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In this paper, a new approach to estimate scaling factors of the fuzzy PID controller is presented. The performance of the fuzzy PID controller is sensitive to the variety of scaling factors. The design procedure dwells on the use of evolutionary computing (more specifically, a genetic algorithm) and estimation algorithm. The tuning of the scaling factors of the fuzzy PID controller is essential to the entire optimization process. And then we estimate scaling factors of the fuzzy PID controller by means of three types of estimation algorithms such as HCM (Hard C-Means) clustering-based regression polynomial, neuro-fuzzy networks, and regression polynomials. Numerical studies are presented in detail along with a detailed comparative analysis. [Copyright &y& Elsevier]

In this paper, we introduce a category of Multi-Fuzzy-Neural Networks (Multi-FNNs) models, analyze the underlying architectures and propose a comprehensive identification framework. The proposed Multi-FNNs are based on a concept of fuzzy rule-based FNNs that use H ard C-M eans (HCM) clustering and evolutionary fuzzy granulation and exploit linear inference being treated as a generic inference mechanism of approximate reasoning. By this nature, this FNN model is geared toward capturing relationships between information granules–fuzzy sets. The form of the information granules themselves (in particular their distribution and a type of membership functions) becomes an important design feature of the FNN model that contributes to its structural and parametric optimization. The genetically guided global optimization is then augmented by more refined gradient-based learning mechanisms such as a standard back-propagation. The HCM algorithm, whose role is to carry out preprocessing of the experimental data, is utilized to determine the structure of Multi-FNNs. The detailed parameters of the Multi-FNN (such as apexes of membership functions, learning rates, and momentum coefficients) are adjusted using genetic algorithms. The proposed aggregate performance index helps achieve a sound balance between approximation and generalization (predictive) abilities of the model. To evaluate an effectiveness of the introduced model, several numeric data sets are experimented with. Those include a time-series data of gas furnace, NOx emission process of gas turbine power plant and some synthetic data. [Copyright &y& Elsevier]

In this paper, we introduce a new topology of Fuzzy Polynomial Neural Networks (FPNN) that is based on a genetically optimized multi-layer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially genetic algorithms (GAs). The development of the ‘conventional’ FPNNs uses an extended Group Method of Data Handling. The network exploits a fixed fuzzy inference type in each FPN of the FPNN as well as considers a fixed number of input nodes at FPNs (or nodes) located in each layer. Here, the proposed FPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. The structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least-square method-based learning. The performance of the networks is quantified through experimentation involving two time series dataset already used in fuzzy modeling. The results demonstrate their superiority over the existing fuzzy and neural models. [Copyright &y& Elsevier]

In this paper, we introduce a general category of multi-fuzzy-neural networks (FNNs), analyze their underlying architecture and propose a comprehensive identification framework. The proposed multi-FNNs dwells on a concept of linear fuzzy inference-based FNNs. The design of the model uses a standard HCM (Hard C-Means) clustering algorithm and carries out an evolutionary fuzzy granulation of experimental data. The performance of the model is quantified through a series of experimental studies involving synthetic and real-world data. [Copyright &y& Elsevier]

The study is concerned with a new temporal version of fuzzy Petri nets—fuzzy timed Petri nets (ftPNs). These nets are augmented by temporal fuzzy sets that allow for the representation of timing effect (e.g., aging of information). We show how the time factor can be added as an integral part of the models of transitions and places. The formalism of the extended net is introduced and studied in depth. A series of illustrative examples are presented with intent of developing a better qualitative insight into the temporal behavior of the nets. A detailed learning scheme for the net is also given. [Copyright &y& Elsevier]

Focuses on the development of a segmentation technique for electrocardiogram (ECG) signals. Determination of the optical segments of data over which they exhibit the highest possible monotonicity of the ECG signal; Level of monotonicity of the ECG data encountered within the segments.

