Academic literature on the topic 'Fuzzy pattern'

Abstract. As one of the important research directions in the spatial data mining, spatial co-location pattern mining aimed at finding the spatial features whose the instances are frequent co-locate in neighbouring domain. With the introduction of fuzzy sets into traditional spatial co-location pattern mining, the research on fuzzy spatial co-location pattern mining has been deepened continuously, which extends traditional spatial co-location pattern mining to deal with fuzzy spatial objects and discover their laws of spatial symbiosis. In this paper, the operation principle of a classical join-based algorithm for mining spatial co-location patterns is briefly described firstly. Then, combining with the definition of classical participation rate and participation degree, a novel hesitant fuzzy spatial co-location pattern mining algorithm is proposed based on the establishment of the hesitant fuzzy participation rate and hesitant fuzzy participation formula according to the characteristics in fusion of hesitant fuzzy set theory, the score function and spatial co-location pattern mining. Finally, the proposed algorithm is written and implemented based on Python language, which uses a NumPy system to the expansion of the open source numerical calculation. The Python program of the proposed algorithm includes the method of computing hesitant fuzzy membership based on score function, the implementation of generating k-order candidate patterns, k-order frequent patterns and k-order table instances. A hesitant fuzzy spatial co-location pattern mining experiment is carried out and the experimental results show that the proposed and implemented algorithm is effective and feasible.

In this paper, we consider a soft computing approach to pattern classification. Our basic tools for soft computing are fuzzy relational calculus (FRC) and genetic algorithm (GA). We introduce a new interpretation of multidimensional fuzzy implication (MFI) to represent our knowledge about the training data set. We also consider the notion of a fuzzy pattern vector to handle the fuzzy information granules of the quantized pattern space and to represent a population of training patterns in the quantized pattern space. The construction of the pattern classifier is essentially based on the estimate of a fuzzy relation Ri between the antecedent clause and consequent clause of each one-dimensional fuzzy implication. For the estimation of Ri we use floating point representation of GA. Thus a set of fuzzy relations is formed from the new interpretation of MFI. This set of fuzzy relations is termed as the core of the pattern classifier. Once the classifier is constructed the non-fuzzy features of a test pattern can be classified. The performance of the proposed scheme is tested on synthetic data. Subsequently, we use the proposed scheme for the vowel classification problem of an Indian language. Finally, a benchmark of performance is established by considering multiplayer perception (MLP), support vector machine (SVM) and the present method. The Abalone, Hosse Colic and Pima Indians data sets, obtained from UCL database repository are used for the said benchmark study. This new tool for pattern classification is very effective for classification of patterns under vegue and imprecise environment. It can provide multiple classification under overlapped classes.

A method is proposed for evaluating fuzzy rules independently of each other in fuzzy rules learning. The proposed method is named α-FUZZI-ES (α-weight-based fuzzy-rule independent evaluations) in this paper. In α-FUZZI-ES, the evaluation value of a fuzzy system is divided out among the fuzzy rules by using the compatibility degrees of the learning data. By the effective use of α-FUZZI-ES, a method for fast fuzzy rules learning is proposed. This is named α-FUZZI-ES learning (α-FUZZI-ES-based fuzzy rules learning) in this paper. α-FUZZI-ES learning is especially effective when evaluation functions are not differentiable and derivative-based optimization methods cannot be applied to fuzzy rules learning. α-FUZZI-ES learning makes it possible to optimize fuzzy rules independently of each other. This property reduces the dimensionality of the search space in finding the optimum fuzzy rules. Thereby, α-FUZZI-ES learning can attain fast convergence in fuzzy rules optimization. Moreover, α-FUZZI-ES learning can be efficiently performed with hardware in parallel to optimize fuzzy rules independently of each other. Numerical results show that α-FUZZI-ES learning is superior to the exemplary conventional scheme in terms of accuracy and convergence speed when the evaluation function is non-differentiable.

Abstract The main objective of this paper is to introduce fuzzy sequential patterns with fuzzy time-intervals in quantitative sequence databases. In the fuzzy sequential pattern with fuzzy time-intervals, both quantitative attributes and time distances are represented by linguistic terms. A new algorithm based on the Apriori algorithm is proposed to find the patterns. The mined patterns can be applied to market basket analysis, stock market analysis, and so on.

