Granular Computing as a Framework of System Modeling
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Granular Computing as a Framework of System Modeling Witold Pedrycz
Received: 2 December 2012 / Revised: 13 January 2013 / Accepted: 31 January 2013 / Published online: 5 March 2013 © Brazilian Society for Automatics–SBA 2013
Abstract The study is concerned with a concept of granular models, which form a generalization of (numeric) models commonly encountered in system modeling. Granular models are developed in the setting of Granular Computing and are predominantly concerned with the processing information granules forming conceptual and functional blocks of models. In particular, the parameters of these models are represented in the form of information granules. We discuss an origin and offer a motivation behind the construction of granular models. To make this study self-contained, a brief introduction to the formalism of information granules (including sets, fuzzy sets, rough sets, and shadowed sets) is presented with an emphasis placed on the key characteristics of these constructs and a role they play in system modeling. Keywords Information granules · Granular Computing · Granular model · Computational Intelligence · Rule-based models 1 Introduction In system modeling we have been continuously faced with new challenges associated with the ever growing complexity W. Pedrycz (B) Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada e-mail: [email protected] W. Pedrycz Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia W. Pedrycz Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
of systems to be modeled, a diversity of ways of looking at the same system and reconciling a variety of models being constructed in this setting, a need to cope with nonlinear and time varying systems, and requests to construct models that are human-centric in which humans play a pivotal role. We have been witnessing a plethora of models where various technologies have been exploited. Each of them has been found of particular interest and relevance with regard to a certain aspect of the rich research agenda. The facets of nonlinearity and variability of systems are quite commonly dealt with the technology of neural networks (Haykin 1999). The learning abilties are augmented by the use of neurocomputing. Likewise Evolutionary Computing (Goldberg 1989) and swarm intelligence (Engelbrecht 2005) are crucial in supporting mechanisms of structural optimization of the models. The human-centricity of system modeling, which becomes more profoundly visible in system modeling, embraces various aspects. In particular, intent is to make models more transparent and user-friendly as well as facilitate more active and visible role of users in the design of models and support further analysis of their results. Fuzzy sets plays here a visible role by giving rise to fuzzy models (Pedrycz and Gomide 2007). The objective of this study is to offer a general view at Granular Computing regarded as a conceptual and algo
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