Many real-world problems require processing information that is incomplete, imprecise, conflicting, or supplied by multiple sources of varying reliability. Evidence theory provides a flexible framework for representing such information and reasoning with it.

Modern Evidence Theory develops a unified mathematical and computational framework that connects Dempster–Shafer theory and possibility theory through the concept of random fuzzy sets, as well as extends evidence-theoretic reasoning from finite frames of discernment to infinite spaces (in particular continuous ones). It covers evidence representation, combination and decision-making, with applications to uncertainty propagation, statistical inference and machine learning. Conceived both as a research monograph and as a textbook, it combines established theory with recent and previously unpublished developments.

Topics and features:

• Provides a unified framework for uncertainty quantification and information fusion
• Connects evidence theory with statistical inference and modern machine learning, including evidential classification and regression
• Includes numerous examples and end-of-chapter exercises
• Introduces practical models for continuous spaces, such as Gaussian random fuzzy numbers and vectors
• Presents rules for evidence combination, conditioning and marginalisation, as well as uncertainty measures and decision criteria
• Places the theory within the valuation-based systems framework, making it amenable to local computation
  
  

This volume is intended for researchers, graduate students and advanced practitioners in uncertainty modelling and quantification, information fusion, artificial intelligence, machine learning, statistics and engineering.It is also eminently suitable for readers in applied mathematics seeking a rigorous introduction to modern evidence theory and its recent developments.

Thierry Denœux is Professor at the Université de technologie de Compiègne, France, and a senior member of the Institut universitaire de France.

Thierry Denœux graduated from École Nationale des Ponts et Chaussées in Paris and earned a PhD from the same institution. He is currently a Full Professor of Exceptional Class with the Computer Science Department at Université de Technologie de Compiègne, France. He is the president of the Belief Functions and Applications Society. In 2019, he was appointed as a senior member of Institut Universitaire de France, and he was reconducted in 2024.

Thierry Denoeux is a renowned world expert in the theory of belief functions and the management of uncertainty in intelligent systems. His main contributions concern reasoning and decision-making under uncertainty, with applications to statistical inference, machine learning, and information fusion. He has authored over 350 papers in journals and conference proceedings and supervised more than 30 PhD theses. Denoeux currently serves as the Editor-in-Chief of the International Journal of Approximate Reasoning (Elsevier) and is an Associate Editor of several other academic journals.