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Objective: Convolutional neural network (CNN), a classical structure in deep learning, has been commonly deployed in the motor imagery brain-computer interface (MIBCI). Many methods have been proposed to evaluate the vulnerability of such CNN models, primarily by attacking them using direct temporal perturbations. In this work, we propose a novel attacking approach based on perturbations in the frequency domain instead., Methods: For a given natural MI trial in the frequency domain, the proposed approach, called frequency domain channel-wise attack (FDCA), generates perturbations at each channel one after another to fool the CNN classifiers. The advances of this strategy are two-fold. First, instead of focusing on the temporal domain, perturbations are generated in the frequency domain where discriminative patterns can be extracted for motor imagery (MI) classification tasks. Second, the perturbing optimization is performed based on differential evolution algorithm in a black-box scenario where detailed model knowledge is not required., Results: Experimental results demonstrate the effectiveness of the proposed FDCA which achieves a significantly higher success rate than the baselines and existing methods in attacking three major CNN classifiers on four public MI benchmarks., Conclusion: Perturbations generated in the frequency domain yield highly competitive results in attacking MIBCI deployed by CNN models even in a black-box setting, where the model information is well-protected., Significance: To our best knowledge, existing MIBCI attack approaches are all gradient-based methods and require details about the victim model, e.g., the parameters and objective function. We provide a more flexible strategy that does not require model details but still produces an effective attack outcome.

A fuzzy cognitive map (FCM) is a graph-based knowledge representation model wherein the connections of the nodes (edges) represent casual relationships between the knowledge items associated with the nodes. This model has been applied to solve various modeling tasks including forecasting time series. In the original FCM-based forecasting model, causal relationships among concepts of the FCM remain unchanged. However, causal relationships may change in time. Therefore, we propose a new learning method for training an FCM resulting in an adaptive FCM which consists of several sub-FCMs. It can select different sub-FCMs at different moments. In an active processing scenario, in which we deal with a large-scale time series with new data being continuously generated, a forecasting model built on the old data should be updated when the new data arrive. Furthermore, retraining an FCM from scratch entails increasing computing overhead that will become a serious obstacle in many practical scenarios. To overcome the above-mentioned shortcomings, this study offers an original design setting in which the FCM is updated by knowledge-guidance learning mechanism for the first time. Compared with the existing classical forecasting models, the proposed model shows higher accuracy and efficiency. Its increased performance is demonstrated through a series of reported experimental studies.

Current fully supervised facial landmark detection methods have progressed rapidly and achieved remarkable performance. However, they still suffer when coping with faces under large poses and heavy occlusions for inaccurate facial shape constraints and insufficient labeled training samples. In this article, we propose a semisupervised framework, that is, a self-calibrated pose attention network (SCPAN) to achieve more robust and precise facial landmark detection in challenging scenarios. To be specific, a boundary-aware landmark intensity (BALI) field is proposed to model more effective facial shape constraints by fusing boundary and landmark intensity field information. Moreover, a self-calibrated pose attention (SCPA) model is designed to provide a self-learned objective function that enforces intermediate supervision without label information by introducing a self-calibrated mechanism and a pose attention mask. We show that by integrating the BALI fields and SCPA model into a novel SCPAN, more facial prior knowledge can be learned and the detection accuracy and robustness of our method for faces with large poses and heavy occlusions have been improved. The experimental results obtained for challenging benchmark datasets demonstrate that our approach outperforms state-of-the-art methods in the literature.

Rule-based fuzzy models play a dominant role in fuzzy modeling and come with extensive applications in the system modeling area. Due to the presence of system modeling error, it is impossible to construct a model that fits exactly the experimental evidence and, at the same time, exhibits high generalization capabilities. To alleviate these problems, in this study, we elaborate on a realization of granular outputs for rule-based fuzzy models with the aim of effectively quantifying the associated modeling errors. Through analyzing the characteristics of modeling errors, an error model is constructed to characterize deviations among the estimated outputs and the expected ones. The resulting granular model comes into play as an aggregation of the regression model and the error model. Information granularity plays a central role in the construction of granular outputs (intervals). The quality of the produced interval estimates is quantified in terms of the coverage and specificity criteria. The optimal allocation of information granularity is determined through a combined index involving these two criteria pertinent to the evaluation of interval outputs. A series of experimental studies is provided to demonstrate the effectiveness of the proposed approach and show its superiority over the traditional statistical-based method.

In the analytic hierarchy process (AHP), the reciprocal matrix is generated based on the pairwise comparisons completed among all the alternatives or attributes under consideration. To ensure reliability and validity of the decision solution, a certain modification of entries of the matrix is usually needed to improve the consistency of the reciprocal matrix. This study aims to present a consistency improvement method by admitting some level of information granularity in the evaluation process. This gives rise to a granular rather than numeric matrix of pairwise comparisons. First, with a given average level of information granularity, we present an optimal granularity model that is characterized by maximal consistency. One can maximize the consistency degree by invoking a process of allocation of information granularity across the corresponding modifications of the reciprocal matrix. Based on the optimal granularity model, an interactive consistency improvement process is presented with the involvement of the decision maker. Then, an adaptive differential evolution algorithm is applied to optimize entries of the modified reciprocal matrix. Detailed experiments along with a thorough comparative analysis are completed to demonstrate the effectiveness of the proposed method.

Information granulation and degranulation play a fundamental role in granular computing (GrC). Given a collection of information granules (referred to as reference information granules), the essence of the granulation process (encoding) is to represent each data (either numeric or granular) in terms of these reference information granules. The degranulation process (decoding) that realizes the reconstruction of original data is associated with a certain level of reconstruction error. An important issue is how to reduce the reconstruction error such that the data could be reconstructed more accurately. In this study, the granulation process is realized by involving fuzzy clustering. A novel neural network is leveraged in the consecutive degranulation process, which could help significantly reduce the reconstruction error. We show that the proposed degranulation architecture exhibits improved capabilities in reconstructing original data in comparison with other methods. A series of experiments with the use of synthetic data and publicly available datasets coming from the machine-learning repository demonstrates the superiority of the proposed method over some existing alternatives.

