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The study proposes a way of developing granular models based on optimized subsets of data with different sampling sizes, in which three generally used models, namely Support Vector Machine, K-Nearest Neighbor, and Long Short-Term Memory, are designed and transformed into granular version for achieving a good performance with sufficient functionality. First, a collection of subsets are determined using different sampling methods, which are subsequently applied to play as an essential prerequisite of the proposed models. Then, the principle of justifiable granularity is utilized to the design of interval information granules based on the subsets of data. The design process is associated with a well-defined optimization problem realized by achieving a sound compromise between two conflicting criteria: coverage and specificity. To evaluate the performance of the granular models, two aspects are considered: (i) sampling methods used in determining suitable subsets of data; (ii) different models applied to be transformed into granular models. A series of experimental studies are conducted to verify the feasibility of the proposed granular models. [ABSTRACT FROM AUTHOR]

This paper works on the claims data generated by individual policies which are randomly exposed to a period of continuous time. The main aim is to model the occurrence times of individual claims, as well as their developments given the feature information and exposure periods of individual policies, and thus project the outstanding liabilities. In this paper, we also propose a method to compute the moments of outstanding liabilities in an analytic form. It is significant for a general insurance company to more accurately project outstanding liabilities in risk management. It is well-known that the features of individual policies have effects on the occurrence of claims and their developments and thus the projection of outstanding liabilities. Neglecting the information can unquestionably decrease the prediction accuracy of stochastic reserving, where the accuracy is measured by the mean square error of prediction (MSEP), whose analytic form is computed according to the derived moments of outstanding liabilities. The parameters concerned in the proposed model are estimated based on likelihood and quasi-likelihood and the properties of estimated parameters are further studied. The asymptotic behavior of stochastic reserving is also investigated. The asymptotic distribution of parameter estimators is multivariate normal distribution which is a symmetric distribution and the asymptotic distribution of the deviation of the estimated loss reserving from theoretical loss reserve also follows a normal distribution. The confidence intervals for the parameter estimators and the deviation can be easily obtained through the symmetry of the normal distribution. Some simulations are conducted in order to support the main theoretical results. [ABSTRACT FROM AUTHOR]

This study proposes an optimized context-based Gustafson Kessel (CGK)-based fuzzy granular model based on the generation of rational information granules and an optimized CGK-based fuzzy granular model with the aggregated structure. The conventional context-based fuzzy-c-means (CFCM) clustering generates clusters considering the input and output spaces. However, the prediction performance decreases when the specific data points with geometric features are used. The CGK clustering solves the above situation by generating valid clusters considering the geometric attributes of data in input and output spaces with the aid of the Mahalanobis distance. However, it is necessary to generate rational information granules (IGs) because there is a significant change in performance according to the context generated in the output space and the shape, size, and several clusters generated in the input space. As a result, the rational IGs are obtained by considering the relationship between the coverage and specificity of IG using the genetic algorithm (GA). Thus, the optimized CGK-based fuzzy granular models with the aggregated structure are designed based on rational IGs. The prediction performance was compared using the two databases to verify the validity of the proposed method. Finally, the experiments revealed that the performance of the proposed method is higher than that of the previous model. [ABSTRACT FROM AUTHOR]

In this paper, we propose context-based GK clustering and design a CGK-based granular model and a hierarchical CGK-based granular model. Existing fuzzy clustering generates clusters using Euclidean distances. However, there is a problem in that performance decreases when a cluster is created from data with strong nonlinearity. To improve this problem, GK clustering is used. GK clustering creates clusters using Mahalanobis distance. In this paper, we propose context-based GK (CGK) clustering, which adds a method that considers the output space in the existing GK clustering, to create a cluster that considers not only the input space but also the output space. there is. Based on the proposed CGK clustering, a CGK-based granular model and a hierarchical CGK-based granular model were designed. Since the output of the CGK-based granular model is in the form of a context, it has the advantage of verbally expressing the prediction result, and the CGK-based granular model with a hierarchical structure can generate high-dimensional information granules, so meaningful information with high abstraction value granules can be created. In order to verify the validity of the method proposed in this paper, as a result of conducting an experiment using the concrete compressive strength database, it was confirmed that the proposed methods showed superior performance than the existing granular models. [ABSTRACT FROM AUTHOR]