This paper introduces an identification method for nonlinear models in the form of Fuzzy-Neural Networks (FNN). In this model, we use two forms of the fuzzy inference methods—a simplified and linear fuzzy inference, and exploit a standard Error Back Propagation learning algorithm. The FNN modeling and identification environment realizes parameter identification through a synergistic usage of clustering techniques, genetic optimization and a complex search method. We use a Hard C-Means (HCM) clustering algorithm to determine initial apexes of the membership functions of the information granules used in this fuzzy model. The parameters such as apexes of membership functions, learning rates, and momentum coefficients are then adjusted using hybrid algorithm. The proposed hybrid identification algorithm is carried out by combining both genetic optimization (genetic algorithm, GA) and the improved complex method. An aggregate objective function (performance index) with a weighting factor is introduced to achieve a sound balance between approximation and generalization of the model. According to the selection and adjustment of the weighting factor of this objective function, we reveal how to design a model with sound approximation and generalization abilities. The proposed model is experimented with using several time series data (gas furnace, sewage treatment process and NOx emission process data of gas turbine power plant). [Copyright &y& Elsevier]

In this study, we introduce and investigate a class of neural architectures of Polynomial Neural Networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. Two kinds of PNN architectures, namely a basic PNN and a modified PNN architecture are discussed. Each of them comes with two types such as the generic and the advanced type. The essence of the design procedure dwells on the Group Method of Data Handling. PNN is a flexible neural architecture whose structure is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but becomes dynamically meaning that the network grows over the training period. In this sense, PNN is a self-organizing network. A comparative analysis shows that the proposed PNN are models with higher accuracy than other fuzzy models. [Copyright &y& Elsevier]

We propose a new category of neurofuzzy networks--self-organizing neural networks (SONN) with fuzzy polynomial neurons (FPNs) and discuss a comprehensive design methodology supporting their development. Two kinds of SONN architectures, namely a basic SONN and a modified SONN architecture are discussed. Each of them comes with two topologies such as a generic and advanced type. Especially in the advanced type, the number of nodes in each layer of the SONN architecture can be modified with new nodes added, if necessary. SONN dwells on the ideas of fuzzy rule-based computing and neural networks. The architecture of the SONN is not fixed in advance as it usually takes place in the case of conventional neural networks, but becomes organized dynamically through a growth process. Simulation involves a series of synthetic as well as real-world data used across various neurofuzzy systems. A comparative analysis shows that the proposed SONN are models exhibiting higher accuracy than some other fuzzy models. [ABSTRACT FROM AUTHOR]

In this paper, we present results of uncertain state estimation of systems that are monitored with limited accuracy. For these systems, the representation of state uncertainty as confidence intervals offers significant advantages over the more traditional approaches with probabilistic representation of noise. While the filtered-white-Gaussian noise model can be defined on grounds of mathematical convenience, its use is necessarily coupled with a hope that an estimator with good properties in idealised noise will still perform well in real noise. In this study we propose a more realistic approach of matching the noise representation to the extent of prior knowledge. Both interval and ellipsoidal representation of noise illustrate the principle of keeping the noise model simple while allowing for iterative refinement of the noise as we proceed. We evaluate one nonlinear and three linear state estimation technique both in terms of computational efficiency and the cardinality of the state uncertainty sets. The techniques are illustrated on a synthetic and a real-life system. [ABSTRACT FROM AUTHOR]

Describes information granules and information granulation carried out in the setting of set theory and interval analysis. Applications of information granulation; Design and characterization of information granules; Assessment and interpretation of information granules through fuzzy clustering; Approaches to capturing the dynamics of time-series; Granular analysis to a time-series of traffic queues.

