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Combining Soft Computing and Statistical Methods in Data Analysis
Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishi...
Soft Methods for Handling Variability and Imprecision
Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy i...
Building Bridges between Soft and Statistical Methodologies for Data Science
Nowadays, data analysis is becoming an appealing topic due to the emergence of new data types, dimensions, and sources. This motivates the development of probabilistic/statistical approaches and tools to cope with these data. Different communities of experts, namely statisticians, mathematicians, computer scientists, engineers, econometricians, and psychologists are more and more interested in facing this challenge. As a consequence, there is a clear need to build bridges between all these communities for Data Science. This book contains more than fifty selected recent contributions aiming to establish the above referred bridges. These contributions address very different and relevant aspects such as imprecise probabilities, information theory, random sets and random fuzzy sets, belief functions, possibility theory, dependence modelling and copulas, clustering, depth concepts, dimensionality reduction of complex data and robustness.
Combining, Modelling and Analyzing Imprecision, Randomness and Dependence
This volume contains more than 65 peer-reviewed papers corresponding to presentations at the 11th Conference on Soft Methods in Probability and Statistics (SMPS) held in Salzburg, Austria, in September 2024. It covers recent advances in the field of probability, statistics, and data science, with a particular focus on dealing with dependence, imprecision and incomplete information. Reflecting the fact that data science continues to evolve, this book serves as a bridge between different groups of experts, including statisticians, mathematicians, computer scientists, and engineers, and encourages interdisciplinary research. The selected contributions cover a wide range of topics such as imprecise probabilities, random sets, belief functions, possibility theory, and dependence modeling. Readers will find discussions on clustering, depth concepts, dimensionality reduction, and robustness, reflecting the conference's commitment to addressing real-world challenges through innovative methods.
The Mathematics of the Uncertain
This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlig...
Uncertainty Modelling in Data Science
This book features 29 peer-reviewed papers presented at the 9th International Conference on Soft Methods in Probability and Statistics (SMPS 2018), which was held in conjunction with the 5th International Conference on Belief Functions (BELIEF 2018) in Compiègne, France on September 17–21, 2018. It includes foundational, methodological and applied contributions on topics as varied as imprecise data handling, linguistic summaries, model coherence, imprecise Markov chains, and robust optimisation. These proceedings were produced using EasyChair. Over recent decades, interest in extensions and alternatives to probability and statistics has increased significantly in diverse areas, including ...
Technologies for Constructing Intelligent Systems 2
Intelligent systems enhance the capacities made available by the internet and other computer-based technologies. This book is devoted to various aspects of the management of intelligent systems. Particular attention is paid to situations in which the available information and data may be imprecise, uncertain, incomplete or of linguistic nature. Various methods developed to manage such information are discussed in the context of several domains of application. Topics included in the book include preference modelling and decision making, learning, clustering and data mining, information retrieval. The paradigm of computing with words is also addressed.
Statistical Modeling, Analysis and Management of Fuzzy Data
The contributions in this book state the complementary rather than competitive relationship between Probability and Fuzzy Set Theory and allow solutions to real life problems with suitable combinations of both theories.
Synergies of Soft Computing and Statistics for Intelligent Data Analysis
In recent years there has been a growing interest to extend classical methods for data analysis. The aim is to allow a more flexible modeling of phenomena such as uncertainty, imprecision or ignorance. Such extensions of classical probability theory and statistics are useful in many real-life situations, since uncertainties in data are not only present in the form of randomness --- various types of incomplete or subjective information have to be handled. About twelve years ago the idea of strengthening the dialogue between the various research communities in the field of data analysis was born and resulted in the International Conference Series on Soft Methods in Probability and Statistics (...
