using the logic rules learned from the upper level. We also propose a new encoding method for tuning the membership functions to overcome the problem of too many constraints. Our proposed GFLC model is compared with other similar GFLC, artificial neural network and fuzzy neural network models, which are trained and validated by the same examples with theoretical and field-observed car-following behaviors. The results reveal that our proposed GFLC has outperformed. [Copyright &y& Elsevier]

Abstract: It is not an easy task to know a priori the most appropriate fuzzy sets that cover the domains of quantitative attributes for fuzzy association rules mining, simply because characteristics of quantitative data are in general unknown. Besides, it is unrealistic that the most appropriate fuzzy sets can always be provided by domain experts. Motivated by this, in this paper we propose an automated method for mining fuzzy association rules. For this purpose, we first present a genetic algorithm (GA) based clustering method that adjusts centroids of the clusters, which are to be handled later as midpoints of triangular membership functions. Next, we give a different method for generating the membership functions by using Clustering Using Representatives (CURE) clustering algorithm, which is known as one of the most efficient clustering algorithms described in the literature. Finally, we compared the proposed GA-based approach with other approaches from the literature. Experiments conducted on 100K transactions from the US census in the year 2000 show that the proposed method exhibits a good performance in terms of execution time and interesting fuzzy association rules. [Copyright &y& Elsevier]

Abstract: Time course measurements are becoming a common type of experiment in the use of microarrays. The temporal order of the data and the varying length of sampling intervals are important and should be considered in clustering time-series. However, the shortness of gene expression time-series data limits the use of conventional statistical models and techniques for time-series analysis. To address this problem, this paper proposes the fuzzy short time-series (FSTS) clustering algorithm, which clusters profiles based on the similarity of their relative change of expression level and the corresponding temporal information. One of the major advantages of fuzzy clustering is that genes can belong to more than one group, revealing distinctive features of each gene''s function and regulation. Several examples are provided to illustrate the performance of the proposed algorithm. In addition, we present the validation of the algorithm by clustering the genes which define the model profiles in Chu et al. (Science, 282 (1998) 699). The fuzzy c-means, k-means, average linkage hierarchical algorithm and random clustering are compared to the proposed FSTS algorithm. The performance is evaluated with a well-established cluster validity measure proving that the FSTS algorithm has a better performance than the compared algorithms in clustering similar rates of change of expression in successive unevenly distributed time points. Moreover, the FSTS algorithm was able to cluster in a biologically meaningful way the genes defining the model profiles. [Copyright &y& Elsevier]

Abstract: Managing a supply chain (SC) is very difficult, since various sources of uncertainty and complex interrelationships between various entities exist in the SC. Moreover, the reducing product life cycle and the heightened expectations of customers have also made the SC even harder to manage, especially for innovative products. Although the innovative products can enable a company to achieve higher profit margins, they make demands for them unpredictable, because no historical data is available. This paper develops a fuzzy decision methodology that provides an alternative framework to handle SC uncertainties and to determine SC inventory strategies, while there is lack of certainty in data or even lack of available historical data. Fuzzy set theory is used to model SC uncertainty. A fuzzy SC model based on possibility theory is developed to evaluate SC performances. Based on the proposed fuzzy SC model, a genetic algorithm approach is developed to determine the order-up-to levels of stock-keeping units in the SC to minimize the SC inventory cost subject to the restriction of fulfilling the target fill rate of the finished product. The proposed model allows decision makers to express their risk attitudes and to analyze the trade-off between customer service level and inventory investment in the SC and better SC inventory strategies can be made. A simulation approach is used to validate the concept developed. [Copyright &y& Elsevier]

Abstract: In knowledge discovery, Genetic Algorithms have been used for classification, model selection, and other optimization tasks. However, behavior and performance of genetic algorithms are directly affected by the values of their input parameters, while poor parameter settings usually lead to several problems such as the premature convergence. Adaptive techniques have been suggested for adjusting the parameters in the process of running the genetic algorithm. None of these techniques have yet shown a significant overall improvement, since most of them remain domain-specific. In this paper, we attempt to improve the performance of genetic algorithms by providing a new, fuzzy-based extension of the LifeTime feature. We use a Fuzzy Logic Controller (FLC) to adapt the crossover probability as a function of the chromosomes’ age. The general principle is that for both young and old individuals the crossover probability is naturally low, while there is a certain age interval, where this probability is high. The concepts of “young”, “old”, and “middle-aged” are modeled as linguistic variables. This approach should enhance the exploration and exploitation capabilities of the algorithm, while reducing its rate of premature convergence. We have evaluated the proposed Lifetime methodology on several benchmark problems by comparing its performance to the basic genetic algorithm and to several adaptive genetic algorithms. The results of our initial experiments demonstrate a clear advantage of the fuzzy-based Lifetime extension over the “crisp” techniques. [Copyright &y& Elsevier]