PurposeThe purpose of this paper is to quickly acquire a cheongsam pattern using the fit quantification method to meet individual fit requirement.Design/methodology/approachBased on the cheongsam pattern database including basic patterns and graded patterns, we defined the main control parts of the cheongsam pattern by analyzing the pattern modification. Combining human body shape characteristics, this paper utilized the fuzzy membership function to quantify the cheongsam fit, and defined the modified model of the cheongsam control part.FindingsThe fitness quantification method can provide suitable primary body characteristics for custom-pattern and helps to produce customized cheongsam quickly.Originality/valueThis paper proposed a method of generating customized cheongsam pattern based on fitness quantification by using fuzzy membership function. The method combined the industry pattern design experience and mathematic knowledge to generate the individual fit pattern rapidly. It can be applied in cheongsam customization.

A first attempt to incorporate Fuzzy Cognitive Maps (FCMs), in pattern classification applications is performed in this paper. Fuzzy Cognitive Maps, as an illustrative causative representation of modeling and manipulation of complex systems, can be used to model the behavior of any system. By transforming a pattern classification problem into a problem of discovering the way the sets of patterns interact with each other and with the classes that they belong to, we could describe the problem in terms of Fuzzy Cognitive Maps. More precisely, some FCM architectures are introduced and studied with respect to their pattern recognition abilities. An efficient novel hybrid classifier is proposed as an alternative classification structure, which exploits both neural networks and FCMs to ensure improved classification capabilities. Appropriate experiments with four well-known benchmark classification problems and a typical computer vision application establish the usefulness of the Fuzzy Cognitive Maps, in a pattern recognition research field. Moreover, the present paper introduces the use of more flexible FCMs by incorporating nodes with adaptively adjusted activation functions. This advanced feature gives more degrees of freedom in the FCM structure to learn and store knowledge, as needed in pattern recognition tasks.

The Objective of this thesis is to talk about the usage of Fuzzy Logic in pattern recognition. There are different fuzzy approaches to recognize the pattern and the structure in data. The fuzzy approach that we choose to process the data is completely depends on the type of data. Pattern reorganization as we know involves various mathematical transforms so as to render the pattern or structure with the desired properties such as the identification of a probabilistic model which provides the explaination of the process generating the data clarity seen and so on and so forth. With this basic school of thought we plunge into the world of Fuzzy Logic for the process of pattern recognition. Fuzzy Logic like any other mathematical field has its own set of principles, types, representations, usage so on and so forth. Hence our job primarily would focus to venture the ways in which Fuzzy Logic is applied to pattern recognition and knowledge of the results. That is what will be said in topics to follow. Pattern recognition is the collection of all approaches that understand, represent and process the data as segments and features by using fuzzy sets. The representation and processing depend on the selected fuzzy technique and on the problem to be solved. In the broadest sense, pattern recognition is any form of information processing for which both the input and output are different kind of data, medical records, aerial photos, market trends, library catalogs, galactic positions, fingerprints, psychological profiles, cash flows, chemical constituents, demographic features, stock options, military decisions.. Most pattern recognition techniques involve treating the data as a variable and applying standard processing techniques to it.

