Fuzzy Sets and Their Extensions: Representation, Aggregation and Models

1. Front Matter

   Pages I-XX

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2. Foundations: Representation and Aggregation

   1. Front Matter

      Pages 1-1

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   2. Type-2 Fuzzy Logic and the Modelling of Uncertainty

      • Simon Coupland, Robert John

      Pages 3-22

   3. My Personal View on Intuitionistic Fuzzy Sets Theory

      • Krassimir T. Atanassov

      Pages 23-43

   4. Hybridization of Fuzzy and Rough Sets: Present and Future

      • Eric C. C. Tsang, QingCai Chen, Suyun Zhao, Daniel S. Yeung, Xizhao Wang

      Pages 45-64

   5. An Overview of Computing with Words using Label Semantics

      • Jonathan Lawry

      Pages 65-87

   6. On the Construction of Models Based on Fuzzy Measures and Integrals

      • Vicenç Torra

      Pages 89-97

   7. Interpolatory Type Construction of General Aggregation Operators

      • Gleb Beliakov, Tomasa Calvo

      Pages 99-120

   8. A Review of Aggregation Functions

      • Radko Mesiar, Anna Kolesárová, Tomasa Calvo, Magda Komorníková

      Pages 121-144

   9. Identification of Weights in Aggregation Operators

      • Tomasa Calvo, Gleb Beliakov

      Pages 145-162

   10. Linguistic Aggregation Operators: An Overview

       • Zeshui Xu

       Pages 163-181

   11. Aggregation Operators in Interval-valued Fuzzy and Atanassov’s Intuitionistic Fuzzy Set Theory

       • Glad Deschrijver, Etienne Kerre

       Pages 183-203

3. From Decision Making to Data Mining, Web Intelligence and Computer Vision

   1. Front Matter

      Pages 205-205

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   2. Fuzzy Preference Modelling: Fundamentals and Recent Advances

      • János Fodor, Bernard de Baets

      Pages 207-217

   3. Preferences and Consistency Issues in Group Decision Making

      • Francisco Chiclana, Enrique Herrera-Viedma, Sergio Alonso, Ricardo Alberto, Marques Pereira

      Pages 219-237

   4. Fuzzy Set Extensions of the Dominance-Based Rough Set Approach

      • Salvatore Greco, Benedetto Matarazzo, Roman Słowiński

      Pages 239-261

   5. On Group Decision Making, Consensus Reaching, Voting and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and some Perspectives

      • Janusz Kacprzyk, Sławomir Zadrożny, Mario Fedrizzi, Hannu Nurmi

      Pages 263-295

   6. Extension of Some Voting Systems to the Field of Gradual Preferences

      • Bonifacio Llamazares, José Luis García-Lapresta

      Pages 297-315

   7. A Linguistic Decision Based Model Applied to Olive Oil Sensory Evaluation

      • Luis Martínez, Luis G. Pérez, Jun Liu

      Pages 317-334

   8. Atanassov’s Intuitionistic Fuzzy Sets as a Promising Tool for Extended Fuzzy Decision Making Models

      • Eulalia Szmidt, Janusz Kacprzyk

      Pages 335-355

Fuzzy Sets and Their Extensions: Representation, Aggregation and Models Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision Fuzzy sets are now more than 40 years old, and have come of age. However, the development of fuzzy set theory at the theoretical level, and its successful appli- tions to science and technology have often run in isolation. Only a little part of the theoretical apparatus was effectively used in past applications. The most prominent ones, namely fuzzy rule-based modeling and control engineering, were directly - spired from a seminal paper by Lot? Zadeh in 1973, suggesting how to use expert knowledge for synthetizing control laws, and from the ?rst experiments published by Abe Mamdani. Later in the eighties, when spectacular applications were bl- soming in Japan, fuzzy rule-based systems were systematized and simpli?ed by Michio Sugeno and colleagues, and became a basic approach to non-linear system modeling and control, soon hybridized with neural networks in the nineties. Thus fuzzy systems signi?cantly contributed to the raise of computational intelligence, and a lot of learning techniques for the construction of (supposedly interpretable) fuzzy models from data were developed under the ?ag of soft computing. Even if this area was quite successful, it is patent that the role, in the success of fuzzy logic, of new fuzzy set-related concepts developed quite at the same time in themathematicalnicheofthefuzzyset communitywaslimited.

• Computer Vision
• Fuzziness
• Fuzzy
• Soft Computing
• algorithms
• data mining
• fuzzy logic
• fuzzy set
• image processing
• intelligent systems
• logic
• machine learning
• model
• modeling
• semantics

• Department of Automatics and Computation, Universidad Pública de Navarra, Spain

  Humberto Bustince

• Department of Computer Science and Artificial Intelligence (DECSAI), University of Granada, Periodista Daniel Saucedo Aranda s/n, Spain

  Francisco Herrera

• Faculty of Mathematics, Universidad Complutense, 28040 Madrid, Spain

  Javier Montero

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