In this study, we introduce a new clustering architecture in which several subsets of patterns can be processed together with an objective of finding a structure that is common to all of them. To reveal this structure, the clustering algorithms operating on the separate subsets of data collaborate by exchanging information about local partition matrices. In this sense, the required communication links are established at the level of information granules (more specifically, fuzzy sets forming the partition matrices) rather than patterns that are directly available in the databases. We discuss how this form of collaboration helps meet requirements of data confidentiality. A detailed clustering algorithm is developed on a basis of the standard FCM method and illustrated by means of numeric examples. [Copyright &y& Elsevier]

The paper is concerned with a logic-based expansion of the standard FCM clustering. The proposed algorithm captures the logic fabric of the structure in a dataset by describing it in the form of a union of the clusters (that is fuzzy relations) determined by the clustering algorithm. In contrast to the standard FCM, the elements (clusters) are combined together as a union of such fuzzy relations—clusters and this form of combination arises as a constraint in the clustering method. In this sense, the introduced clustering environment gives rise to the clustering that is regarded as a logic-driven data decomposition. A detailed algorithm is presented along with some illustrative examples. [Copyright &y& Elsevier]

In this study, we elaborate on an important issue of membership function determination. The main point is that any membership estimation procedure should reconcile the semantics of a fuzzy set (regarded as an information granule arising at some level of information abstraction) with the experimental evidence conveyed by numeric data. This, in the sequel, calls for the development of the hybrid two-phase approach that starts from a rough specification of the support of the fuzzy set that is followed by detailed computations involving a specific type of membership function and an estimation of its parameters. The role of robust statistics in this setting is also raised. A number of experimental results are discussed. [ABSTRACT FROM AUTHOR]

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0, 1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices. The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples. [ABSTRACT FROM AUTHOR]

This paper proposes an identification method for nonlinear models realized in the form of implicit rule-based fuzzy-neural networks (FNN). The design of the model dwells on the technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithm. The FNN modeling and identification environment realizes parameter estimation through a synergistic usage of clustering techniques, genetic optimization and a complex search method. An HCM (Hard C-Means) clustering algorithm helps determine an initial location (parameters) of the membership functions of the information granules to be used in this fuzzy model. The parameters such as apexes of membership functions, learning rates, and momentum coefficients are then adjusted using the optimization algorithm of a GA hybrid scheme. The proposed GA hybrid scheme combines GA with the improved complex method to guarantee both global optimization and local convergence. An aggregate objective function (performance index) is used in the model design in order to achieve a sound balance between its approximation and generalization abilities. The proposed type of the model is experimented with several time series data (gas furnace, sewage treatment process, and NOx emission process data of gas turbine power plant). [Copyright &y& Elsevier]

In this study, we are concerned with a two-objective developmerit of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such, it is oriented toward coping with the underlying relational aspects of the experimental data. The second goal deals with the formation of a mapping between information granules constructed in two spaces (thus, it concentrates on the directional aspect of information granulation). The quality of the mapping is directly affected by the information granules over which it operates, so in essence, we are interested in the granules that not only reflect the data, but also contribute to the performance of such mapping. The optimization of information granules is realized through a collaboration occurring at the level of data and the mapping between the data sets. The operational facet of the problem is cast in the realm of fuzzy clustering. As the standard techniques of fuzzy clustering (including a well-known approach of FCM) are aimed exclusively at the first objective identified above, we augment them in order to accomplish sound mapping properties between the granules. This leads to a generalized version of the FCM (and any other clustering technique for this matter). We propose a generalized version of the objective function that includes an additional collaboration component to make the formed information granules in rapport with the mapping requirements (that comes with a directional component captured by the information granules). The additive form of the objective function with a modifiable component of collaborative activities makes it possible to express a suitable level of collaboration and avoid a phenomenon of potential competition in the case of incompatible structures and the associated mapping. The logic-based type of the mapping (that invokes the use of fuzzy relational equations) comes as a consequence of the logic... [ABSTRACT FROM AUTHOR]