We have developed, in this paper, a genetic-fuzzy system, in which a genetic algorithm (GA) is used to improve the performance of a fuzzy logic controller (FLC). The performance of an FLC depends on its knowledge base (KB), which consists of both the data base (membership function distributions of the variables) as well as rule base. In the developed genetic-fuzzy system, the KB of the FLC is optimized, off-line, using a GA. Three approaches are developed, in the present work. In the first approach, the membership function distributions of the variables are assumed to be triangular, whereas a second-order polynomial function and a third-order polynomial function are used in the second and third approaches, respectively. The results of these approaches are compared for making prediction of surface finish and power requirement in grinding, a machining process used to generate smooth surface on the job. For some of the test cases, comparisons are also made of the results predicted by the genetic-fuzzy system with those obtained through the real experiments. [Copyright &y& Elsevier]

This paper exploits the ability of Symbiotic Evolution (SE), as a generic methodology, to elicit a fuzzy rule-base of the Mamdani-type. Almost all fuzzy rule-base generation algorithms produce rule-bases with redundant and overlapped membership functions that limit their interpretability elegance in their application. We address this problem by applying an algorithm to merge any similar membership functions. It is shown that our proposed algorithm leads generally to a more transparent and more interpretable rule-base with a minimum number of membership functions and a reduced number of rules. In addition, a new post-processing approach is proposed for recovering any probable performance lost after membership functions merging. The proposed methodology has been applied successfully for the design of an active control suspension system using a non-linear Bond Graphs (BG) based half-car model with parameters that relate to a Ford Fiesta MK2. [Copyright &y& Elsevier]

This paper addresses the structure and an associated learning algorithm of a feedforward multilayered connectionist network for realizing the basic elements and functions of a traditional fuzzy logic controller. The genetic algorithm-based neural fuzzy system (GA-NFS) is based on Takagi–Sugeno–Kang (TSK) type model possessing a neural network''s learning ability. A hybrid learning algorithm is proposed for parameters learning. The proposed algorithm combines the genetic algorithm (GA) and the least-squares estimate (LSE) method to construct the GA-NFS. The genetic algorithm is used to tune membership functions at the precondition part of fuzzy rules while the LSE method is used to tune parameters at the consequent part of fuzzy rules. The performance of the GA-NFS is compared to that of the traditional PID controller and fuzzy logic controller on the water bath temperature control system. [Copyright &y& Elsevier]

This paper proposes a systematic approach for designing a multistage fuzzy logic controller (MFLC) for large scale nonlinear systems. In designing such a controller, the major tasks are to derive fuzzy rule bases, determine membership functions of input/output variables, and design input/output scaling factors. In this work, the fuzzy rule bases are generated by rule-generated functions which are based on the negative gradient of a system performance index. The membership functions of isosceles triangle of input/output variables are fixed in the same cardinality, and only the input/output scaling factors are optimized from a genetic algorithm based on a fitness function. As a result, the search space of the parameters is narrowed down to a small space so that the MFLC can be quickly constructed and the fuzzy rules and scaling factors can easily be determined. The performance of the proposed approach is examined by computer simulations on an inverted pendulum system. The performance of single stage structure, binary tree structure and skew-binary tree structure are compared. The binary tree structure has better performance and use fewer fuzzy rules in the illustrative example. [Copyright &y& Elsevier]

An Intelligent Fuzzy Agent for Meeting Scheduling Decision Support System is proposed in this paper. The proposed Intelligent Fuzzy Agent including Meeting Negotiation Agent, Fuzzy Inference Agent and Genetic Learning Agent can search and decide the suitable meeting time for the specified meeting in an organization. When a meeting host requests a meeting, the Meeting Negotiation Agent immediately sends the invitees’ names to Meeting Scheduling Decision Support System for retrieving their schedules from Group Calendar Data Base, then Meeting Scheduling Decision Support System will compute the possible meeting time and respond the results to Meeting Negotiation Agent. Moreover, the Fuzzy Inference Agent infers the adequate meeting time based on the information provided by Meeting Negotiation Agent and Personalized Knowledge Base, and sends the computing result back to Meeting Scheduling Decision Support System. The meeting host will decide the final meeting time based on Meeting Scheduling Decision Support System and announce the meeting information by various devices including PDA, WAP, FAX, or E-mail. Furthermore, the invitees’ decisions for attending the meeting or not will be stored into Meeting Information Knowledge Base, then the Genetic Learning Agent will adjust the Personalized Knowledge Base for the next meeting. By the experimental results, the proposed Intelligent Fuzzy Agent can work efficiently and effectively for Meeting Scheduling Decision Support System. [Copyright &y& Elsevier]