In this article, we present a semantic semisupervised learning (Semantic SSL) approach targeted at unifying two machine-learning paradigms in a mutually beneficial way, where the classical support vector machine (SVM) learns to reveal primitive logic facts from data, while axiomatic fuzzy set (AFS) theory is utilized to exploit semantic knowledge and correct the wrongly perceived facts for improving the machine-learning model. This novel semisupervised method can easily produce interpretable semantic descriptions to outline different categories by forming a fuzzy set with semantic explanations realized on the basis of the AFS theory. Besides, it is known that disagreement-based semisupervised learning (SSL) can be viewed as an excellent schema so that a co-training approach with SVM and the AFS theory can be utilized to improve the resulting learning performance. Furthermore, an evaluation index is used to prune descriptions to deliver promising performance. Compared with other semisupervised approaches, the proposed approach can build a structure to reflect data-distributed information with unlabeled data and labeled data, so that the hidden information embedded in both labeled and unlabeled data can be sufficiently utilized and can potentially be applied to achieve good descriptions of each category. Experimental results demonstrate that this approach can offer a concise, comprehensible, and precise SSL frame, which strikes a balance between the interpretability and the accuracy.

In this article, we are concerned with the formation of type-2 information granules in a two-stage approach. We present a comprehensive algorithmic framework which gives rise to information granules of a higher type (type-2, to be specific) such that the key structure of the local granular data, their topologies, and their diversities become fully reflected and quantified. In contrast to traditional collaborative clustering where local structures (information granules) are obtained by running algorithms on the local datasets and communicating findings across sites, we propose a way of characterizing granular data (formed) by forming a suite of higher type information granules to reveal an overall structure of a collection of locally available datasets. Information granules built at the lower level on a basis of local sources of data are weighted by the number of data they represent while the information granules formed at the higher level of hierarchy are more abstract and general, thus facilitating a formation of a hierarchical description of data realized at different levels of detail. The construction of information granules is completed by resorting to fuzzy clustering algorithms (more specifically, the well-known Fuzzy C-Means). In the formation of information granules, we follow the fundamental principle of granular computing, viz., the principle of justifiable granularity. Experimental studies concerning selected publicly available machine-learning datasets are reported.

The two issues on dynamically generated hierarchical neural networks such as the sort of basic neurons and how to compose a layer are considered in this article. On the first issue, a variant version of the least-square support vector regression (SVR) is chosen as a basic neuron. Support vector machine (SVM) is a representative classifier which usually shows good classification performance. Along with the SVMs, SVR was introduced to deal with the regression problem. Especially, least-square SVR has the advantages of high learning speed due to the substitution of the inequality constraints by the equality constraint in the formulation of the optimization problem. Based on the least-square SVR, the multiple least-square (MLS) SVR, which is a type of a linear combination of least-square SVRs with fuzzy clustering, is proposed to improve the modeling performance. In addition, a hierarchical neural network, where the MLS SVR is utilized as the generic node instead of the conventional polynomial, is developed. The key issues of hierarchical neural networks, which are generated dynamically layer by layer, are discussed on how to retain the diversity of the nodes located at the same layer according to the increase of the layer. In order to maintain the diversity of the nodes, various selection methods such as truncation selection and roulette wheel selection (RWS) to choose the nodes among candidate nodes are proposed. In addition, in order to reduce the computational overhead to determine all candidates which exhibit all compositions of the input variables, a new implementation method is proposed. From the viewpoint of the diversity of the selected nodes and the computational aspects, it is shown that the proposed method is preferred over the conventional design methodology.

A granular structure of intuitionistic fuzzy (IF) information presents simultaneously the similarity and diversity of samples. However, this structural representation has rarely displayed its technical capability in data mining and information processing due to the lack of suitable constructive methods and semantic interpretation for IF information with regard to real data. To pursue better performance of the IF-based technique in real-world data mining, in this article, we examine information granularity, information entropy of IF granular structures, and their applications to data reduction of IF information systems. First, several types of partial-order relations at different hierarchical levels are defined to reveal the granularity of IF granular structures. Second, the granularity invariance between different IF granular structures is characterized by using relational mappings. Third, Shannon's entropies are generalized to IF entropies and their relationships with the partial-order relations are addressed. Based on the theoretical analysis above, the significance of intuitionistic attributes using the information measures is then introduced and the information-preserving algorithm for data reduction of IF information systems is constructed. Finally, by inducing substantial IF relations from public datasets that take both the similarity/diversity between the samples from the same/different classes into account, a collection of numerical experiments is conducted to confirm the performance of the proposed technique.

In this article, we propose a two-stage time-series clustering approach to cluster time series with different shapes. The first step is to represent the time series by a suite of information granules following the principle of justifiable granularity to perform dimensionality reduction, while the second step is to realize the fuzzy clustering of the time series in the transformed representation space (viz., the space of information granules). In the dimensionality reduction process, the numerical data are granulated using a collection of information granules forming a new sequence that can well describe the original time series. Then, when clustering the time series, dynamic time warping (DTW) is employed to measure the similarity between time series and DTW barycenter averaging (DBA) is generalized to weighted DBA to be involved in the fuzzy C -means (FCMs) algorithm. Finally, the experiments are conducted on the datasets coming from UCR time-series database and Chinese stocks to demonstrate the effectiveness and advantages of the proposed fuzzy clustering approach.

In order to deal with the sequential decision problems with large or continuous state spaces, feature representation and function approximation have been a major research topic in reinforcement learning (RL). In this paper, a clustering-based graph Laplacian framework is presented for feature representation and value function approximation (VFA) in RL. By making use of clustering-based techniques, that is, K-means clustering or fuzzy C-means clustering, a graph Laplacian is constructed by subsampling in Markov decision processes (MDPs) with continuous state spaces. The basis functions for VFA can be automatically generated from spectral analysis of the graph Laplacian. The clustering-based graph Laplacian is integrated with a class of approximation policy iteration algorithms called representation policy iteration (RPI) for RL in MDPs with continuous state spaces. Simulation and experimental results show that, compared with previous RPI methods, the proposed approach needs fewer sample points to compute an efficient set of basis functions and the learning control performance can be improved for a variety of parameter settings.

Although Particle Swarm Optimization (PSO) has demonstrated competitive performance in solving global optimization problems, it exhibits some limitations when dealing with optimization problems with high dimensionality and complex landscape. In this paper, we integrate some problem-oriented knowledge into the design of a certain PSO variant. The resulting novel PSO algorithm with an inner variable learning strategy (PSO-IVL) is particularly efficient for optimizing functions with symmetric variables. Symmetric variables of the optimized function have to satisfy a certain quantitative relation. Based on this knowledge, the inner variable learning (IVL) strategy helps the particle to inspect the relation among its inner variables, determine the exemplar variable for all other variables, and then make each variable learn from the exemplar variable in terms of their quantitative relations. In addition, we design a new trap detection and jumping out strategy to help particles escape from local optima. The trap detection operation is employed at the level of individual particles whereas the trap jumping out strategy is adaptive in its nature. Experimental simulations completed for some representative optimization functions demonstrate the excellent performance of PSO-IVL. The effectiveness of the PSO-IVL stresses a usefulness of augmenting evolutionary algorithms by problem-oriented domain knowledge.