A process of information granulation takes care of an enormous flood of numerical details that becomes summarized and hidden (encapsulated in the form of fuzzy sets) at the time of the design of a neural network. Information granules play an important role in the development of neural networks. First, they substantially reduce the amount of training as the designed network needs to deal with a significantly reduced and highly compressed number of data that falls far below the size of the original training set. The same granulation mechanism delivers some highly advantageous regularization properties. Second, information granules support the design of more transparent and easily interpretable neural networks. The necessary effect of information granulation is accomplished in the framework of fuzzy sets, especially via context-sensitive (conditional) fuzzy clustering. Subsequently, the resulting neural network becomes an architecture with nonnumeric connections. A thorough analysis of results of computing carried out in the setting of linguistic neurocomputing is also given. [Copyright &y& Elsevier]

In this study, we introduce a notion of stability of information granules. Granulation of information results in a series of chunks of information usually referred to as information granules. Information granules are basic building entities involved in the formation of a broad class of systems. Information granules are percepts — entities being perceived by humans as being essential when working with some real-world phenomena, especially describing and interacting with them. The percepts need to be comprehensible. They should also reflect the experimental evidence. All in all, they should be stable meaning that they are conceptual entities that reconcile experimental reality with the subjective and ultimately observerbased judgment about the environment. Once being stable, information granules could be viewed as architecture-independent. The proposed algorithmic environment supporting this concept dwells on the ideas of statistical inference that helps quantify stability through a nonparametric testing. The Χ² goodness-of-fit test is used here as a validation mechanism. First, the study elaborates on the formation of information granules and concentrates on the descriptive and prescriptive ways of their design. In the sequel, it is revealed how these two ways interact with the construction of stable information granules. A number of experimental studies are also included. [ABSTRACT FROM AUTHOR]

Examines the granular analysis of data. Discussion on the use of a clustering algorithm that organizes data findings; Background on the principle of granular clustering; Indices expressing relationships between information granules.

Modeling of temporal functions has been studied extensively in last few decades. Temporal functions or time series are found practically in the gamut of applications, ranging from engineering analysis to financial and commercial transactions.Numerous time series models been proposed, and they can be found in the relevant time series literature. Deterministic and stochastic models have dominated much of the research in this area. Nonetheless, these models have their limitations, and particularly specific models solve specific problem domains. Therefore, there is no general mechanism that can address the issues of modeling of temporal functions.Granular information is now being used to address a few of the problems in the theory of time series. This paper proposes two models that use the concepts of regression and interleaved information granules—intervals and fuzzy sets to identify the structure existing in a given time series. In brevity, we are attempting to combine regression and fuzzy rules to model temporal systems. [ABSTRACT FROM AUTHOR]

This study focuses on fuzzy relational calculus viewed as a basis of data compression. Images are fuzzy relations. We investigate fuzzy relational equations as a basis of image compression. It is shown that both compression and decompression (reconstruction) phases are closely linked with the way in which fuzzy relational equations are developed and solved. The theoretical findings encountered in the theory of these equations are easily accommodated as the backbone of the relational compression. The character of the solutions to the equations makes them ideal for reconstruction purposes as they specify the extremal elements of the solution set and in such a way help establish some envelopes of the original images under compression. The flexibility of the conceptual and algorithmic framework arising there is also discussed. Numerical examples provide a suitable illustrative material emphasizing the main features of the compression mechanisms. [ABSTRACT FROM AUTHOR]

In this study, we introduce and discuss a development of a highly interactive and user-friendly environment for an ECG signal analysis. The underlying neural architecture being a crux of this environment comes in the form of a self-organizing map. This map helps discover a structure in a set of ECG patterns and visualize a topology of the data. The role of the designer is to choose from some already visualized regions of the self-organizing map characterized by a significant level of data homogeneity and substantial difference from other regions. In the sequel, the regions are described by means of information granules—fuzzy sets that are essential in the characterization of the main relationships existing in the ECG data. The study introduces an original method of constructing membership functions that incorporates class membership as an important factor affecting changes in membership grades. The study includes a comprehensive descriptive modeling of highly dimensional ECG data. [Copyright &y& Elsevier]

Focuses on a study which investigated the decomposition of fuzzy relations. Optimization problem with regard to the decomposition of fuzzy relation; Experiments on fuzzy relations; Experimental studies; Conclusion.