In this paper, a dynamic fuzzy network and its design based on genetic algorithm with variable-length chromosomes is proposed. First, the dynamic fuzzy network constituted from a series of dynamic fuzzy if–then rules is proposed. One characteristic of this network is its ability to deal with temporal problems. Then, the proposed genetic algorithm with variable-length chromosomes is adopted into the design process as a means of allowing the application of the network in situations where the actual desired output is unavailable. In the proposed genetic algorithm, the length of each chromosome varies with the number of rules coded in it. Using this algorithm, no pre-assignment of the number of rules in the dynamic fuzzy network is required, since it can always help to find the most suitable number of rules. All free parameters in the network, including the spatial input partition, consequent parameters and feedback connection weights, are tuned concurrently. To further promote the design performance, genetic algorithm with variable-length chromosomes and relative-based mutated reproduction operation is proposed. In this algorithm, the elite individuals are directly reproduced to the next generation only when their averaged similarity value is smaller than a similarity threshold; otherwise, the elites are mutated to the next generation. To show the efficiency of this dynamic fuzzy network designed by genetic algorithm with variable-length chromosomes and relative-based mutated reproduction operation, two temporal problems are simulated. The simulated results and comparisons with recurrent neural and fuzzy networks verify the efficacy and efficiency of the proposed approach. [Copyright &y& Elsevier]

In this paper a coevolutionary genetic approach is devised to support hierarchical, collaborative relations between individuals representing different parameters of Takagi–Sugeno fuzzy models. The coevolutionary approach assumes species to mean partial solutions of fuzzy modeling problems organized into four hierarchical levels. Individuals at each hierarchical level encode membership functions, individual rules, rule-bases and fuzzy systems, respectively. A shared fitness evaluation scheme is used to measure the performance of each individual. Constraints are observed and particular targets are defined throughout the hierarchical levels, with the purpose of promoting the occurrence of valid individuals and inducing rule compactness, rule base consistency, and partition set visibility. The performance of the approach is evaluated via an example of function approximation with noisy data, and a nonlinearly separable classification problem. [Copyright &y& Elsevier]

This paper introduces a new fuzzy control technique, which belongs to the popular family of control algorithms, called Model Predictive Controllers. The method is based on a dynamic fuzzy model of the process to be controlled, which is used for predicting the future behavior of the output variables. A non-linear optimization problem is then formulated, which minimizes the difference between the model predictions and the desired trajectory over the prediction horizon and the control energy over a shorter control horizon. The problem is solved on line using a specially designed genetic algorithm, which has a number of advantages over conventional non-linear optimization techniques. The method can be used with any type of fuzzy model and is particularly useful when a direct fuzzy controller cannot be designed due to the complexity of the process and the difficulty in developing fuzzy control rules. The method is illustrated via the application to a non-linear single-input single-output reactor, where a Takagi–Sugeno model serves as a predictor of the process future behavior. [Copyright &y& Elsevier]

The design of fuzzy logic systems (FLS) generally involves determining the structure of the rules and the parameters of the membership functions. In this paper we present a methodology based on evolutionary computation for simultaneously designing membership functions and appropriate rule sets. This property makes it different from many techniques that address these goals separately with the result of suboptimal solutions because the design elements are mutually dependent. We also apply a new approach in which the evolutionary algorithm is applied directly to a FLS data structure instead of a binary or other codification. Results on function approximation show improvements over other incremental and analytical methods. [Copyright &y& Elsevier]

The fuzzy basis function network which was proposed in Wang and Mendel (IEEE Trans. Neural Networks 3(5) (1992b) 807) provides a way of representing fuzzy inference systems in a simple structure similar to those of radial basis function networks. In this paper, two new algorithms based on the least-squares method and genetic algorithm are proposed for autonomous learning and construction of fuzzy basis function networks when training data are available. The proposed algorithms add a significant fuzzy basis function node at each iteration during training, based on error reduction measures. The first, a least-squares algorithm, provides a way of sequentially constructing meaningful fuzzy systems which are not possible to achieve with the orthogonal least-squares algorithm, while the second, an adaptive least-squares algorithm based on the combined least-squares and genetic algorithm, realizes hybrid structure-parameter learning without human intervention. Simulation studies are performed with numerical examples for comparison of its performance against the orthogonal least-squares algorithm, backpropagation algorithm, and conventional genetic algorithm. The adaptive least-squares algorithm is also applied to a real world problem to construct a fuzzy basis function network model for surface roughness in a grinding process using experimental data. [Copyright &y& Elsevier]

A modeling method is suggested in this paper that permits building fuzzy models for short-term load forecasting (STLF). The model building process is divided in three parts: (a) the structure identification based on a fuzzy C-regression method, (b) selection of the proper model inputs which is achieved using a genetic algorithm based selection mechanism, and (c) fine tuning by means of a hybrid genetic/least squares algorithm. To obtain simple and efficient models we employ two descriptions for the load curves (LC''s), namely, the feature description for the premise part and the cubic B-spline curve for the consequent part of the rules. The simulation results demonstrate that the suggested model exhibits very good forecast capabilities. The suggested model is favorably compared with the ANN model in terms of prediction accuracy, robustness and model complexity. [Copyright &y& Elsevier]