Die Arbeit ordnet sich in das Gebiet der unscharfen Klassifikation ein und stellt im Detail eine Weiterführung der Forschung zur Fuzzy-Pattern-Klassifikation dar. Es handelt sich dabei um eine leistungsfähige systemtheoretische Methodik zur klassifikatorischen Modellierung komplexer, hochdimensionaler, technischer oder nichttechnischer Systeme auf der Basis von metrischen Messgrößen und/oder nichtmetrischen Experten-Bewertungen. Die Beschreibung der Unschärfe von Daten, Zuständen und Strukturen wird hierbei durch einen einheitlichen Typ einer Zugehörigkeitsfunktion des Potentialtyps realisiert. Ziel der Betrachtungen ist die weiterführende Nutzung des bestehenden Klassenmodells zur unscharfen Beschreibung nichtkonvexer Objektmengenmorphologien. Ausgehend vom automatischen datengetriebenen Aufbau der konvexen Klassenbeschreibung, deren vorteilhaften Eigenschaften sowie Defiziten wird im Rahmen der Arbeit eine Methodik vorgestellt, die eine Modellierung beliebiger Objektmengenmorphologien erlaubt, ohne das bestehende Klassifikationskonzept zu verlassen. Kerngedanken des Vorgehens sind: 1.) Die Aggregation von Fuzzy-Pattern-Klassen auf der Basis so genannter komplementärer Objekte. 2.) Die sequentielle Verknüpfung von Fuzzy-Pattern-Klassen und komplementären Klassen im Sinne einer unscharfen Mengendifferenz. 3.) Die Strukturierung des Verknüpfungsprozesses durch die Clusteranalyse von Komplementärobjektmengen und damit der Verwendung von Konfigurationen aus komplementären Fuzzy-Pattern-Klassen. Das dabei gewonnene nichtkonvexe Fuzzy-Klassifikationsmodell impliziert eine Vernetzung von Fuzzy-Klassifikatoren in Form von Klassifikatorbäumen. Im Ergebnis entstehen Klassifikatorstrukturen mit hoher Transparenz, die - neben der üblichen zustandsorientierten klassifikatorischen Beschreibung in den Einzelklassifikatoren - zusätzliche Informationen über den Ablauf der Klassifikationsentscheidungen erfassen. Der rechnergestützte Entwurf und die Eigenschaften der entstehenden Klassifikatorstruktur werden an akademischen Teststrukturen und realen Daten demonstriert. Die im Rahmen der Arbeit dargestellte Methodik wird in Zusammenhang mit dem Fuzzy-Pattern-Klassifikationskonzept realisiert, ist jedoch aufgrund ihrer Allgemeingültigkeit auf eine beliebige datenbasierte konvexe Klassenbeschreibung übertragbar
This work contributes to the field of fuzzy classification. It dedicates itself to the subject of "Fuzzy-Pattern-Classification", a versatile method applied for classificatory modeling of complex, high dimensional systems based on metric and nonmetric data, i.e. sensor readings or expert statements. Uncertainties of data, their associated morphology and therewith classificatory states are incorporated in terms of fuzziness using a uniform and convex type of membership function. Based on the properties of the already existing convex Fuzzy-Pattern-Class models and their automatic, data-driven setup a method for modeling nonconvex relations without leaving the present classification concept is introduced. Key points of the elaborated approach are: 1.) The aggregation of Fuzzy-Pattern-Classes with the help of so called complementary objects. 2.) The sequential combination of Fuzzy-Pattern-Classes and complementary Fuzzy-Pattern-Classes in terms of a fuzzy set difference. 3.) A clustering based structuring of complementary Fuzzy-Pattern-Classes and therewith a structuring of the combination process. A result of this structuring process is the representation of the resulting nonconvex fuzzy classification model in terms of a classifier tree. Such a nonconvex Fuzzy-Classifier features high transparency, which allows a structured understanding of the classificatory decision in working mode. Both the automatic data-based design as well as properties of such tree-like fuzzy classifiers will be illustrated with the help of academic and real word data. Even though the proposed method is introduced for a specific type of membership function, the underlying idea may be applied to any convex membership function