In this study, we revisit the well-known notion of fuzzy state machines and discuss their development through learning. The systematic development of fuzzy state machines has not been pursued as intensively as it could have been expected from the breadth of the possible usage of them as various modelling platforms. We concentrate on the generalization of the well known architectures exploited in Boolean system synthesis, namely Moore and Mealy machines and show how these can be implemented in terms of generic functional modules such as fuzzy JK flip-flops and fuzzy logic neurons (AND and OR neurons) organized in the form of logic processors. It is shown that the design of the fuzzy state machines can be accomplished through their learning. The detailed learning algorithm is presented and illustrated with a series of numeric examples. The study reveals an interesting option of constructing digital systems through learning: the original problem is solved in the setting of fuzzy state machines and afterwards "binarised" into the two-valued format realized via the standard digital hardware. [ABSTRACT FROM AUTHOR]

Introduces a model of generalization and specialization of information granules. Use of fuzzy sets or fuzzy relations in generalization; Logic operators realized through triangular norms; Generalization process and its optimization.

Introduces a concept of relevance of fuzzy mappings regarded as fundamental constructs of granular computing and rule-based systems. Summary of the essence of shadowed-sets; Quantification of the relevance of the fuzzy mappings; Improvements to the level of the relevance of the mappings.

Applies fuzzy sets as a well-rounded algorithmic vehicle in the development of decision trees. Use of decision trees to solve classification problems; Elements of the clustering method used in exploratory data analysis; Efficacy of context-based clustering and the esulting discretization of attributes.

Information granules have been considered as the fundamental constructs of Granular Computing. As a useful unsupervised learning technique, Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information granules. The FCM-based granulation–degranulation mechanism plays a pivotal role in Granular Computing. In this paper, to enhance the quality of the degranulation (reconstruction) process, we augment the FCM-based degranulation mechanism by introducing a vector of fuzzification factors (fuzzification factor vector) and setting up an adjustment mechanism to modify the prototypes and the partition matrix. The design is regarded as an optimization problem, which is guided by a reconstruction criterion. In the proposed scheme, the initial partition matrix and prototypes are generated by the FCM. Then a fuzzification factor vector is introduced to form an appropriate fuzzification factor for each cluster to build up an adjustment scheme of modifying the prototypes and the partition matrix. With the supervised learning mode of the granulation–degranulation​ process, we construct a composite objective function of the fuzzification factor vector, the prototypes and the partition matrix. Subsequently, the particle swarm optimization is employed to optimize the fuzzification factor vector to refine the prototypes and develop the optimal partition matrix. Finally, the reconstruction performance of the FCM algorithm is enhanced. Overall, we show that the enhanced version of the degranulation process is beneficial to reduce the deterioration of the reconstruction results and improve the performance of the mechanism of granulation–degranulation, which is also meaningful for transforming data between numeric form and granular format. We offer a thorough analysis of the developed scheme. In particular, we show that the classical FCM algorithm forms a special case of the proposed scheme. Experiments completed for both synthetic and publicly available datasets demonstrate that the proposed approach outperforms the generic data reconstruction approach. [ABSTRACT FROM AUTHOR]

This research is a review and analysis paper that offers a transdisciplinary, methodological, and strategic vision for soft computing development towards a wider favorable impact in data analytics. Strategies are defined, explained, and illustrated by examples. The paper also shows how these strategies are expressed in three dimensions of an ambitious actions plan. They are all integrated into a master strategy called wide knowledge discovery, which offers a way towards the augmented analytics paradigm. Some contributions of this work are defining what kind of mathematical elements should be introduced into soft computing towards a better impact on the area of data analytics, offering orientation towards building new mathematical elements, and defining why and how they can be introduced. [ABSTRACT FROM AUTHOR]

