Puzzle of Granular Computing

Bruno Apolloni is Full Professor in Computer Science in the University of Milano, Italy. His main research interests are at the frontier area between probability and mathematical statistics and computer science, with special interest to pattern recognition and multivariate data analysis, probabilistic analysis of algorithms, subsymbolic and symbolic learning processes, and fuzzy systems. Witold Pedrycz is Professor and Canada Research Chair (CRC) in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. He is also with the Systems Research Institute of the Polish Academy of Sciences. His dominant research is in Computational Intelligence, fuzzy modeling, knowledge discovery and data mining, pattern recognition, and knowledge-based neural networks. Dario Malchiodi is Assistant Professor in the Computer Science Department, University of Milano, Italy. His research activities concern the treatment of uncertain information and related aspects of mathematical statistics and artificial intelligence, including applications to machine learning and relevance learning. Simone Bassis is an assistant professor in the Department of Computer Science, University of Milano, Italy. His main research activities concern the inference of spatial and temporal processes, including linear and nonlinear statistical regression, fractal processes identification, and evolutionary dynamics.

• The General Framework.- Granule Formation Around Data.- I: Algorithmic Inference.- Modeling Samples.- Inferring from Samples.- II: The Development of Fuzzy Sets.- Construction of Information Granules: From Data and Perceptions to Information Granules.- Estimating Fuzzy Sets.- III: Expanding Granula into Boolean Functions.- The Clustering Problem.- Suitably Representing Data.- IV: Directing Populations.- The Main Paradigms of Social Computation.- If also Ants Are Able....- V: Granular Constructs.- Granular Constructs.- Identifying Fuzzy Rules.- A Conceptual Synthesis.- Knowledge Engineering.