Der Gesetzgeber fordert von den Energieversorgungsunternehmen, ¨die Versorgung so sicher und billig wie moeglich zu gestalten¨. Um jederzeit ein stoerungsfreies und kostenguenstiges Angebot von elektrischer Energie zu gewaehrleisten, bedarf es einer moeglichst genauen Prognose der zu erwartenden Belastung im Versorgungsgebiet. Aufbauend auf den Erfahrungen bei der Prognose von Zeitreihen aus den Bereichen Umwelt und Verkehr wird in dieser Arbeit eine kurzfristige Vorhersage der elektrischen Belastung mit Hilfe der ¨Fuzzy-Pattern- Klassifikation¨ dargestellt. Dabei erfolgt die Modellbildung nicht allein auf der Basis der elektrischen Leistung, sondern wird durch zusaetzliche energiewirtschaftlich relevante Informationen, wie z.B. Klimadaten unterstuetzt. Zentraler Gegenstand der Untersuchungen ist die Frage, ob durch den Einsatz ergaenzender Informationen die Genauigkeit der Prognose bei kurzfristigen Vorhersagehorizonten (15 bis 120 Minuten) verbessert werden kann. Die mannigfaltigen Abhaengigkeiten zwischen elektrischer Belastung und ursaechlich wirkenden Einflussgroessen fuehren auf differenzierte Strategien zur Analyse und Prognose des Datenmaterials. Ausfuehrlich werden die Vorstrukturierung der Datenbasis, eine Prototypenmaskierung sowie die dynamische Parametrierung der Prognose erlaeutert und deren Wirksamkeit an realen Daten ueberprueft. Die Einschaetzungen zur Brauchbarkeit der Zusatzinformationen beruhen auf einem Vergleich von Prognoseresultaten der unterschiedlichen Modelle.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Esta dissertação investiga a utilização de sistemas Neuro- Fuzzy Hierárquicos BSP (Binary Space Partitioning) para classificação de padrões e para extração de regras fuzzy em bases de dados. O objetivo do trabalho foi criar modelos específicos para classificação de registros a partir do modelo Neuro-Fuzzy Hierárquico BSP que é capaz de gerar sua própria estrutura automaticamente e extrair regras fuzzy, lingüisticamente interpretáveis, que explicam a estrutura dos dados. O princípio da tarefa de classificação de padrões é descobrir relacionamentos entre os dados com a intenção de prever a classe de um padrão desconhecido. O trabalho consistiu fundamentalmente de quatro partes: um estudo sobre os principais métodos de classificação de padrões; análise do sistema Neuro-Fuzzy Hierárquico BSP (NFHB) original na tarefa de classificação; definição e implementação de dois sistemas NFHB específicos para classificação de padrões; e o estudo de casos. No estudo sobre os métodos de classificação foi feito um levantamento bibliográfico da área, resultando em um "survey" onde foram apresentadas as principais técnicas utilizadas para esta tarefa. Entre as principais técnicas destacaram-se: os métodos estatísticos, algoritmos genéticos, árvores de decisão fuzzy, redes neurais, e os sistemas neuro-fuzzy. Na análise do sistema NFHB na classificação de dados levou- se em consideração as peculiaridades do modelo, que possui: aprendizado da estrutura, particionamento recursivo do espaço de entrada, aceita maior número de entradas que os outros sistemas neuro-fuzzy, além de regras fuzzy recursivas. O sistema NFHB, entretanto, não é um modelo exatamente desenvolvido para classificação de padrões. O modelo NFHB original possui apenas uma saída e para utilizá- lo como um classificador é necessário criar um critério de faixa de valores (janelas) para representar as classes. Assim sendo, decidiu-se criar novos modelos que suprissem essa deficiência. Foram definidos dois novos sistemas NFHB para classificação de padrões: NFHB-Invertido e NFHB-Class. O primeiro utiliza a arquitetura do modelo NFHB original no aprendizado e em seguida a inversão da mesma para a validação dos resultados. A inversão do sistema consistiu de um meio de adaptar o novo sistema à tarefa específica de classificação, pois passou-se a ter o número de saídas do sistema igual ao número de classes ao invés do critério de faixa de valores utilizado no modelo NFHB original. Já o sistema NFHB-Class utilizou, tanto para a fase de aprendizado, quanto para a fase de validação, o modelo NFHB original invertido. Ambos os sistemas criados possuem o número de saídas igual ao número de classes dos padrões, o que representou um grande diferencial em relação ao modelo NFHB original. Além do objetivo de classificação de padrões, o sistema NFHB-Class foi capaz de extrair conhecimento em forma de regras fuzzy interpretáveis. Essas regras são expressas da seguinte maneira: SE x é A e y é B então padrão pertence à classe Z. Realizou-se um amplo estudo de