The study introduces a concept of mappings realized in presence of information granules and offers a design framework supporting the formation of such mappings. Information granules are conceptually meaningful entities formed on a basis of a large number of experimental input–output numeric data available for the construction of the model. We develop a conceptually and algorithmically sound way of forming information granules. Considering the directional nature of the mapping to be formed, this directionality aspect needs to be taken into account when developing information granules. The property of directionality implies that while the information granules in the input space could be constructed with a great deal of flexibility, the information granules formed in the output space have to inherently relate to those built in the input space. The input space is granulated by running a clustering algorithm; for illustrative purposes, the focus here is on fuzzy clustering realized with the aid of the fuzzy C-means algorithm. The information granules in the output space are constructed with the aid of the principle of justifiable granularity (being one of the underlying fundamental conceptual pursuits of Granular Computing). The construct exhibits two important features. First, the constructed information granules are formed in the presence of information granules already constructed in the input space (and this realization is reflective of the direction of the mapping from the input to the output space). Second, the principle of justifiable granularity does not confine the realization of information granules to a single formalism such as fuzzy sets but helps form the granules expressed any required formalism of information granulation. The quality of the granular mapping (viz. the mapping realized for the information granules formed in the input and output spaces) is expressed in terms of the coverage criterion (articulating how well the experimental data are “covered” by information granules produced by the granular mapping for any input experimental data). Some parametric studies are reported by quantifying the performance of the granular mapping (expressed in terms of the coverage and specificity criteria) versus the values of a certain parameters utilized in the construction of output information granules through the principle of justifiable granularity. The plots of coverage–specificity dependency help determine a knee point and reach a sound compromise between these two conflicting requirements imposed on the quality of the granular mapping. Furthermore, quantified is the quality of the mapping with regard to the number of information granules (implying a certain granularity of the mapping). A series of experiments is reported as well.

Granular computing, as a new and rapidly growing paradigm of information processing, has attracted many researchers and practitioners. Granular computing is an umbrella term to cover any theories, methodologies, techniques, and tools that make use of information granules in complex problem solving. The aim of this paper is to review foundations and schools of research and to elaborate on current developments in granular computing research. We first review some basic notions of granular computing. Classification and descriptions of various schools of research in granular computing are given. We also present and identify some research directions in granular computing.

Discovering and utilizing problem domain knowledge is a promising direction towards improving the efficiency of evolutionary algorithms (EAs) when solving optimization problems. We propose a knowledge-based variable reduction strategy (VRS) that can be integrated into EAs to solve unconstrained and first-order derivative optimization functions more efficiently. VRS originates from the knowledge that, in an unconstrained and first-order derivative optimization function, the optimal solution locates in a local extreme point at which the partial derivative over each variable equals zero. Through this collective of partial derivative equations, some quantitative relations among different variables can be obtained. These variable relations have to be satisfied in the optimal solution. With the use of such relations, VRS could reduce the number of variables and shrink the solution space when using EAs to deal with the optimization function, thus improving the optimizing speed and quality. When we apply VRS to optimization problems, we just need to modify the calculation approach of the objective function. Therefore, practically, it can be integrated with any EA. In this study, VRS is combined with particle swarm optimization variants and tested on several benchmark optimization functions and a real-world optimization problem. Computational results and comparative study demonstrate the effectiveness of VRS.

In this paper, we introduce a concept of a granular neural network and develop its comprehensive design process. The proposed granular network is formed on the basis of a given (numeric) neural network whose structure is augmented by the formation of granular connections (being realized as intervals) spanned over the numeric ones. Owing to its simplicity of the underlying processing, the interval connections become an appealing alternative of information granules to clarify the main idea. We introduce a concept of information granularity and its quantification (viewed as a level of information granularity). Being treated as an essential design asset, the assumed level of information granularity is distributed (allocated) among the connections of the network in several different ways so that certain performance index becomes maximized. Due to the high dimensionality nature of some protocols of allocation of information granularity and the nature of the allocation process itself, single-objective versions of particle swarm optimization is considered a suitable optimization vehicle. As we are concerned with the granular output of the network, which has to be evaluated with regard to the numeric target of data, two criteria are considered; namely, coverage of numeric data and specificity of information granules (intervals). A series of numeric studies completed for synthetic data and data coming from the machine learning and StatLib repositories provide a useful insight into the effectiveness of the proposed algorithm.

Clustering forms one of the most visible conceptual and algorithmic framework of developing information granules. In spite of the algorithm being used, the representation of information granules-clusters is predominantly numeric (coming in the form of prototypes, partition matrices, dendrograms, etc.). In this paper, we consider a concept of granular prototypes that generalizes the numeric representation of the clusters and, in this way, helps capture more details about the data structure. By invoking the granulation-degranulation scheme, we design granular prototypes being reflective of the structure of data to a higher extent than the representation that is provided by their numeric counterparts (prototypes). The design is formulated as an optimization problem, which is guided by the coverage criterion, meaning that we maximize the number of data for which their granular realization includes the original data. The granularity of the prototypes themselves is treated as an important design asset; hence, its allocation to the individual prototypes is optimized so that the coverage criterion becomes maximized. With this regard, several schemes of optimal allocation of information granularity are investigated, where interval-valued prototypes are formed around the already produced numeric representatives. Experimental studies are provided in which the design of granular prototypes of interval format is discussed and characterized.

Fuzzy cognitive maps (FCMs) are convenient and widely used architectures for modeling dynamic systems, which are characterized by a great deal of flexibility and adaptability. Several recent works in this area concern strategies for the development of FCMs. Although a few fully automated algorithms to learn these models from data have been introduced, the resulting FCMs are structurally considerably different than those developed by human experts. In particular, maps that were learned from data are much denser (with the density over 90% versus about 40% density of maps developed by humans). The sparseness of the maps is associated with their interpretability: the smaller the number of connections is, the higher is the transparency of the map. To this end, a novel learning approach, sparse real-coded genetic algorithms (SRCGAs), to learn FCMs is proposed. The method utilizes a density parameter to guide the learning toward a formation of maps of a certain predefined density. Comparative tests carried out for both synthetic and real-world data demonstrate that, given a suitable density estimate, the SRCGA method significantly outperforms other state-of-the-art learning methods. When the density estimate is unknown, the new method can be used in an automated fashion using a default value, and it is still able to produce models whose performance exceeds or is equal to the performance of the models generated by other methods.