This paper works on the claims data generated by individual policies which are randomly exposed to a period of continuous time. The main aim is to model the occurrence times of individual claims, as well as their developments given the feature information and exposure periods of individual policies, and thus project the outstanding liabilities. In this paper, we also propose a method to compute the moments of outstanding liabilities in an analytic form. It is significant for a general insurance company to more accurately project outstanding liabilities in risk management. It is well-known that the features of individual policies have effects on the occurrence of claims and their developments and thus the projection of outstanding liabilities. Neglecting the information can unquestionably decrease the prediction accuracy of stochastic reserving, where the accuracy is measured by the mean square error of prediction (MSEP), whose analytic form is computed according to the derived moments of outstanding liabilities. The parameters concerned in the proposed model are estimated based on likelihood and quasi-likelihood and the properties of estimated parameters are further studied. The asymptotic behavior of stochastic reserving is also investigated. The asymptotic distribution of parameter estimators is multivariate normal distribution which is a symmetric distribution and the asymptotic distribution of the deviation of the estimated loss reserving from theoretical loss reserve also follows a normal distribution. The confidence intervals for the parameter estimators and the deviation can be easily obtained through the symmetry of the normal distribution. Some simulations are conducted in order to support the main theoretical results.

This study proposes an optimized context-based Gustafson Kessel (CGK)-based fuzzy granular model based on the generation of rational information granules and an optimized CGK-based fuzzy granular model with the aggregated structure. The conventional context-based fuzzy-c-means (CFCM) clustering generates clusters considering the input and output spaces. However, the prediction performance decreases when the specific data points with geometric features are used. The CGK clustering solves the above situation by generating valid clusters considering the geometric attributes of data in input and output spaces with the aid of the Mahalanobis distance. However, it is necessary to generate rational information granules (IGs) because there is a significant change in performance according to the context generated in the output space and the shape, size, and several clusters generated in the input space. As a result, the rational IGs are obtained by considering the relationship between the coverage and specificity of IG using the genetic algorithm (GA). Thus, the optimized CGK-based fuzzy granular models with the aggregated structure are designed based on rational IGs. The prediction performance was compared using the two databases to verify the validity of the proposed method. Finally, the experiments revealed that the performance of the proposed method is higher than that of the previous model.

In this paper, we propose context-based GK clustering and design a CGK-based granular model and a hierarchical CGK-based granular model. Existing fuzzy clustering generates clusters using Euclidean distances. However, there is a problem in that performance decreases when a cluster is created from data with strong nonlinearity. To improve this problem, GK clustering is used. GK clustering creates clusters using Mahalanobis distance. In this paper, we propose context-based GK (CGK) clustering, which adds a method that considers the output space in the existing GK clustering, to create a cluster that considers not only the input space but also the output space. there is. Based on the proposed CGK clustering, a CGK-based granular model and a hierarchical CGK-based granular model were designed. Since the output of the CGK-based granular model is in the form of a context, it has the advantage of verbally expressing the prediction result, and the CGK-based granular model with a hierarchical structure can generate high-dimensional information granules, so meaningful information with high abstraction value granules can be created. In order to verify the validity of the method proposed in this paper, as a result of conducting an experiment using the concrete compressive strength database, it was confirmed that the proposed methods showed superior performance than the existing granular models.

This paper addresses the performance index (PI) of an incremental granular model (IGM) with information granules of linguistic intervals. For this purpose, IGM is designed by combining a linear regression (LR) and an interval-based granular model (GM). The fundamental scheme of IGM construction comprises two essential phases: (1) development of LR as a basic model and (2) design of a local granular model, which attempts to reduce errors obtained by the LR model. Here, the local interval-based GM is based on an interval-based fuzzy clustering algorithm, which is materialized by information granulations. The PI of IGM is calculated by multiplying the coverage with specificity property, because the output of IGM is not a numerical value but a linguistic interval value. From the concept of coverage and specificity, we can construct information granules; thus, it is justified by the available experimental proof and presented as clearly defined semantics. To validate the PI method, an experiment is conducted on concrete compressive strength for civil engineering applications. The experimental results confirm that the PI of IGM is an effective performance evaluation method. [ABSTRACT FROM AUTHOR]