casos, abrangendo diversas bases de dados Benchmark para a tarefa de classificação, tais como: Iris Dataset, Wine Data, Pima Indians Diabetes Database, Bupa Liver Disorders e Heart Disease, e foram feitas comparações com diversos modelos e algoritmos de classificação de padrões. Os resultados encontrados com os modelos NFHB-Invertido e NFHB-Class mostraram-se, na maioria dos casos, superiores ou iguais aos melhores resultados encontrados pelos outros modelos e algoritmos aos quais foram comparados.O desempenho dos modelos NFHB-Invertido e NFHB-Class em relação ao tempo de processamento também se mostrou muito bom. Para todas as bases de dados descritas no estudo de casos (capítulo 8), os modelos convergiram para uma ótima solução de classificação, além da extração das regras fuzzy, em
This dissertation investigates the use of Neuro-Fuzzy Hierarchical BSP (Binary Space Partitioning) systems for pattern classification and extraction of fuzzy rules in databases. The objective of this work was to create specific models for the classification of registers based on the Neuro-Fuzzy BSP model that is able to create its structure automatically and to extract linguistic rules that explain the data structure. The task of pattern classification is to find relationships between data with the intention of forecasting the class of an unknown pattern. The work consisted of four parts: study about the main methods of the pattern classification; evaluation of the original Neuro-Fuzzy Hierarchical BSP system (NFHB) in pattern classification; definition and implementation of two NFHB systems dedicated to pattern classification; and case studies. The study about classification methods resulted in a survey on the area, where the main techniques used for pattern classification are described. The main techniques are: statistic methods, genetic algorithms, decision trees, neural networks, and neuro-fuzzy systems. The evaluation of the NFHB system in pattern classification took in to consideration the particularities of the model which has: ability to create its own structure; recursive space partitioning; ability to deal with more inputs than other neuro-fuzzy system; and recursive fuzzy rules. The original NFHB system, however, is unsuited for pattern classification. The original NFHB model has only one output and its use in classification problems makes it necessary to create a criterion of band value (windows) in order to represent the classes. Therefore, it was decided to create new models that could overcome this deficiency. Two new NFHB systems were developed for pattern classification: NFHB-Invertido and NFHB-Class. The first one creates its structure using the same learning algorithm of the original NFHB system. After the structure has been created, it is inverted (see chapter 5) for the generalization process. The inversion of the structure provides the system with the number of outputs equal to the number of classes in the database. The second system, the NFHB-Class uses an inverted version of the original basic NFHB cell in both phases, learning and validation. Both systems proposed have the number of outputs equal to the number of the pattern classes, what means a great differential in relation to the original NFHB model. Besides the pattern classification objective, the NFHB- Class system was able to extract knowledge in form of interpretable fuzzy rules. These rules are expressed by this way: If x is A and y is B then the pattern belongs to Z class. The two models developed have been tested in many case studies, including Benchmark databases for classification task, such as: Iris Dataset, Wine Data, Pima Indians Diabetes Database, Bupa Liver Disorders and Heart Disease, where comparison has been made with several traditional models and algorithms of pattern classification. The results found with NFHB-Invertido and NFHB-Class models, in all cases, showed to be superior or equal to the best results found by the others models and algorithms for pattern classification. The performance of the NFHB- Invertido and NFHB-Class models in terms of time-processing were also very good. For all databases described in the case studies (chapter 8), the models converged to an optimal classification solution, besides the fuzzy rules extraction, in a time-processing inferior to a minute.