• A novel locality preserving based fuzzy C-means clustering method (LPFCM) is presented. • An orthogonally projected space, which preserves the locality of structural properties, can be generated in LPFCM. • The capability of FCM for handling high-dimensional data can be enhanced. • The ideas of fuzzy clustering, geometric structure preservation and feature extraction are seamlessly integrated. • Experimental results on some benchmark data sets show the effectiveness of LPFCM. Traditional partition-based clustering algorithms, hard or fuzzy version of C-means, could not deal with high-dimensional data sets effectively as redundant features may impact the computation of distances and local spatial structures among patterns are rarely considered. High dimensionality of space gives rise to so-called concentration effect that is detrimental. In this paper, a novel locality preserving based fuzzy C-means (LPFCM) clustering method and its optimization are presented. An orthogonally projected space, which preserves the locality of structural properties, can be generated in LPFCM, thus enhancing the capability of fuzzy C-means (FCM) for handling high-dimensional data. It is the first time to introduce projection techniques to the FCM optimization objective function directly, and the ideas of fuzzy clustering, geometric structure preservation and feature extraction are seamlessly integrated. LPFCM is also regarded as a unified model that combines two separate stages of spectral clustering. Experimental results on some benchmark data sets show the effectiveness of LPFCM in comparison with FCM and some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Fuzzy rule-based models are widely employed to tackle regression problems due to their simplicity and comprehensibility. Numeric functions (e.g., linear ones) are generally utilized to represent the conclusion part of a rule, but this simple module cannot well describe the behavior of data located within local area defined by the premise part. In this study, a novel reinforced fuzzy clustering-based rule model (RFCRM) is presented to address this issue. First, information granulation (Fuzzy C-Means) approach is used to reveal the structure in the data and divide the input space into local regions, as well as form the premise parts. Second, the augmented Random Vector Functional Link Networks (RVFLNs) are employed as the conclusion parts to strengthen the description and representation of the behavior of data positioned within the local regions. Weighted Least Squares Error estimation with regularization is exploited to estimate the coefficients of the connection weights of RVFLN. Also, an exponential weight method benefited from the weight function theory encountered in harmonic analysis is introduced to improve the penalty strategy of regularization in coefficient estimation. More specifically, an exponential weighted ℓ 2 regularization (EW ℓ 2) strategy equipped with the exponential functions as the penalty terms is proposed to realize the targeted penalty on coefficients. The merit of EW ℓ 2 over ordinary ℓ 2 is that different types of polynomial terms can be identified and penalized separately in coefficient estimation. This strategy not only prevents the decline of generalization ability, but also effectively enhances the prediction potential of the model. By combining weighted LSE based on EW ℓ 2 with FCM partition and the augmented RVFLN leads to better prediction accuracy as well as lower complexity (viz., number of rules). Finally, detailed experimental studies are conducted to demonstrate the effectiveness of the proposed RFCRM. [ABSTRACT FROM AUTHOR]

• We propose a joint framework that integrates estimation, consistency improvement and consensus reaching into one phase. • We propose a minimum adjustment model with completeness, consistency, and consensus control (MAM-CCCC). • We present a completeness, consistency, and consensus reaching process (CCCRP) to support the GDM problems with incomplete fuzzy preference relations (FPRs). • We verify the effectiveness of MAM-CCCC through simulation and comparison analyses. In group decision making (GDM), there exists a situation in which experts may not able to provide comparative judgements regarding all pairs of alternatives, and therefore leading to the expression of incomplete preference. The existing frameworks to manage the GDM problem with incomplete preference relations have been investigated intensively and followed a common resolution scheme composed of three processes: estimation, consistency improvement, and consensus reaching. However, the consensus reaching process is applied after the estimation process and consistency improvement processes, leading to the destruction of the consistency of estimated preference relations, which will duplicate the process of improving consistency and consensus, resulting in significant adjustments of experts' preferences. To avoid this issue, we first propose a joint framework to integrate the consensus reaching process with estimation and consistency improvement. This framework is designed based on a minimum adjustment optimization model with completeness, consistency, and consensus control. It can produce complete preference relations with acceptable consistency and consensus, and simultaneously guarantee the minimum adjustment of experts' preferences. Finally, simulation and comparative analyses are used to justify the validity of the proposal. [ABSTRACT FROM AUTHOR]

