Granular Computing

1. Front Matter

   Pages i-xvii

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2. Methodology and Mathematical Framework

   1. Front Matter

      Pages xix-xix

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   2. Granular Computing as an Emerging Paradigm of Information Processing

      • Andrzej Bargiela, Witold Pedrycz

      Pages 1-18

   3. Sets and Intervals

      • Andrzej Bargiela, Witold Pedrycz

      Pages 19-46

   4. Fuzzy Sets

      • Andrzej Bargiela, Witold Pedrycz

      Pages 47-79

   5. Rough Sets

      • Andrzej Bargiela, Witold Pedrycz

      Pages 81-97

   6. Generalizations of Information Granules

      • Andrzej Bargiela, Witold Pedrycz

      Pages 99-124

3. Algorithms of Information Granulation

   1. Front Matter

      Pages N1-N1

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   2. From Numbers to Information Granules

      • Andrzej Bargiela, Witold Pedrycz

      Pages 125-160

   3. Recursive Information Granulation

      • Andrzej Bargiela, Witold Pedrycz

      Pages 161-192

   4. Granular Prototyping in Fuzzy Clustering

      • Andrzej Bargiela, Witold Pedrycz

      Pages 193-215

   5. Logic-Based Fuzzy Clustering

      • Andrzej Bargiela, Witold Pedrycz

      Pages 217-233

   6. Semantical Stability of Information Granules

      • Andrzej Bargiela, Witold Pedrycz

      Pages 235-254

4. Granular World Communications

   1. Front Matter

      Pages N2-N2

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   2. Communications Between Granular Worlds: Fundamentals

      • Andrzej Bargiela, Witold Pedrycz

      Pages 255-265

   3. Networking of Granular Worlds: Collaborative Clustering

      • Andrzej Bargiela, Witold Pedrycz

      Pages 267-299

   4. Directional Models of Granular Communication

      • Andrzej Bargiela, Witold Pedrycz

      Pages 301-322

   5. Intelligent Agents and Granular Worlds

      • Andrzej Bargiela, Witold Pedrycz

      Pages 323-348

5. Granular Systems Applications

   1. Front Matter

      Pages N3-N3

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   2. Self-Organizing Maps in the Design and Processing of Granular Information

      • Andrzej Bargiela, Witold Pedrycz

      Pages 349-376

This book is about Granular Computing (GC) - an emerging conceptual and of information processing. As the name suggests, GC concerns computing paradigm processing of complex information entities - information granules. In essence, information granules arise in the process of abstraction of data and derivation of knowledge from information. Information granules are everywhere. We commonly use granules of time (seconds, months, years). We granulate images; millions of pixels manipulated individually by computers appear to us as granules representing physical objects. In natural language, we operate on the basis of word-granules that become crucial entities used to realize interaction and communication between humans. Intuitively, we sense that information granules are at the heart of all our perceptual activities. In the past, several formal frameworks and tools, geared for processing specific information granules, have been proposed. Interval analysis, rough sets, fuzzy sets have all played important role in knowledge representation and processing. Subsequently, information granulation and information granules arose in numerous application domains. Well-known ideas of rule-based systems dwell inherently on information granules. Qualitative modeling, being one of the leading threads of AI, operates on a level of information granules. Multi-tier architectures and hierarchical systems (such as those encountered in control engineering), planning and scheduling systems all exploit information granularity. We also utilize information granules when it comes to functionality granulation, reusability of information and efficient ways of developing underlying information infrastructures.

• Fuzzy
• Information
• Signal
• algorithm
• algorithms
• calculus
• communication
• data compression
• fuzzy set
• intelligent systems
• modeling
• set theory

• The Nottingham Trent University, Nottingham, UK

  Andrzej Bargiela

• University of Alberta, Edmonton, Canada

  Witold Pedrycz

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