Esta disertación investiga el uso de sistemas Neuro- Fuzzy Herárquicos BSP (Binary Space Partitioning) en problemas de clasificación de padrones y de extracción de reglas fuzzy en bases de datos. El objetivo de este trabajo fue crear modelos específicos para clasificación de registros a partir del modelo Neuro-Fuzzy Jerárquico BSP que es capaz de generar automáticamente su propia extructura y extraer reglas fuzzy, lingüisticamente interpretables, que explican la extructura de los datos. El principio de la clasificación de padrones es descubrir relaciones entre los datos con la intención de prever la clase de un padrón desconocido. El trabajo está constituido por cuatro partes: un estudio sobre los principales métodos de clasificación de padrones; análisis del sistema Neuro-Fuzzy Jerárquico BSP (NFHB) original en la clasificación; definición e implementación de dos sistemas NFHB específicos para clasificación de padrones; y el estudio de casos. En el estudio de los métodos de clasificación se realizó un levatamiento bibliográfico, creando un "survey" donde se presentan las principales técnicas utilizadas. Entre las principales técnicas se destacan: los métodos estadísticos, algoritmos genéticos, árboles de decisión fuzzy, redes neurales, y los sistemas neuro-fuzzy. En el análisis del sistema NFHB para clasificación de datos se tuvieron en cuenta las peculiaridades del modelo, que posee : aprendizaje de la extructura, particionamiento recursivo del espacio de entrada, acepta mayor número de entradas que los otros sistemas neuro-fuzzy, además de reglas fuzzy recursivas. El sistema NFHB, sin embargo, no es un modelo exactamente desarrollado para clasificación de padrones. El modelo NFHB original posee apenas una salida y para utilizarlo conmo un clasificador fue necesario crear un criterio de intervalos de valores (ventanas) para representar las clases. Así, se decidió crear nuevos modelos que supriman esta deficiencia. Se definieron dos nuevos sistemas NFHB para clasificación de padrones: NFHB- Invertido y NFHB-Clas. El primero utiliza la arquitectura del modelo NFHB original en el aprendizaje y en seguida la inversión de la arquitectura para la validación de los resultados. La inversión del sistema es un medio para adaptar el nuevo sistema, específicamente a la clasificación, ya que el sistema pasó a tener número de salidas igual al número de clases, al contrario del criterio de intervalo de valores utilizado en el modelo NFHB original. En el sistema NFHB-Clas se utilizó, tanto para la fase de aprendizajeo, cuanto para la fase de validación, el modelo NFHB original invertido. Ambos sistemas poseen el número de salidas igual al número de clases de los padrones, lo que representa una gran diferencia en relación al modelo NFHB original. Además del objetivo de clasificación de padrones, el sistema NFHB-Clas fue capaz de extraer conocimento en forma de reglas fuzzy interpretables. Esas reglas se expresan de la siguiente manera: Si x es A e y es B entonces el padrón pertenece a la clase Z. Se realizó un amplio estudio de casos, utilizando diversas bases de datos Benchmark para la clasificación, tales como: Iris Dataset, Wine Data, Pima Indians Diabetes Database, Bupa Liver Disorders y Heart Disease. Los resultados se compararon con diversos modelos y algoritmos de clasificación de padrones. Los resultados encontrados con los modelos NFHB-Invertido y NFHB-Clas se mostraron, en la mayoría de los casos, superiores o iguales a los mejores resultados encontrados por los otros modelos y algoritmos con los cuales fueron comparados. El desempeño de los modelos NFHB-Invertido y NFHB-Clas en relación al tiempo de procesamiento tambiém se mostró muy bien. Para todas las bases de datos descritas en el estudio de casos (capítulo 8), los modelos convergieron para una solución óptima, además de la extracción de las reglas fuzzy, con tiemp

In this thesis we develop a novel network model that extends the traditional artificial neural network (ANN) model to include oscillatory behaviour. This model is able to correctly classify combinations of previously learned input patterns by grouping features that belong to the same category. This grouping process is termed segmentation and we show how synchrony of oscillations is the necessary missing component of ANNs to be able to perform this segmentation. Using this model we go on to show that top-down modulatory feedback is necessary to enable separation of multiple objects in a scene and segmentation of their individual features. This type of feedback is distinctly different than recurrency and is what enables the rich dynamics between the nodes of our network. Additionally, we show how our model's dynamics avoid the combinatorial explosion in required training repetitions of traditional feed-forward classification networks. In these networks, relations between objects must explicitly be learned. In contrast, the dynamics of modulatory feedback allow us to defer calculation of these relations until run-time, thus creating a more robust system. We call our model Fuzzy Oscillations, and it achieves good results when compared to existing models. However, oscillatory neural network models successful in achieving segmentation are a relatively recent development. We thus feel that our model is a contribution to the field of oscillatory neural networks.