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We present an experimental study of effective potential for several particle concentration cases in a bi-dimensional granular model of a glass-forming liquid during cooling. From particle positions, we obtained the radial distribution function and then based on it, the effective potential for the interparticle interaction is extracted via the Ornstein–Zernike equation using Percus–Yevick, hypernetted chain, and Rogers–Young closure relations. We note that the effective potential obtained via the Percus–Yevick approach is the one that best describes our system. The resulting effective potential shows how the spatial correlation increases, as observed through the formation of attractive wells while, the temperature decreases. In cases of high particle concentration close to the glass transition, we observed that several attractive wells appear in the effective potential curve. Under these conditions, particles are arrested by neighboring particles but retain enough kinetic energy to interact at long distances and produce structural changes in the system. For cases of low particle concentration, the changes in the effective potential as the system cools are very small. • Effective potential evolves from repulsive to attractive as temperature decreases. • Structures present higher local order as particle concentration increases. • The Perkus–Yevick approach describes better the physical behavior of the system. • Near glass transition temperature effective potential attractive wells are deeper. • As the temperature diminishes a well first appears and then goes deeper. [ABSTRACT FROM AUTHOR]

This paper addresses the performance index (PI) of an incremental granular model (IGM) with information granules of linguistic intervals. For this purpose, IGM is designed by combining a linear regression (LR) and an interval-based granular model (GM). The fundamental scheme of IGM construction comprises two essential phases: (1) development of LR as a basic model and (2) design of a local granular model, which attempts to reduce errors obtained by the LR model. Here, the local interval-based GM is based on an interval-based fuzzy clustering algorithm, which is materialized by information granulations. The PI of IGM is calculated by multiplying the coverage with specificity property, because the output of IGM is not a numerical value but a linguistic interval value. From the concept of coverage and specificity, we can construct information granules; thus, it is justified by the available experimental proof and presented as clearly defined semantics. To validate the PI method, an experiment is conducted on concrete compressive strength for civil engineering applications. The experimental results confirm that the PI of IGM is an effective performance evaluation method.

Processing realized in fuzzy rule-based models is associated with matching individual rules with the existing input data and aggregation of the levels of matching and conclusions of the rules. Rules are processed as individual entities. In this study, we introduce an augmentation of fuzzy models by facilitating interaction among the rules leading to more flexible type membership functions of fuzzy sets forming conditions of the rules (thus resulting in substantially advanced topology of the partition of the input space). Different ways of realizing interaction among the rules are studied. In the sequel, we develop a granular fuzzy model implied by the rule-based model showing how granular parameters of the original rule-based model enhance its quality expressed in terms of coverage of experimental data. The two evaluation criteria of the constructed granular model, namely coverage and specificity are studied. Experimental results are reported for a series of publicly available data. [ABSTRACT FROM AUTHOR]

In the present study, granular modelling with an interstitial power-law fluid was used to simulate the filling process in powder injection moulding (PIM). The granular model enables direct prediction of the density distribution. The feedstock, consisting of stainless steel powder and a multicomponent binder system, was injected in two moulds with designed features to verify the simulation results. The effects of the moulding parameters on the homogeneity of the powder particle distribution were investigated. The experimental results agreed well with the predictions. The results indicated that the granular model presented herein could be used for mould design and the determination of injection parameters. [ABSTRACT FROM AUTHOR]

The paper presents an automated system to report the evolution of a process in natural language expressions, analyzing wireless sensor data with process patterns by the linguistic description of complex phenomena approach. An implemented system generates reports of the composting process using the temperature measured in the core of a compost pile regarding the temperature pattern during the composting phases. The linguistic reports include sentences about the current status, trend, and behavior of the composting process. The automated system posts each linguistic report via a messaging app, such as Twitter , allowing instant and continuous communication with authorized users on mobile devices. The resulting expressions show that this real-time linguistic report system is a suitable and practical framework to inform users of the process evolution, in preference and complement to a database or graph tools, supporting the users to make decisions for processes that require proper data-interpretation-based supervision. • A proposed linguistic reporting system to describe the process evolution from a process pattern and real-time measured data. • Reports inform the user about the current status, tend, and behavior of the process. • Reports are natural language sentences posted to authorized users. • The real-time linguistic report system is a suitable framework for making decision support. • The composting process was reported using a pattern and data of temperature [ABSTRACT FROM AUTHOR]

