Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published “Fuzzy Sets” [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory

BigFCM: Fast, Precise and Scalable FCM on Hadoop

Clustering plays an important role in mining big data both as a modeling technique and a preprocessing step in many data mining process implementations. Fuzzy clustering provides more flexibility than non-fuzzy methods by allowing each data record to belong to more than one cluster to some degree. However, a serious challenge in fuzzy clustering is the lack of scalability. Massive datasets in emerging fields such as geosciences, biology and networking do require parallel and distributed computations with high performance to solve real-world problems. Although some clustering methods are already improved to execute on big data platforms, but their execution time is highly increased for large datasets. In this paper, a scalable Fuzzy C-Means (FCM) clustering named BigFCM is proposed and designed for the Hadoop distributed data platform. Based on the map-reduce programming model, it exploits several mechanisms including an efficient caching design to achieve several orders of magnitude reduction in execution time. Extensive evaluation over multi-gigabyte datasets shows that BigFCM is scalable while it preserves the quality of clustering

Fuzzy Systems

This book presents some recent specialized works of theoretical study in the domain of fuzzy systems. Over eight sections and fifteen chapters, the volume addresses fuzzy systems concepts and promotes them in practical applications in the following thematic areas: fuzzy mathematics, decision making, clustering, adaptive neural fuzzy inference systems, control systems, process monitoring, green infrastructure, and medicine. The studies published in the book develop new theoretical concepts that improve the properties and performances of fuzzy systems. This book is a useful resource for specialists, engineers, professors, and students

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Color Image Segmentation Using Fuzzy C-Regression Model

Image segmentation is one important process in image analysis and computer vision and is a valuable tool that can be applied in fields of image processing, health care, remote sensing, and traffic image detection. Given the lack of prior knowledge of the ground truth, unsupervised learning techniques like clustering have been largely adopted. Fuzzy clustering has been widely studied and successfully applied in image segmentation. In situations such as limited spatial resolution, poor contrast, overlapping intensities, and noise and intensity inhomogeneities, fuzzy clustering can retain much more information than the hard clustering technique. Most fuzzy clustering algorithms have originated from fuzzy c-means (FCM) and have been successfully applied in image segmentation. However, the cluster prototype of the FCM method is hyperspherical or hyperellipsoidal. FCM may not provide the accurate partition in situations where data consists of arbitrary shapes. Therefore, a Fuzzy C-Regression Model (FCRM) using spatial information has been proposed whose prototype is hyperplaned and can be either linear or nonlinear allowing for better cluster partitioning. Thus, this paper implements FCRM and applies the algorithm to color segmentation using Berkeley’s segmentation database. The results show that FCRM obtains more accurate results compared to other fuzzy clustering algorithms

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

Fuzzy logic based approach for object feature tracking

This thesis introduces a novel technique for feature tracking in sequences of greyscale images based on fuzzy logic. A versatile and modular methodology for feature tracking using fuzzy sets and inference engines is presented. Moreover, an extension of this methodology to perform the correct tracking of multiple features is also presented. To perform feature tracking three membership functions are initially defined. A membership function related to the distinctive property of the feature to be tracked. A membership function is related to the fact of considering that the feature has smooth movement between each image sequence and a membership function concerns its expected future location. Applying these functions to the image pixels, the corresponding fuzzy sets are obtained and then mathematically manipulated to serve as input to an inference engine. Situations such as occlusion or detection failure of features are overcome using estimated positions calculated using a motion model and a state vector of the feature. This methodology was previously applied to track a single feature identified by the user. Several performance tests were conducted on sequences of both synthetic and real images. Experimental results are presented, analysed and discussed. Although this methodology could be applied directly to multiple feature tracking, an extension of this methodology has been developed within that purpose. In this new method, the processing sequence of each feature is dynamic and hierarchical. Dynamic because this sequence can change over time and hierarchical because features with higher priority will be processed first. Thus, the process gives preference to features whose location are easier to predict compared with features whose knowledge of their behavior is less predictable. When this priority value becomes too low, the feature will no longer tracked by the algorithm. To access the performance of this new approach, sequences of images where several features specified by the user are to be tracked were used. In the final part of this work, conclusions drawn from this work as well as the definition of some guidelines for future research are presented.Nesta tese é introduzida uma nova técnica de seguimento de pontos característicos de objectos em sequências de imagens em escala de cinzentos baseada em lógica difusa. É apresentada uma metodologia versátil e modular para o seguimento de objectos utilizando conjuntos difusos e motores de inferência. É também apresentada uma extensão desta metodologia para o correcto seguimento de múltiplos pontos característicos. Para se realizar o seguimento são definidas inicialmente três funções de pertença. Uma função de pertença está relacionada com a propriedade distintiva do objecto que desejamos seguir, outra está relacionada com o facto de se considerar que o objecto tem uma movimentação suave entre cada imagem da sequência e outra função de pertença referente à sua previsível localização futura. Aplicando estas funções de pertença aos píxeis da imagem, obtêm-se os correspondentes conjuntos difusos, que serão manipulados matematicamente e servirão como entrada num motor de inferência. Situações como a oclusão ou falha na detecção dos pontos característicos são ultrapassadas utilizando posições estimadas calculadas a partir do modelo de movimento e a um vector de estados do objecto. Esta metodologia foi inicialmente aplicada no seguimento de um objecto assinalado pelo utilizador. Foram realizados vários testes de desempenho em sequências de imagens sintéticas e também reais. Os resultados experimentais obtidos são apresentados, analisados e discutidos. Embora esta metodologia pudesse ser aplicada directamente ao seguimento de múltiplos pontos característicos, foi desenvolvida uma extensão desta metodologia para esse fim. Nesta nova metodologia a sequência de processamento de cada ponto característico é dinâmica e hierárquica. Dinâmica por ser variável ao longo do tempo e hierárquica por existir uma hierarquia de prioridades relativamente aos pontos característicos a serem seguidos e que determina a ordem pela qual esses pontos são processados. Desta forma, o processo dá preferência a pontos característicos cuja localização é mais fácil de prever comparativamente a pontos característicos cujo conhecimento do seu comportamento seja menos previsível. Quando esse valor de prioridade se torna demasiado baixo, esse ponto característico deixa de ser seguido pelo algoritmo. Para se observar o desempenho desta nova abordagem foram utilizadas sequências de imagens onde várias características indicadas pelo utilizador são seguidas. Na parte final deste trabalho são apresentadas as conclusões resultantes a partir do desenvolvimento deste trabalho, bem como a definição de algumas linhas de investigação futura