Rule number reduction is important for fuzzy control of complex processes with high dimensionality. It is stated in the paper that this issue can be treated effectively by means of learning premises with general structure. Since conditions of rules are generalised by a genetic algorithm (GA) rather than enumerated according to every AND-connection of input fuzzy sets, a parsimonious knowledge base with a reduced number of rules can be expected. On the other hand, to give a numerical evaluation of possible conflicts among rules, a consistency index of the rule set is established. This index is integrated into the fitness function of the GA to search for a set of optimal rule premises yielding not only good control performance but also little or no inconsistency in the fuzzy knowledge base. The advantage of the proposed method is demonstrated by the case study of development of a compact fuzzy controller to balance an inverted pendulum in the laboratory. [Copyright &y& Elsevier]

The design and implementation of an on-line fuzzy identification method using genetic algorithms (GAs) is reported in this paper. In the proposed algorithm, the rule-table of a fuzzy system is first divided into several independent and much smaller fuzzy systems, which in turn are encoded into separate bit strings for genetic operations. A novel GA updating architecture is then proposed to search the optimal rule-base of these fuzzy systems at each sample interval. The performance of this identification algorithm is evaluated by simulation of a non-linear system. Moreover, an experiment on simple behavior learning of a mobile robot is also reported. The results indicate an improvement in design cycle and convergence to the optimal rule-base within a relatively short period of time. [Copyright &y& Elsevier]

This paper proposes a new genetic-based modeling method for building simple and well-defined TSK models with scatter-type input partitions. Our approach manages all attributes characterizing the structure of a TSK model, simultaneously. Particularly, it determines the number of rules, the input partition, the participating inputs in each rule and the consequent parameters. The model building process is divided into two phases. In phase one, the structure learning task is formulated as a multi-objective optimization problem which is resolved using a novel genetic-based structure learning (GBSL) scheme. Apart from the mean square error (MSE) and the number of rules, three additional criteria are introduced in the fitness function for measuring the quality of the partitions. Optimization of these measures leads to models with representative rules, small overlapping and efficient data cover. In order to obtain models with accurate data fitting and good local performance, the consequent parameters are determined using a local MSE function while the overall model is evaluated on the basis of a global MSE function. The search capabilities of the suggested structure learning scheme are significantly enhanced by including a highly effective local search operator implemented by a micro-genetic algorithm and four problem-specific operators. Finally, a genetic-based parameter learning (GBPL) scheme is suggested in phase two, which performs fine-tuning of the initial models obtained after structure learning. The performance of the proposed modeling approach is evaluated using a static example and a well-known dynamic benchmark problem. Simulation results demonstrate that our models outperform those suggested by other methods with regard to simplicity, model structure, and accuracy. [Copyright &y& Elsevier]

Gyro-mirror line-of-sight stabilization platform is a nonlinear, multivariable and highly coupled system. It forms the basis of a wide range of practical instruments used for the purposes of sighting and targeting in both surface and airborne vehicles, which is capable of maintaining the sightline of a mirror when it is subjected to external disturbances. However, a spinning gyro has a property known as precession such that when a torque is applied to one axis, it will contrary to the intuition of mechanics, and results the rotation in the direction of another axis. This behavior poses a problem in controlling the line-of-sight since movement about one axis will cause a coupled movement in the other. In this paper, an efficient full-matrix fuzzy logic controller is designed and implemented for a practical nonlinear gyro-mirror line-of-sight stabilization platform. Both simulation and real-time experimental results demonstrate the effectiveness of the designed full-matrix fuzzy gyroscope control system, which offers an excellent closed-loop response for the transient and tracking performances, with significant reduction in the coupling effect against cross-axis interactions. [Copyright &y& Elsevier]

This paper formulates two-level nonconvex programming problems with fuzzy parameters by considering the experts’ vague or fuzzy understanding of the nature of the parameters in the problem-formulation process, and presents an interactive fuzzy programming method through genetic algorithms. Using the level sets of fuzzy parameters characterized as fuzzy numbers, the corresponding nonfuzzy two-level nonconvex programming problem is introduced. The fuzzy goals of the decision makers for the nonconvex objective functions at both levels are quantified by eliciting the corresponding membership functions. In our interactive method, having specified the level sets of the fuzzy parameters, by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance between both levels, an overall satisfactory solution is derived efficiently through genetic algorithms which are effective for nonconvex programming problems. An illustrative numerical example for two-level nonconvex programming problems with fuzzy parameters is provided to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]