Abstract: In this study, we introduce and discuss a concept of knowledge transfer in system modeling. In a nutshell, knowledge transfer is about forming ways on how a source of knowledge (namely, an existing model) can be used in presence of new, very limited experimental evidence. In virtue of the nature of the problem at hand (a situation encountered quite commonly, e.g. in project cost estimation), new data could be very limited and this scarcity of data makes it insufficient to construct a new model. At the same time, the new data originate from a similar (but not the same) phenomenon (process) for which the original model has been constructed so the existing model, even though it could applied, has to be treated with a certain level of reservation. Such situations can be encountered, e.g. in software engineering where in spite existing similarities, each project, process, or product exhibits its own unique characteristics. Taking this into consideration, the existing model is generalized (abstracted) by forming its granular counterpart – granular model where its parameters are regarded as information granules rather than numeric entities, viz. their non-numeric (granular) version is formed based on the values of the numeric parameters present in the original model. The results produced by the granular model are also granular and in this manner they become reflective of the differences existing between the current phenomenon and the process for which the previous model has been formed. In the study on knowledge transfer and reusability, information granularity is viewed as an important design asset and as such it is subject to optimization. We formulate an optimal information granularity allocation problem: assuming a certain level of granularity, distribute it optimally among the parameters of the model (making them granular) so that a certain data coverage criterion is maximized. While the underlying concept is general and applicable to a variety of models, in this study, we discuss its use to fuzzy neural networks with intent to clearly visualize the advantages of the approach and emphasize various ways of forming granular versions of the weights (parameters) of the connections of the network. Several granularity allocation protocols (ranging from a uniform distribution of granularity, symmetric and asymmetric schemes of allocation) are discussed and the effectiveness of each of them is quantified. The use of Particle Swarm Optimization (PSO) as the underlying optimization tool to realize optimal granularity allocation is discussed. [Copyright &y& Elsevier]

Two important factors affecting hot tearing – semi-solid constitutive behaviour and grain percolation – have been simulated through the use of microstructure models based on granular structures. The semi-solid model geometry is based on a modified Voronoi tessellation, and includes rounded corners to approximate an equiaxed-globular grain structure with liquid surrounding the grains. The percolation model combines solidification and thermodynamic aspects to predict the gradual transition within the mushy zone from a continuous liquid to a coherent solid network, while the constitutive behaviour model uses experimentally-derived data to describe the behaviour of the solid grains. By performing a series of model runs over ranges of grain size and fraction solid, the simulations have revealed an important link between grain size, semi-solid yield stress, strain localisation, and grain coalescence. Furthermore, the models provide insight on the relative importance of each mechanism on hot tear formation, and show promise for improving quantitative hot tearing predictions. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of granular modelling as a strategy to construct human-centred virtual prototype and environment models. This approach aims at providing a granular strategy for virtual prototype models in order to allow the change from a coarse-grain description to a fine-grain one according to the level of specification desired. The granular model is built from the aggregation of several component models and their interaction models, representing the interaction between two components. Component models must include information not only about themselves but also about the environmental part related to them. This is important as environmental conditions may have different effects at different scales/levels. Additionally, it leads to a higher level of communication, only allowed through the interaction models. This implies that new different objects might be integrated only by including their component models and their required interaction. The foreseen advantage is that the human is integrated in a simple manner: a component model corresponding to a haptic interface and an interaction model relating it to the virtual product. The first step, identification and organic description, consists of establishing an interaction graph from the hierarchical structure of the virtual product and all the objects that will be present in its future environment. Subsequently, the component and interactions models are constructed. The model is expected to be implemented into a multi-agent system where every component model derives into a component agent. [ABSTRACT FROM AUTHOR]