Objective: We propose and develop a concept of a granular representation of a collection of signals (patterns) where a prototype (representative) of such numeric signals is formed as a certain information granule (say, a set, fuzzy set, rough set, and alike) instead of a single numeric entity. As being more abstract, the granular format of the representative of the family of signals is more in rapport with the nature of the representation task itself. It is instrumental in quantifying the diversity of data and capture their inherent distribution characteristics., Methods and Materials: In the realization of the granular representation of the signals, we introduce a certain level of granularity (supplied in advance), which in the construction of the granular representative is regarded as an essential important modeling asset. A two-phase design is developed whose ultimate goal is to optimally allocate (distribute) the predefined level of granularity to the individual elements of the universe of discourse over which the signals are described. Given the nature of the required optimization, the ensuing optimization problem is solved by engaging a machinery of population-based optimization, namely Particle Swarm Optimization (PSO). Furthermore a number of information granularity distribution protocols are proposed. The numerical experiments completed for synthetic data and ECG MIT-BIH database signals are used to demonstrate the performance of the overall optimization algorithm and quantify the effectiveness of the allocation of information granularity realized by the PSO. An area under curve (AUC) criterion is proposed as a measure to express the quality of the overall optimization framework., Results: For both synthetic as well as ECG signals, it is shown that the method endowed with the PSO identifies the best prototype and spans the lower and upper bounds of its granular counterpart. In addition to the numeric quantification of the best (optimized) granular prototype, the method helps visualizing its bounds. The relative difference in mapping performance between the best and the weakest granular prototypes is in the range of 18% (for normal ECG complexes) and over 26% in case of complexes of premature ventricular contraction., Conclusions: A complete algorithm of the construction of granular prototypes is presented. Treating the granular prototype as a template of a given class of electrocardiogram (ECG) signals, a matching process is facilitated and used as a basis for the design of signal classification algorithms. Various realizations of granular prototypes can be completed with the use of fuzzy sets or rough sets., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Linguistic interface is a group of linguistic terms or fuzzy descriptions that describe variables in a system utilizing corresponding membership functions. Its transparency completely or partly decides the interpretability of fuzzy models. This paper proposes a GRadiEnt-descEnt-based Transparent lInguistic iNterface Generation (GREETING) approach to overcome the disadvantage of traditional linguistic interface generation methods where the consideration of the interpretability aspects of linguistic interface is limited. In GREETING, the widely used interpretability criteria of linguistic interface are considered and optimized. The numeric experiments on the data sets from University of California, Irvine (UCI) machine learning databases demonstrate the feasibility and superiority of the proposed GREETING method. The GREETING method is also applied to fuzzy decision tree generation. It is shown that GREETING generates better transparent fuzzy decision trees in terms of better classification rates and comparable tree sizes.

The objective of this paper is to study facility-location problems in the presence of a hybrid uncertain environment involving both randomness and fuzziness. A two-stage fuzzy-random facility-location model with recourse (FR-FLMR) is developed in which both the demands and costs are assumed to be fuzzy-random variables. The bounds of the optimal objective value of the two-stage FR-FLMR are derived. As, in general, the fuzzy-random parameters of the FR-FLMR can be regarded as continuous fuzzy-random variables with an infinite number of realizations, the computation of the recourse requires solving infinite second-stage programming problems. Owing to this requirement, the recourse function cannot be determined analytically, and, hence, the model cannot benefit from the use of techniques of classical mathematical programming. In order to solve the location problems of this nature, we first develop a technique of fuzzy-random simulation to compute the recourse function. The convergence of such simulation scenarios is discussed. In the sequel, we propose a hybrid mutation-based binary ant-colony optimization (MBACO) approach to the two-stage FR-FLMR, which comprises the fuzzy-random simulation and the simplex algorithm. A numerical experiment illustrates the application of the hybrid MBACO algorithm. The comparison shows that the hybrid MBACO finds better solutions than the one using other discrete metaheuristic algorithms, such as binary particle-swarm optimization, genetic algorithm, and tabu search.

Multiagent systems are inherently associated with their distributivity, which enforces a great deal of communication mechanisms. To effectively arrive at meaningful solutions in a vast array of problem-solving tasks, it becomes imperative to establish a sound machinery of reconciling findings which might form partial solutions to an overall problem. In this paper, we focus on a broad category of problems of collaborative data analysis realized by a collection of agents having access to their individual data and exchanging findings through their collaboration activities. Such problems of data analysis arise in the context of building a global view at a certain phenomenon (process) by viewing it from different perspectives (and thus engaging various collections of attributes by various agents). Our goal is to develop some interaction between the agents so that they could form an overall perspective, where the knowledge available locally is shared and reconciled. The underlying format of knowledge built by the agents is that of information granules and fuzzy sets in particular. We develop a comprehensive optimization scheme and discuss its two-phase nature in which the communication phase of the granular findings intertwines with the local optimization being realized by the agents at the level of the individual datasite and exploits the evidence collected from other sites. We show how the mechanism of fuzzy granulation realized in the form of a well-known fuzzy c-means (FCM) clustering can be augmented to support collaborative activities required by the agents. For this purpose, we introduce augmented versions of the original objective function used in the FCM and derive algorithmic details. We also discuss an issue of optimizing the strength of collaborative linkages, so that the reconciled findings attain the highest level of consistency (agreement). The presented experimental studies include some synthetic data and selected data sets coming from the Machine Learning repository.

We develop a new approach to the design of neural networks, which utilizes a collaborative framework of knowledge-driven experience. In contrast to the "standard" way of developing neural networks, which explicitly exploits experimental data, this approach incorporates a mechanism of knowledge-driven experience. The essence of the proposed scheme of learning is to take advantage of the parameters (connections) of neural networks built in the past for the same phenomenon (which might also exhibit some variability over time or space) for which are interested to construct the network on a basis of currently available data. We establish a conceptual and algorithmic framework to reconcile these two essential sources of information (data and knowledge) in the process of the development of the network. To make a presentation more focused and come up with a detailed quantification of the resulting architecture, we concentrate on the experience-based design of radial basis function neural networks (RBFNNs). We introduce several performance indexes to quantify an effect of utilization of the knowledge residing within the connections of the networks and establish an optimal level of their use. Experimental results are presented for low-dimensional synthetic data and selected datasets available at the Machine Learning Repository.

