This book presents the main tools for aggregation of information given by several members of a group or expressed in multiple criteria, and for fusion of data provided by several sources. It focuses on the case where the availability knowledge is imperfect, which means that uncertainty and/or imprecision must be taken into account. The book contains both theoretical and applied studies of aggregation and fusion methods in the main frameworks: probability theory, evidence theory, fuzzy set and possibility theory. The latter is more developed because it allows to manage both imprecise and uncertain knowledge. Applications to decision-making, image processing, control and classification are described.
This book presents the main tools for aggregation of information given by several members of a group or expressed in multiple criteria, and for fusion of data provided by several sources. It focuses on the case where the availability knowledge is imperfect, which means that uncertainty and/or imprecision must be taken into account. The book contains both theoretical and applied studies of aggregation and fusion methods in the main frameworks: probability theory, evidence theory, fuzzy set and possibility theory. The latter is more developed because it allows to manage both imprecise and uncertain knowledge. Applications to decision-making, image processing, control and classification are described.
Bayesian hypothesis testing inevitably requires prior probabilities of hypotheses. Motivated by human decision makers, this thesis studies how binary decision making is performed when the decision-making agents use imperfect prior probabilities. Three detection models with multiple agents are investigated: distributed detection with symmetric fusion, sequential detection with social learning, and distributed detection with symmetric fusion and social learning. In the distributed detection with symmetric fusion, we consider the agents to be a team aiming to minimize the Bayes risk of the team's decision. In this model, incorrect beliefs reduce the chance of the agents from being right so always lead to an increase in the Bayes risk of the decision-making team. In contrast, the role of beliefs is more complicated in the sequential detection model with social learning, where agents observe public signals, which are decisions made by other agents. Since each agent affects the minimum possible Bayes risk for subsequent agents, she may have a mixed objective including her own Bayes risk and the Bayes risks of subsequent agents. For an earlier-acting agent, it is shown that being informative to later-acting agents is different from being right. When private signals are described by Gaussian likelihoods, informative earlier-acting agents should be open-minded toward the unlikely hypothesis. Social learning helps imperfect agents who have favorable incorrect beliefs outperform perfect agents who have correct beliefs. Compared to in the sequential detection model, social learning is less influential in the distributed detection model with symmetric fusion. This is because social learning induces the evolution of the fusion rule in the distributed detection model, which countervails the other effect of social learning-belief update. In particular, social learning is futile when the agents observe conditionally independent and identically distributed private signals or when the agents require unanimity to make a decision. Since social learning is ineffective, imperfect agents cannot outperform perfect agents, unlike in the sequential detection model. Experiments about human behavior were performed in team decision-making situations when people should optimally ignore public signals. The experiments suggest that when people vote with equal qualities of information, the ballots should be secret.
This book collects the contributions presented at AGOP 2019, the 10th International Summer School on Aggregation Operators, which took place in Olomouc (Czech Republic) in July 2019. It includes contributions on topics ranging from the theory and foundations of aggregation functions to their various applications. Aggregation functions have numerous applications, including, but not limited to, data fusion, statistics, image processing, and decision-making. They are usually defined as those functions that are monotone with respect to each input and that satisfy various natural boundary conditions. In particular settings, these conditions might be relaxed or otherwise customized according to the user’s needs. Noteworthy classes of aggregation functions include means, t-norms and t-conorms, uninorms and nullnorms, copulas and fuzzy integrals (e.g., the Choquet and Sugeno integrals). This book provides a valuable overview of recent research trends in this area.
This book constitutes the proceedings of the 13th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2023, and 12th International Summer School on Aggregation Operators, AGOP 2023, jointly held in Palma de Mallorca, Spain, during September 4–8, 2023. The 71 full papers presented in this book were carefully reviewed and selected from 161 submissions. The papers are divided into special sessions on: Interval uncertainty; information fusion techniques based on aggregation functions, preaggregation functions and their generalizations; evaluative linguistic expressions, generalized quantifiers and applications; neural networks under uncertainty and imperfect information; imprecision modeling and management in XAI systems; recent trends in mathematical fuzzy logics; fuzzy graph-based models: theory and application; new frontiers of computational intelligence for pervasive healthcare systems; fuzzy implication functions; and new challenges and ideas in statistical inference and data analysis.
Information fusion is becoming a major requirement in data mining and knowledge discovery in databases. This book presents some recent fusion techniques that are currently in use in data mining, as well as data mining applications that use information fusion. Special focus of the book is on information fusion in preprocessing, model building and information extraction with various applications.
In 1982, Professor Pawlak published his seminal paper on what he called "rough sets" - a work which opened a new direction in the development of theories of incomplete information. Today, a decade and a half later, the theory of rough sets has evolved into a far-reaching methodology for dealing with a wide variety of issues centering on incompleteness and imprecision of information - issues which playa key role in the conception and design of intelligent information systems. "Incomplete Information: Rough Set Analysis" - or RSA for short - presents an up-to-date and highly authoritative account of the current status of the basic theory, its many extensions and wide-ranging applications. Edited by Professor Ewa Orlowska, one of the leading contributors to the theory of rough sets, RSA is a collection of nineteen well-integrated chapters authored by experts in rough set theory and related fields. A common thread that runs through these chapters ties the concept of incompleteness of information to those of indiscernibility and similarity.
Approximate reasoning is a key motivation in fuzzy sets and possibility theory. This volume provides a coherent view of this field, and its impact on database research and information retrieval. First, the semantic foundations of approximate reasoning are presented. Special emphasis is given to the representation of fuzzy rules and specialized types of approximate reasoning. Then syntactic aspects of approximate reasoning are surveyed and the algebraic underpinnings of fuzzy consequence relations are presented and explained. The second part of the book is devoted to inductive and neuro-fuzzy methods for learning fuzzy rules. It also contains new material on the application of possibility theory to data fusion. The last part of the book surveys the growing literature on fuzzy information systems. Each chapter contains extensive bibliographical material. Fuzzy Sets in Approximate Reasoning and Information Systems is a major source of information for research scholars and graduate students in computer science and artificial intelligence, interested in human information processing.