Optimization for Decision Making II

In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner

New rough set based maximum partitioning attribute algorithm for categorical data clustering

Clustering a set of data into homogeneous groups is a fundamental operation in data mining. Recently, consideration has been put on categorical data clustering, where the data set consists of non-numerical attributes. However, implementing several existing categorical clustering algorithms is challenging as some cannot handle uncertainty while others have stability issues. The Rough Set theory (RST) is a mathematical tool for dealing with categorical data and handling uncertainty. It is also used to identify cause-effect relationships in databases as a form of learning and data mining. Therefore, this study aims to address the issues of uncertainty and stability for categorical clustering, and it proposes an improved algorithm centred on RST. The proposed method employed the partitioning measure to calculate the information system's positive and boundary regions of attributes. Firstly, an attributes partitioning method called Positive Region-based Indiscernibility (PRI) was developed to address the uncertainty issue in attribute partitioning for categorical data. The PRI method requires the positive and boundary regions-based partitioning calculation method. Next, to address the computational complexity issue in the clustering process, a clustering attribute selection method called Maximum Mean Partitioning (MMP) is introduced by computing the mean. The MMP method selects the maximum degree of the mean attribute, and the attribute with the maximum mean partitioning value is chosen as the best clustering attribute. The integration of proposed PRI and MMP methods generated a new rough set hybrid clustering algorithm for categorical data clustering algorithm named Maximum Partitioning Attribute (MPA) algorithm. This hybrid algorithm is an all-inclusive solution for uncertainty, computational complexity, cluster purity, and higher accuracy in attribute partitioning and selecting a clustering attribute. The proposed MPA algorithm is compared against the baseline algorithms, namely Maximum Significance Attribute (MSA), Information-Theoretic Dependency Roughness (ITDR), Maximum Indiscernibility Attribute (MIA), and simple classical K-Mean. In addition, seven small data sets from previously utilized research cases and 21 UCI repository and benchmark datasets are used for validation. Finally, the results were presented in tabular and graphical form, showing the proposed MPA algorithm outperforms the baseline algorithms for all data sets. Furthermore, the results showed that the proposed MPA algorithm improves the rough accuracy against MSA, ITDR, and MIA by 54.42%. Hence, the MPA algorithm has reduced the computational complexity compared to MSA, ITDR, and MIA with 77.11% less time and 58.66% minimum iterations. Similarly, a significant percentage improvement, up to 97.35%, was observed for overall purity by the MPA algorithm against MSA, ITDR, and MIA. In addition, the increment up to 34.41% of the overall accuracy of simple K-means by MPA has been obtained. Hence, it is proven that the proposed MPA has given promising solutions to address the categorical data clustering problem

Interpretive structural model of key performance indicators for sustainable manufacturing evaluation in automotive companies

This paper aims to analyze the interrelationships among the key performance indicators of sustainable manufacturing evaluation in automotive companies. The initial key performance indicators have been identified and derived from literature and were then validated by industry survey. Interpretive structural modeling (ISM) methodology is applied to develop a hierarchical structure of the key performance indicators in three levels. Of nine indicators, there are five unstable indicators which have both high driver and dependence power, thus requiring further attention. It is believed that the model can provide a better insight for automotive managers in assessing their sustainable manufacturing performance