This paper is concerned with an enhanced independent component analysis (ICA) and its application to face recognition. Typically, face representations obtained by ICA involve unsupervised learning and high-order statistics. In this paper, we develop an enhancement of the generic ICA by augmenting this method by the Fisher linear discriminant analysis (LDA); hence, its abbreviation, FICA. The FICA is systematically developed and presented along with its underlying architecture. A comparative analysis explores four distance metrics, as well as classification with support vector machines (SVMs). We demonstrate that the FICA approach leads to the formation of well-separated classes in low-dimension subspace and is endowed with a great deal of insensitivity to large variation in illumination and facial expression. The comprehensive experiments are completed for the facial-recognition technology (FERET) face database; a comparative analysis demonstrates that FICA comes with improved classification rates when compared with some other conventional approaches such as eigenface, fisherface, and the ICA itself.

In this paper, we develop a general framework of a granular representation of ECG signals. The crux of the approach lies in the development and ongoing processing realized in the setting of information granules-fuzzy sets. They serve as basic conceptual and semantically meaningful entities using which we describe signals and build their models (such as various predictive schemes or classifiers). A comprehensive two-phase scheme of the design of the information granules is proposed and described. At the first phase, we discuss the temporal granulation through a series of temporal windows (granular windows) and an aggregation of the values of signal by means of fuzzy sets. To address this issue, offered is a detailed method of building a fuzzy set based on numeric data and a certain optimization criterion that strikes a balance between the highest experimental relevance of the fuzzy set supported by numeric data and its substantial specificity. At the next phase of the granular design, a collection of information granules is further summarized with the use of fuzzy clustering (Fuzzy C-Means). The resulting prototypes (centroids) formed by this grouping process serve as elements of the granular vocabulary. We discuss ways of using these vocabularies in the knowledge-based representation, modeling, and classification of ECG beats.

In this study, we introduce a novel clustering architecture, in which several subsets of patterns can be processed together with an objective of finding a common structure. The structure revealed at the global level is determined by exchanging prototypes of the subsets of data and by moving prototypes of the corresponding clusters toward each other. Thereby, the required communication links are established at the level of cluster prototypes and partition matrices, without hampering the security concerns. A detailed clustering algorithm is developed by integrating the advantages of both fuzzy sets and rough sets, and a measure of quantitative analysis of the experimental results is provided for synthetic and real-world data.

In this paper, we are concerned with the concept of fuzzy logic networks and logic-based data analysis realized within this framework. The networks under discussion are homogeneous architectures comprising of OR/AND neurons originally introduced by Hirota and Pedrycz. Being treated here as generic processing units, OR/AND neurons are neurofuzzy constructs that exhibit well-defined logic characteristics and are endowed with a high level of parametric flexibility and come with significant interpretation abilities. The composite logic nature of the logic neurons becomes instrumental in covering a broad spectrum of logic dependencies whose character spread in-between between those being captured by plain and and or logic descriptors (connectives). From the functional standpoint, the developed network realizes a logic approximation of multidimensional mappings between unit hypercubes, that is transformations from [0, 1]n to [0, 1]m. The way in which the structure of the network has been formed is highly modular and becomes reflective of a general concept of decomposition of logic expressions and Boolean functions (as being commonly encountered in two-valued logic). In essence, given a collection of input variables, selected is their subset and transformed into new composite variable, which in turn is used in the consecutive module of the network. These intermediate synthetic variables are the result of the successive problem (mapping) decomposition. The development of the network is realized through genetic optimization. This helps address important issues of structural optimization (where we are concerned with a selection of a subset of variables and their allocation within the network) and reaching a global minimum when carrying out an extensive parametric optimization (adjustments of the connections of the neurons). The paper offers a comprehensive and user-interactive design procedure including a simple pruning mechanism whose intention is to enhance the interpretability of the network while reducing its size. The experimental studies comprise of three parts. First, we demonstrate the performance of the network on Boolean data (that leads to some useful comparative observations considering a wealth of optimization tools available in two-valued logic and digital systems). Second, we discuss synthetic multivalued data that helps focus on the approximation abilities of the network. Finally, show the generation of logic expressions describing selected data sets coming from the machine learning repository.

In this paper, we develop an efficient fuzzy wavelet packet (WP) based feature extraction method for the classification of high-dimensional biomedical data such as magnetic resonance spectra. The key design phases involve: 1) a WP transformation mapping the original signals to many WP feature spaces and finding optimal WP decomposition for signal classification; 2) feature extraction based on the optimal WP decomposition; and 3) signal classification realized by a linear classifier. In contrast to the standard method of feature extraction used in WPs, guided by the criteria of signal compression or signal energy, our method is used to extract discriminatory features from the WP coefficients of the optimal decomposition. The extraction algorithm constructs fuzzy sets of features (via fuzzy clustering) to assess their discriminatory effectiveness. This paper includes a number of numerical experiments using magnetic resonance spectra. Classification results are compared with those obtained from common feature extraction methods in the WP domain.

The recent trend in the development of neurofuzzy systems has profoundly emphasized the importance of synergy between the fundamentals of fuzzy sets and neural networks. The resulting frameworks of the neurofuzzy systems took advantage of an array of learning mechanisms primarily originating within the theory of neurocomputing and the use of fuzzy models (predominantly rule-based systems) being well established in the realm of fuzzy sets. Ideally, one can anticipate that neurofuzzy systems should fully exploit the linkages between these two technologies while strongly preserving their evident identities (plasticity or learning abilities to be shared by the transparency and full interpretability of the resulting neurofuzzy constructs). Interestingly, this synergy still becomes a target yet to be satisfied. This study is an attempt to address the fundamental interpretability challenge of neurofuzzy systems. Our underlying conjecture is that the transparency of any neurofuzzy system links directly with the logic fabric of the system so the logic fundamentals of the underlying architecture become of primordial relevance. Having this in mind the development of neurofuzzy models hinges on a collection of logic driven processing units named here fuzzy (logic) neurons. These are conceptually simple logic-oriented elements that come with a well-defined semantics and plasticity. Owing to their diversity, such neurons form essential building blocks of the networks. The study revisits the existing categories of logic neurons, provides with their taxonomy, helps understand their functional features and sheds light on their behavior when being treated as computational components of any neurofuzzy architecture. The two main categories of aggregative and reference neurons are deeply rooted in the fundamental operations encountered in the technology of fuzzy sets (including logic operations, linguistic modifiers, and logic reference operations). The developed heterogeneous networks come with a well-defined semantics and high interpretability (which directly translates into the rule-based representation of the networks). As the network takes advantage of various logic neurons, this imposes an immediate requirement of structural optimization, which in this study is addressed by utilizing various mechanisms of genetic optimization (genetic algorithms). We discuss the development of the networks, elaborate on the interpretation aspects and include a number of illustrative numeric examples.