• A novel forecasting model of LSTM-FPNN based on E_RWS is proposed to enhance the generalization abilities for time-series forecasting. • A new neuron driven by deep learning of LSTM is proposed to effectively learn temporal features. • A fuzzy polynomial neuron is used to capture the nonlinear characteristics of the data. • A hybrid selection strategy is developed to effectively increase the diversity of neurons. • The proposed LSTM-FPNN is applied to two practical domain problems to demonstrate its superiority. In this study, we propose a new self-organizing deep network architecture of fuzzy polynomial neural networks (FPNN) based on Fuzzy rule-based Polynomial Neurons (FPNs) and a long short-term memory (LSTM) network to solve the task of time-series forecasting. In the existing regression model based on polynomial neural networks (PNN), it is difficult to achieve high quality performance when predicting time series data, because this model lacks the ability to extract temporal and spatial information. Therefore, we propose a new architecture consisting of one LSTM (temporal) layer and several fuzzy polynomial (spatial) layers to overcome the above-mentioned shortcomings of PNN and enhance its predictive ability to approximate the data. The temporal layer consists of LSTM neurons that have inherently strong modeling capabilities to learn sequential information. The spatial layers are composed of Rule-based Polynomial Neurons (FPNs) that can effectively reflect the complex nonlinear structure found in the input space and granulate it using of the Fuzzy C-Means (FCM) clustering method. An elitism-driven roulette-wheel selection (E_RWS) is used to select appropriate neurons. E_RWS not only ensures that the neuron with the strongest fitting ability is selected but also increases the diversity of candidate neurons. According to the experimental results, the proposed model has a high prediction performance and outperforms many state-of-the-art prediction methods when applied to the real-world time-series. [ABSTRACT FROM AUTHOR]

This paper introduces some recent approaches to the fuzzy fractional Abel integral equations with respect to another function, which is called the fuzzy fractional Abel k −integral equations. The problem proposed here allows for the interpolation of different types of fuzzy classical fractional Abel integral equations, and the solvability of each type of integral equation is also discussed. Additionally, a new approach to the linear fuzzy fractional differential equations in the space of generalized fuzzy functions is introduced. Unlike previous approaches with gH-differentiability, this approach avoids making any prior assumptions about the solution's monotonic behavior during the solving process. It also overcomes the problem of multiple solutions for fuzzy fractional differential equations. To demonstrate the benefits of this approach, two initial value problems of linear fuzzy differential equations are compared using two different concepts of fractional derivatives: the Caputo fractional gH-differentiability and the Caputo fractional derivative in the generalized fuzzy space. Furthermore, some applications are provided in a viscoelastic material model and a population growth with harvesting model. [ABSTRACT FROM AUTHOR]

