Interpretations of Association Rules by Granular Computing

We present interpretations for association rules. We first introduce Pawlak's method, and the corresponding algorithm of finding decision rules (a kind of association rules). We then use extended random sets to present a new algorithm of finding interesting rules. We prove that the new algorithm is faster than Pawlak's algorithm. The extended random sets are easily to include more than one criterion for determining interesting rules. We also provide two measures for dealing with uncertainties in association rules

Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

Dynamics of small-scale convective motions

Previous studies have discovered a population of small granules with diameters less than 800 km showing differing physical properties. High resolution simulations and observations of the solar granulation, in combination with automated segmentation and tracking algorithms, allow us to study the evolution of the structural and physical properties of these granules and surrounding vortex motions with high temporal and spatial accuracy. We focus on the dynamics of granules (lifetime, fragmentation, size, position, intensity, vertical velocity) over time and the influence of strong vortex motions. Of special interest are the dynamics of small granules compared to regular-sized granules. We developed a temporal tracking algorithm based on our developed segmentation algorithm for solar granulation. This was applied to radiation hydrodynamics simulations and high resolution observations of the quiet Sun by SUNRISE/IMaX. The dynamics of small granules differ in regard to their diameter, intensity and depth evolution compared to regular granules. The tracked granules in the simulation and observations reveal similar dynamics (lifetime, evolution of size, vertical velocity and intensity). The fragmentation analysis shows that the majority of granules in simulations do not fragment, while the opposite was found in observations. Strong vortex motions were detected at the location of small granules. Regions of strong vertical vorticity show high intensities and downflow velocities, and live up to several minutes. The analysis of granules separated according to their diameter in different groups reveals strongly differing behaviors. The largest discrepancies can be found within the groups of small, medium-sized and large granules and have to be analyzed independently. The predominant location of vortex motions on and close to small granules indicates a strong influence on the dynamics of granules

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

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

Sistemas granulares evolutivos

Orientador: Fernando Antonio Campos GomideTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Recentemente tem-se observado um crescente interesse em abordagens de modelagem computacional para lidar com fluxos de dados do mundo real. Métodos e algoritmos têm sido propostos para obtenção de conhecimento a partir de conjuntos de dados muito grandes e, a princípio, sem valor aparente. Este trabalho apresenta uma plataforma computacional para modelagem granular evolutiva de fluxos de dados incertos. Sistemas granulares evolutivos abrangem uma variedade de abordagens para modelagem on-line inspiradas na forma com que os humanos lidam com a complexidade. Esses sistemas exploram o fluxo de informação em ambiente dinâmico e extrai disso modelos que podem ser linguisticamente entendidos. Particularmente, a granulação da informação é uma técnica natural para dispensar atenção a detalhes desnecessários e enfatizar transparência, interpretabilidade e escalabilidade de sistemas de informação. Dados incertos (granulares) surgem a partir de percepções ou descrições imprecisas do valor de uma variável. De maneira geral, vários fatores podem afetar a escolha da representação dos dados tal que o objeto representativo reflita o significado do conceito que ele está sendo usado para representar. Neste trabalho são considerados dados numéricos, intervalares e fuzzy; e modelos intervalares, fuzzy e neuro-fuzzy. A aprendizagem de sistemas granulares é baseada em algoritmos incrementais que constroem a estrutura do modelo sem conhecimento anterior sobre o processo e adapta os parâmetros do modelo sempre que necessário. Este paradigma de aprendizagem é particularmente importante uma vez que ele evita a reconstrução e o retreinamento do modelo quando o ambiente muda. Exemplos de aplicação em classificação, aproximação de função, predição de séries temporais e controle usando dados sintéticos e reais ilustram a utilidade das abordagens de modelagem granular propostas. O comportamento de fluxos de dados não-estacionários com mudanças graduais e abruptas de regime é também analisado dentro do paradigma de computação granular evolutiva. Realçamos o papel da computação intervalar, fuzzy e neuro-fuzzy em processar dados incertos e prover soluções aproximadas de alta qualidade e sumário de regras de conjuntos de dados de entrada e saída. As abordagens e o paradigma introduzidos constituem uma extensão natural de sistemas inteligentes evolutivos para processamento de dados numéricos a sistemas granulares evolutivos para processamento de dados granularesAbstract: In recent years there has been increasing interest in computational modeling approaches to deal with real-world data streams. Methods and algorithms have been proposed to uncover meaningful knowledge from very large (often unbounded) data sets in principle with no apparent value. This thesis introduces a framework for evolving granular modeling of uncertain data streams. Evolving granular systems comprise an array of online modeling approaches inspired by the way in which humans deal with complexity. These systems explore the information flow in dynamic environments and derive from it models that can be linguistically understood. Particularly, information granulation is a natural technique to dispense unnecessary details and emphasize transparency, interpretability and scalability of information systems. Uncertain (granular) data arise from imprecise perception or description of the value of a variable. Broadly stated, various factors can affect one's choice of data representation such that the representing object conveys the meaning of the concept it is being used to represent. Of particular concern to this work are numerical, interval, and fuzzy types of granular data; and interval, fuzzy, and neurofuzzy modeling frameworks. Learning in evolving granular systems is based on incremental algorithms that build model structure from scratch on a per-sample basis and adapt model parameters whenever necessary. This learning paradigm is meaningful once it avoids redesigning and retraining models all along if the system changes. Application examples in classification, function approximation, time-series prediction and control using real and synthetic data illustrate the usefulness of the granular approaches and framework proposed. The behavior of nonstationary data streams with gradual and abrupt regime shifts is also analyzed in the realm of evolving granular computing. We shed light upon the role of interval, fuzzy, and neurofuzzy computing in processing uncertain data and providing high-quality approximate solutions and rule summary of input-output data sets. The approaches and framework introduced constitute a natural extension of evolving intelligent systems over numeric data streams to evolving granular systems over granular data streamsDoutoradoAutomaçãoDoutor em Engenharia Elétric

An Effective Multi-Resolution Hierarchical Granular Representation based Classifier using General Fuzzy Min-Max Neural Network

IEEE Motivated by the practical demands for simplification of data towards being consistent with human thinking and problem solving as well as tolerance of uncertainty, information granules are becoming important entities in data processing at different levels of data abstraction. This paper proposes a method to construct classifiers from multi-resolution hierarchical granular representations (MRHGRC) using hyperbox fuzzy sets. The proposed approach forms a series of granular inferences hierarchically through many levels of abstraction. An attractive characteristic of our classifier is that it can maintain a high accuracy in comparison to other fuzzy min-max models at a low degree of granularity based on reusing the knowledge learned from lower levels of abstraction. In addition, our approach can reduce the data size significantly as well as handle the uncertainty and incompleteness associated with data in real-world applications. The construction process of the classifier consists of two phases. The first phase is to formulate the model at the greatest level of granularity, while the later stage aims to reduce the complexity of the constructed model and deduce it from data at higher abstraction levels. Experimental analyses conducted comprehensively on both synthetic and real datasets indicated the efficiency of our method in terms of training time and predictive performance in comparison to other types of fuzzy min-max neural networks and common machine learning algorithms