Functional piecewise approximation seeks data representation that is compact, highly simplified and meaningful. This study presents a genetic algorithm (GA)-based approach for computing a piecewise polynomial representation of functions, with the focus being on piecewise linear approximation in an application of biomedical spectral data. The area of piecewise linear approximation has been researched in the past four decades approximately, and the method presented here is compared with another well-known approach. The expansion of this method to piecewise polynomial representation is shown to be straightforward. Finally, the application of this method as a feature extraction method for classification of a dataset of feature vectors, specifically biomedical spectra, is demonstrated.

In this paper, we develop a method for recognizing face images by combining wavelet decomposition, Fisherface method, and fuzzy integral. The proposed approach is comprised of four main stages. The first stage uses the wavelet decomposition that helps extract intrinsic features of face images. As a result of this decomposition, we obtain four subimages (namely approximation, horizontal, vertical, and diagonal detailed images). The second stage of the approach concerns the application of the Fisherface method to these four decompositions. The choice of the Fisherface method in this setting is motivated by its insensitivity to large variation in light direction, face pose, and facial expression. The two last phases are concerned with the aggregation of the individual classifiers by means of the fuzzy integral. Both Sugeno and Choquet type of fuzzy integral are considered as the aggregation method. In the experiments we use n-fold cross-validation to assure high consistency of the produced classification outcomes. The experimental results obtained for the Chungbuk National University (CNU) and Yale University face databases reveal that the approach presented in this paper yields better classification performance in comparison to the results obtained by other classifiers.

This paper is concerned with a development of a segmentation technique for electrocardiogram (ECG) signals. Such segmentation is aimed at a lossy signal compression in which each segment can be captured by a simple geometric construct such as, e.g., a linear or quadratic function. The crux of the proposed construct lies in the determination of the optimal segments of data over which they exhibit the highest possible monotonicity (or lowest variability) of the ECG signal. In this sense, the proposed approach generalizes a fundamental and commonly encountered problem of function (data) linearization. The segments are genetically developed using a standard technique of genetic algorithms (GAs). The two fundamental GA constructs, namely a topology of a chromosome and a fitness function governing the optimization process are discussed in detail. The chromosome being coded as a series of floating point numbers contains the endpoints of the segments (segmentation points). The fitness function to be maximized quantifies a level of monotonicity of the ECG data encountered within the segments and takes into consideration differences between the extreme values (minimum and maximum) of its derivatives. As a result of the genetic optimization, we build segments of ECG signals encompassing monotonic (increasing or decreasing) regions of the signal exhibiting a minimal level of variability. A series of experiments dealing with several classes of ECG signals (namely, normal, left bundle branch block beat, and right bundle branch block beat) visualize the effectiveness of the approach and shows the specificity of the linear segments of data. Furthermore, we elaborate on the relationship between the values of the fitness function and the approximation capabilities (quantified by a sum of squared errors between the local model and the data) of the segments of the signal and show that these two descriptors are highly related.

In the era of big data, the demand for multivariate time series prediction has surged, drawing increased attention to feature selection and neural networks in machine learning. However, certain feature selection methods neglect the alignment between actual data sample differences and clustering results, while neural networks lack automatic parameter adjustment in response to changing target features. This paper presents the MBSSA-Bi-AESN model, a Bi-directional Adaptive Echo State Network that utilizes the modified salp swarm algorithm (MBSSA) and feature selection to address the limitations of manually set parameters. Initial feature subset selection involves assigning weights based on the consistency of clustering results with differences. Subsequently, the four critical parameters in the Bi-AESN model are optimized using MBSSA. The optimized Bi-AESN model and selected feature subset are then integrated for simultaneous model learning and optimal feature subset selection. Experimental analysis on eight datasets demonstrates the superior prediction accuracy of the MBSSA-Bi-AESN model compared to benchmark models, underscoring its feasibility, validity, and universality. [ABSTRACT FROM AUTHOR]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.sysarc.2006.10.012 Byline: Madhura Purnaprajna, Marek Reformat, Witold Pedrycz Keywords: Hardware-software partitioning; Genetic algorithms; Reconfiguration Abstract: A scheme for time and power efficient embedded system design, using hardware and software components, is presented. Our objective is to reduce the execution time and the power consumed by the system, leading to the simultaneous multi-objective minimization of time and power. The goal of suitably partitioning the system into hardware and software components is achieved using Genetic Algorithms (GA). Multiple tests were conducted to confirm the consistency of the results obtained and the versatile nature of the objective functions. An enhanced resource constrained scheduling algorithm is used to determine the system performance. To emulate the characteristics of practical systems, the influence of inter-processor communication is examined. The suitability of introducing a reconfigurable hardware resource over pre-configured hardware is explored for the same objectives. The distinct difference in the task to resource mapping with the variation in design objective is studied. Further, the procedure to allocate optimal number of resources based on the design objective is proposed. The implementation is constrained for power and time individually, with GA being used to arrive at the resource count to suit the objective. The results obtained are compared by varying the time and power constraints. The test environment is developed using randomly generated task graphs. Exhaustive sets of tests are performed on the set design objectives to validate the proposed solution. Author Affiliation: Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G2V4 Article History: Received 7 September 2004; Revised 24 August 2005; Accepted 3 October 2006