In this study, we introduce and discuss a concept of an incremental granular model. In contrast to typical rule-based systems encountered in fuzzy modeling, the underlying principle exploited here is to consider a two-phase development of fuzzy models. First, we build a standard regression model which could he treated as a preliminary construct capturing the linear part of the data and in this way forming a backbone of the entire construct. Next, all modeling discrepancies are compensated by a collection of rules that become attached to the regions of the input space where the error is localized. The incremental model is constructed by building a collection of information granules through some specialized fuzzy clustering, called context-based (conditional) fuzzy C-meaas that is guided by the distribution of error of the linear part of the model. The architecture of the model is discussed along with the major algorithmic phases of its development. In particular, the issue of granularity of fuzzy sets of context and induced clusters is discussed vis-a-vis the performance of the model. Numeric studies concern some Iow-dimensionul synthetic data and several datasets coming from the machine learning repository. [ABSTRACT FROM AUTHOR]

A description of quantitative dependencies by a novel type of fuzzy rules like ‘If X is SMALL then Y is QUICKLY INCREASING’ is considered. The use of such rules for representation of perception based and numerical information about dependencies between variables is discussed. These rules are based on a granulation of directions of function change or slope values. Perception based information given by rules is represented by a fuzzy function Y(X). A method of solution of a fuzzy equation Y(X)=B is considered. A linguistic representation of given numerical information about dependencies between variables X and Y is based on a fuzzy partition of the domain of X on fuzzy intervals, on a linear approximations of data on these intervals and on a linguistic retranslation of results. A genetic algorithm is used for obtaining fuzzy partitions. In conclusion, the possible applications of proposed methods in petroleum industry are discussed. [Copyright &y& Elsevier]

Highly conducting polymers such as polyaniline and polypyrrole in a metallic state have unusual frequency-dependent conductivity, including multiple zero crossing of the dielectric function. A low-frequency electromagnetic response in terms of a Drude metal is provided by an extremely small fraction of the total number of conduction electrons ∼0.1% but with extremely high mobility or anomalously long scattering time ∼10−13 s. We show that a network of metallic grains connected by resonance quantum tunneling has a Drude-type response for both the high- and low-frequency regimes and behaves as a dielectric at intermediate frequency in agreement with experimental observations. The metallic grains in polymers represent crystalline domains of well-packed chains with delocalized electrons embedded in the amorphous media of poor chain order. Intergrain resonance tunneling occurs through the strongly localized states in the amorphous media. [Copyright &y& Elsevier]

The nonlinear behaviour of a simply supported granular column loaded by an axial force is studied in this paper. The granular column is composed of rigid grains (discs) elastically connected by some shear and rotational springs. The in-plane buckling and post-buckling analysis in a geometrically exact framework is numerically investigated from a nonlinear difference eigenvalue problem. The granular column asymptotically behaves as an Engesser–Timoshenko column for a sufficiently large number of grains. An exact analytical solution of the buckling load of this discrete shear granular system is obtained from the linearization of the granular elastica problem. An asymptotic expansion is applied to the difference eigenvalue problem, to efficiently approximate the equation of the primary post-bifurcation branch of the discrete problem. Exact analytical solutions of the post-buckling branches are also available for the granular problem with few numbers of grains. Bifurcation diagrams of the granular elastica problem composed of few grains are numerically obtained with the simplex algorithm (for an exhaustive capture of all post-bifurcation branches). It is shown that the post-buckling of this granular column reveals complex behaviour similarly to the post-buckling of a generalized shear Hencky column (also called discrete Engesser elastica). Complex higher-order branches are exhibited, a phenomenon very similar to the discrete elastica problem. These branches reveal the specific nature of the discrete granular problem, as opposed to its continuum limit valid for an infinite number of grains • This paper presents exact bifurcation diagrams for the post-buckling branches of the granular elastica (granular column). • The in-plane buckling and post-buckling analysis in a geometrically exact framework is numerically investigated from a nonlinear difference eigenvalue problem. • The granular column asymptotically behaves as an Engesser–Timoshenko column for a sufficiently large number of grains. • An exact analytical solution of the buckling load of this discrete shear granular system is obtained from the linearization of the granular elastica problem. • Exact analytical solutions of the post-buckling branches are also available for the granular problem with few numbers of grains. • An asymptotic method is used to approximate the primary post-bifurcation branch. • Bifurcation diagrams of the granular elastica problem composed of few grains are numerically obtained with the simplex algorithm. • The post-buckling of this granular column reveals very rich behaviour in the bifurcation diagram. [ABSTRACT FROM AUTHOR]