The product–service system (PSS) is a strategic design approach proposed to address sustainability in socio-economic systems amidst rapid industrialization and transition. Evaluating the concept design of a PSS is a crucial and initial step prior to implementation. This study presents an innovative framework for evaluating concept designs of sustainable PSS based on a well-defined evaluation index system via integrating quality function deployment (QFD) and the technique for order preference by similarity to ideal solution (TOPSIS) while accommodating extended basic uncertain linguistic information (EBULI). Specifically, a QFD-based framework is first developed to identify the requirements of various stakeholders and then to establish the multi-dimensional criteria for evaluating sustainable PSS. Then, a House of Quality-based relationship matrix is introduced to determine the weights of criteria more accurately. Further, an adaptive consensus-reaching process method based on an expert weighting optimization model is proposed to ensure a collective outputs recognized by multiple involved stakeholders. Finally, an improved EBULI-based TOPSIS method is presented to determine the priority ranking of alternative sustainable PSS concepts. A case study on a car-sharing PSS project demonstrates the viability and effectiveness of the proposed QFD–TOPSIS integrated approach under EBULI settings. The alternative PSS concept design, which demonstrates relatively good performance in criteria of high importance, is selected as the most suitable option. Moreover, relevant comparative and sensitivity analyses reveal that the proposed approach exhibits superiorities in appropriate criteria elicitation, accurate weights determination, and high consensus ranking outputs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a cascade AdaBoost neural network (CANN) based on concepts and construct of AdaBoost neurons and cascade structure. Compared with AdaBoost, CANN can represent complex relationships between features. In CANN, representation learning is performed through AdaBoost, and the method of random selection features is utilized to encourage the diversity of AdaBoost neurons. Through the cascade structure, CANN has the context structure for complex feature representation. At the same time, in order to avoid the problem of feature disappearance, shortcut connection is used to add the previous information to the later nodes. Furthermore, particle swarm optimization (PSO) algorithm is utilized to optimize the structure of CANN, it can obtain the number of iterations to achieve better performance. Two types of CANN are proposed based — binary-classification CANN (BCANN) or multi-classification CANN (MCANN). The performance of CANN is evaluated with two kinds of data sets: machine learning data sets and atrial fibrillation data set. A comparative analysis illustrates that the proposed CANN leads to better performance than the models reported in the literature. [ABSTRACT FROM AUTHOR]

Granular Computing (GrC) is a human-centric way to discover the fundamental structure of data sets. The resulting information granules can be efficiently exploited to organize knowledge and reveal data descriptions, which can play a pivotal role in the classification problems. Furthermore, information granules are abstract collections of data entities and exhibit flexibility and tolerance when it comes to the representation of incomplete data. However, most of the existing methods focused on the data imputation and classification separately. They also require better interpretability. The crux of this study is to develop a novel information granule-based classification method for incomplete data and a way of representing missing entities and regarding them as information granules in a unified framework. The first aspect focuses on revealing the structural backbone of multiple labeled subspaces of data by fuzzy clustering of missing values. It emerges a classifier with interpretable "IF-THEN" rules by the refinement of fuzzy prototypes in a supervised mode to capture the critical relationship of the multi-class incomplete data. The second aspect concerns the construction of some information granules to impute and represent missing values according to the refined prototypes and classification findings. The experimental studies involved synthetic and publicly available datasets in quantifying the advantages of the classification and representation abilities of the proposed methods on incomplete data. • We proposed a novel information granule-based classifier to reveal the structural of the subspaces of data, which is easier to be interpreted. • We considered incomplete data among classification modeling, so that this classifier can deal with the incomplete data straightforwardly. • We present a refinement mechanism for the information granule-based classifier to optimize the prototypes of the classification rules. • As a byproduct of the classification, the imputed information granules are distinguished from present data and have more tolerance to the imputation error. [ABSTRACT FROM AUTHOR]

Discusses the preprocessing phase of the design of radial basis function (RBF) neural networks accomplished through the mechanisms of data clustering. Information on the general architecture of the network along with computational details; Illumination of a role of clustering in the development of the radial basis units; Discussion on the role of conditional clustering regarded as a mechanism of search for data structure.

Presents a study which discussed a linguistic approach for the design of a category of fuzzy models. Features of the approach; Methodology; Conclusions.

Presents information on a study on fuzzy relational calculus regarded as a basis of data compression. Comparison of phases; Relational calculus in image compression; Experimental studies.

Proposes an idea of partial supervision realized in the form of a neural-network front end to the schemes of unsupervised learning (clustering). Development of neural-network front end to clustering algorithms; Learning of the preprocessor (NN); Simulation of the study; Conclusion.

Introduces a concept of shadowed sets that can be regarded as a certain operational framework simplifying processing carried out with the aid of fuzzy sets and enhancing interpretation of results obtained therein. Introduction of a constructive way in which shadowed sets are developed based on fuzzy sets; Problem of a formal definition and basic operations on shadowed sets; Discussion on the detailed computational aspects of shadowed sets.