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jss.2004.06.018 Byline: Witold Pedrycz (a)(b), Giancarlo Succi (c) Keywords: Software quality; Hyperbox geometry of classifiers; Software measures; Genetic algorithms; Fuzzy clustering; Fuzzy C-Means (FCM) Abstract: Hyperbox classifiers are one of the most appealing and intuitively transparent classification schemes. As the name itself stipulates, these classifiers are based on a collection of hyperboxes--generic and highly interpretable geometric descriptors of data belonging to a given class. The hyperboxes translate into conditional statements (rules) of the form "if feature.sub.1 is in [a, b] and feature.sub.2 is in [d, f] and ... and feature.sub.n is in [w, z] then class I" where the intervals ([a, b],...,[w, z]) are the respective edges of the hyperbox. The proposed design process of hyperboxes comprises of two main phases. In the first phase, a collection of "seeds" of the hyperboxes is formed through data clustering (realized by means of the Fuzzy C-Means algorithm, FCM). In the second phase, the hyperboxes are "grown" (expanded) by applying mechanisms of genetic optimization (and genetic algorithm, in particular). We reveal how the underlying geometry of the hyperboxes supports an immediate interpretation of software data concerning software maintenance and dealing with rules describing a number of changes made to software modules and their linkages with various software measures (such as size of code, McCabe cyclomatic complexity, number of comments, number of characters, etc.). Author Affiliation: (a) Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada T6G 2G7 (b) Systems Research Institute of Polish Academy of Sciences, Warsaw, Poland (c) Department of Computer Science, University of Bozen, I-39100 Bozen, Italy Article History: Received 4 July 2003; Revised 9 June 2004; Accepted 12 June 2004

A new variant of the two-echelon routing problem is investigated, where the truck and the drone are used to cooperatively complete the deliveries of all parcels. The truck not only acts as a tool for parcel delivery but also serves as a moving depot for the drone. The drone can carry several parcels and take off from the truck, while returning to the truck after completing the delivery. The energy consumption model for the routing process of the drone is analyzed, when it is utilized to deliver multiple parcels. A two-stage route-based modeling approach is proposed to optimize both the truck’s main route and the drone’s adjoint flying routes. A hybrid heuristic integrating nearest neighbor and cost saving strategies is developed to quickly construct a feasible solution. The simulated annealing algorithm is integrated with Tabu search, to improve the quality of the solution as well as the search efficiency. Random instances at different scales are used to test the performance of the proposed algorithm. A case study based on the practical road network in Changsha, China, is presented, through which the sensitivity analysis is conducted with respect to some critical factors. [ABSTRACT FROM AUTHOR]

In industrial areas, most of databases are dynamic databases, and the volume of the databases has grown with the passage of time. Especially, pattern mining for incremental database needs different approaches from static database because the profit or the accuracy of the previously inserted data can be reduced. Since data is time‐ sensitive, the recent data has a relatively higher value than the old data. In this paper, we suggest the damped window based average utility driven data analytics for intelligent systems, which the damped window reflects the importance according to the arrival time of the transactions. The proposed mining approach adopts novel data structure, which modify the importance of item as the passage of time, and it improves mining efficiency with several pruning strategies and without generating candidate patterns. To evaluate the performance of the proposed mining approach, we conducted various experiments using several real and synthetic data sets. The result of the experiments presented that the suggested method performs better in terms of runtime and memory usage than the other state‐of‐the‐art mining techniques. Moreover, through the scalability experiments, which changed the number of different items or transactions, we verified that the proposed algorithm maintained a stable performance under various environmental changes. [ABSTRACT FROM AUTHOR]

With the increase in the number of optimization objectives, balancing the convergence and diversity in evolutionary multiobjective optimization becomes more intractable. So far, a variety of evolutionary algorithms have been proposed to solve many-objective optimization problems (MaOPs) with more than three objectives. Most of the existing algorithms, however, find difficulties in simultaneously counterpoising convergence and diversity during the whole evolutionary process. To address the issue, this paper proposes to solve MaOPs via multistage evolutionary search. To be specific, a two-stage evolutionary algorithm is developed, where the convergence and diversity are highlighted during different search stages to avoid the interferences between them. The first stage pushes multiple subpopulations with different weight vectors to converge to different areas of the Pareto front. After that, the nondominated solutions coming from each subpopulation are selected for generating a new population for the second stage. Moreover, a new environmental selection strategy is designed for the second stage to balance the convergence and diversity close to the Pareto front. This selection strategy evenly divides each objective dimension into a number of intervals, and then one solution having the best convergence in each interval will be retained. To assess the performance of the proposed algorithm, 48 benchmark functions with 7, 10, and 15 objectives are used to make comparisons with five representative many-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity. To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous t-norms are employed. Furthermore, four numerical fuzzy inference examples are provided, and it is found that the entropy-based differently implicational algorithm can obtain more reasonable solution in contrast with the fuzzy entropy full implication algorithm. Finally, in the entropy-based differently implicational algorithm, we point out that the first fuzzy implication reects the effect of rule base, and that the second fuzzy implication embodies the inference mechanism. [ABSTRACT FROM AUTHOR]

Information granules form an abstract and efficient characterization of large volumes of numeric data. Fuzzy clustering is a commonly encountered information granulation approach. A reconstruction (degranulation) is about decoding information granules into numeric data. In this study, to enhance quality of reconstruction, we augment the generic data reconstruction approach by introducing a transformation mapping of the originally produced partition matrix and setting up an adjustment mechanism modifying a localization of the prototypes. We engage several population-based search algorithms to optimize interaction matrices and prototypes. A series of experimental results dealing with both synthetic and publicly available data sets are reported to show the enhancement of the data reconstruction performance provided by the proposed method. [ABSTRACT FROM AUTHOR]

For any two one-dimensional time series of equal or non-equal length, we propose a new method to determine their shape distance. Each of the original time series is represented by a sequence of linear segments which are produced by l 1 trend filtering. As the dimensionality of this representation ranges between time series, dynamic time warping (DTW) method is used to calculate the distance between time series. In contrast to the standard dynamic time warping method, here the element of the new distance matrix concerns the distance between two linear segments instead of two elements of the original time series. More specifically, the distance between the two linear segments is calculated as the area of a triangle which is formed by the two linear segments after their translation and connection. In brief, the new measure can be regarded as the dynamic time warping distance computed in a piecewise linear space. Furthermore, we show that new distance measure quantitatively reflects the shape's difference between two one-dimensional time series. The simulation experiments presented in this paper illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Backgrounds: The heartbeat is fundamental cardiac activity which is straightforwardly detected with a variety of measurement techniques for analyzing physiological signals. Unfortunately, unexpected noise or contaminated signals can distort or cut out electrocardiogram (ECG) signals in practice, misleading the heartbeat detectors to report a false heart rate or suspend itself for a considerable length of time in the worst case. To deal with the problem of unreliable heartbeat detection, PhysioNet/CinC suggests a challenge in 2014 for developing robust heart beat detectors using multimodal signals.Methods: This article proposes a multimodal data association method that supplements ECG as a primary input signal with blood pressure (BP) and electroencephalogram (EEG) as complementary input signals when input signals are unreliable. If the current signal quality index (SQI) qualifies ECG as a reliable input signal, our method applies QRS detection to ECG and reports heartbeats. Otherwise, the current SQI selects the best supplementary input signal between BP and EEG after evaluating the current SQI of BP. When BP is chosen as a supplementary input signal, our association model between ECG and BP enables us to compute their regular intervals, detect characteristics BP signals, and estimate the locations of the heartbeat. When both ECG and BP are not qualified, our fusion method resorts to the association model between ECG and EEG that allows us to apply an adaptive filter to ECG and EEG, extract the QRS candidates, and report heartbeats.Results: The proposed method achieved an overall score of 86.26 % for the test data when the input signals are unreliable. Our method outperformed the traditional method, which achieved 79.28 % using QRS detector and BP detector from PhysioNet. Our multimodal signal processing method outperforms the conventional unimodal method of taking ECG signals alone for both training and test data sets.Conclusions: To detect the heartbeat robustly, we have proposed a novel multimodal data association method of supplementing ECG with a variety of physiological signals and accounting for the patient-specific lag between different pulsatile signals and ECG. Multimodal signal detectors and data-fusion approaches such as those proposed in this article can reduce false alarms and improve patient monitoring. [ABSTRACT FROM AUTHOR]

In this paper, a fuzzy c-means clustering algorithm based on interval-valued weights is proposed for improving clustering performance. In the proposed algorithm, the interval-valued weights are first constructed by synergy of the ReliefF algorithm and the analytic hierarchy process (AHP) method, and then they are transformed into a constraint condition associating with each weight variable in the weighted clustering objective function. In the sequence, the weighted clustering objective function is solved by combining the Lagrange multiplier method with the gradient-based iteration computation. In the whole process of algorithm iteration, a compulsion strategy with human-computer cooperation is adopted to ensure each weight variable satisfies interval constraint itself. Three well-known data set are used to perform profound experiments. Experimental results clearly show that the proposed algorithm has better clustering performance than other the weighted fuzzy c-means clustering algorithm. [ABSTRACT FROM AUTHOR]

Highlights: [•] Introduction of the principle of justifiable granularity. [•] Comprehensive algorithmic framework supporting the design of information granules. [•] Discussed are two essential requirements of information granularity. [•] Provided is a series of experimental studies. [ABSTRACT FROM AUTHOR]

Abstract: In this study, the use of conditional Fuzzy C-Means (CFCM) aimed at estimation of desired states of an unknown digital communication channel is considered for blind channel equalization. In the proposed CFCM, a collection of estimated centers is treated as a set of pre-defined desired channel states, and used to extract channel output states. By considering the combinations of the extracted channel output states, all possible sets of desired channel states are constructed. The set of desired states characterized by the maximal value of the Bayesian fitness function is subsequently selected for the next clustering epoch. This modification of CFCM makes it possible to search for the optimal desired channel states of an unknown channel. Finally, given the desired channel states, the Bayesian equalizer is implemented to reconstruct transmitted symbols. In a series of simulations, binary signals are generated at random with Gaussian noise, and both linear and nonlinear channels are evaluated. The experimental studies demonstrate that the performance (being expressed in terms of accuracy and speed) of the proposed CFCM is superior to the performance of the existing method exploiting the “conventional” Fuzzy C-Means (FCM). [ABSTRACT FROM AUTHOR]

Abstract: Finding a global optimum of an unknown system has attracted a great deal of interest in many engineering problems. In this settings, meta-heuristics are very common as efficient approaches for solving complex real-world problems in global continuous optimization problems (GCOPs) as they can approximate solutions without considering mathematical constraints such as differentiability. In this study, we propose a method based on tabu search (TS) and Nelder–Mead (NM) search strategy in application to GCOPs. To increase the robustness of the proposed method, we add a new phase, referred to as partitioning phase, before diversification which is realized by the TS. The TS is improved and then followed by the NM search strategy. The partitioning phase aims at distributing initial random solutions in the search space. By doing this, we increase the robustness of the method. The TS has an interesting ability of covering a wide solution space by promoting the search far away from the current solution and consecutively decreasing the possibility of trapping in local minima. The neighbour search-strategy of the TS is improved to accelerate the speed of finding the near optimum solution. Instead of just generating random neighbours around the current solution, we generate some neighbours in the direction of the previous move as well as some neighbours in the previous best crown. When certain criteria are reached for the diversification of the search space, the NM search strategy is carried out with the focus on the intensification of the solution found in the diversification phase. We assess the performance of the algorithm for a range of standard test functions available in the literature and compare the obtained results with those available in the literature. There are two main advantages of the proposed method; first, it can apply to any GCOP without considering any constraints and secondly, it shows better performance (in terms of function evaluation, success rate, and average error) for the functions with less than four input variables and relatively small or medium input domains. In other cases, the method still has acceptable perfomance and produces the results that are comparable with the results produced by other methods. [Copyright &y& Elsevier]

Abstract: The underlying objective of this study is to show how fuzzy sets (and information granules in general) and grammatical inference play an interdependent role in information granularization and knowledge-based problem characterization. The bottom-up organization of the material starts with a concept and selected techniques of data compactification which involves information granulation and gives rise to higher-order constructs (type-2 fuzzy sets). The detailed algorithmic investigations are provided. In the sequel, we focus on Computing with Words (CW), which in this context is treated as a general paradigm of processing information granules. We elaborate on a role of randomization and offer a detailed example illustrating the essence of the granular constructs along with the grammatical aspects of the processing. [Copyright &y& Elsevier]

Feature selection plays an important role in pattern recognition and machine learning. Feature evaluation and classification complexity estimation arise as key issues in the construction of selection algorithms. To estimate classification complexity in different feature subspaces, a novel feature evaluation measure, called the neighborhood decision error rate (NDER), is proposed, which is applicable to both categorical and numerical features. We first introduce a neighborhood rough-set model to divide the sample set into decision positive regions and decision boundary regions. Then, the samples that fall within decision boundary regions are further grouped into recognizable and misclassified subsets based on class probabilities that occur in neighborhoods. The percentage of misclassified samples is viewed as the estimate of classification complexity of the corresponding feature subspaces. We present a forward greedy strategy for searching the feature subset, which minimizes the NDER and, correspondingly, minimizes the classification complexity of the selected feature subset. Both theoretical and experimental comparison with other feature selection algorithms shows that the proposed algorithm is effective for discrete and continuous features, as well as their mixture. [ABSTRACT FROM AUTHOR]