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Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications

  • Book
  • © 2020

Overview

Editors:
  1. Olga Kosheleva

    1. Department of Teacher Education, University of Texas at El Paso, El Paso, USA

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  2. Sergey P. Shary

    1. Institute of Computational Technologies SB RAS, Novosibirsk, Russia

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  3. Gang Xiang

    1. Johns Creek, USA

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  4. Roman Zapatrin

    1. Deptartment of Informatics, The State Russian Museum, Saint Petersburg, Russia

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  • This book is about going beyond traditional probabilistic data processing techniques, to pursue interval, fuzzy, etc. methods – how to do it, and what the applications of the resulting non-traditional approaches are
  • Dedicated to Vladik Kreinovich on the occasion of his 65th birthday
  • Includes papers on constructive mathematics, fuzzy techniques, interval computations, uncertainty in general, and neural networks

Part of the book series: Studies in Computational Intelligence (SCI, volume 835)

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Table of contents (36 chapters)

  1. Front Matter

    Pages i-xi
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  2. Symmetries Are Important

    • Vladik Kreinovich
    Pages 1-5

  3. Constructive Mathematics

    1. Front Matter

      Pages 7-7
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    2. Constructive Continuity of Increasing Functions

      • Douglas S. Bridges
      Pages 9-19

    3. A Constructive Framework for Teaching Discrete Mathematics

      • Nelson Rushton
      Pages 21-46

  4. Fuzzy Techniques

    1. Front Matter

      Pages 47-47
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    2. Fuzzy Logic for Incidence Geometry

      • Rafik Aliev, Alex Tserkovny
      Pages 49-85

    3. Interval Valued Intuitionistic Fuzzy Sets Past, Present and Future

      • Krassimir Atanassov
      Pages 87-110

    4. Strengths of Fuzzy Techniques in Data Science

      • Bernadette Bouchon-Meunier
      Pages 111-119

    5. How to Enhance, Use and Understand Fuzzy Relational Compositions

      • Nhung Cao, Martin Štěpnička, Michal Burda, Aleš Dolný
      Pages 121-136

    6. Łukasiewicz Logic and Artificial Neural Networks

      • Antonio Di Nola, Gaetano Vitale
      Pages 137-149

    7. Impact of Time Delays on Networked Control of Autonomous Systems

      • Prasanna Kolar, Nicholas Gamez, Mo Jamshidi
      Pages 151-178

    8. Intervals and More: Aggregation Functions for Picture Fuzzy Sets

      • Erich Peter Klement, Radko Mesiar
      Pages 179-194

    9. The Interval Weighted Average and Its Importance to Type-2 Fuzzy Sets and Systems

      • Jerry M. Mendel
      Pages 195-211

    10. Fuzzy Answer Set Programming: From Theory to Practice

      • Mushthofa Mushthofa, Steven Schockaert, Martine De Cock
      Pages 213-228

    11. Impact and Applications of Fuzzy Cognitive Map Methodologies

      • Chrysostomos D. Stylios, Evaggelia Bourgani, Voula C. Georgopoulos
      Pages 229-246

  5. Interval Computations

    1. Front Matter

      Pages 247-247
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    2. Rigorous Global Filtering Methods with Interval Unions

      • Ferenc Domes, Tiago Montanher, Hermann Schichl, Arnold Neumaier
      Pages 249-267

    3. On the Computational Complexity of the Range Computation Problem

      • Peter Hertling
      Pages 269-293

    4. An Overview of Polynomially Computable Characteristics of Special Interval Matrices

      • Milan Hladík
      Pages 295-310
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Keywords

About this book

Data processing has become essential to modern civilization. The original data for this processing comes from measurements or from experts, and both sources are subject to uncertainty. Traditionally, probabilistic methods have been used to process uncertainty. However, in many practical situations, we do not know the corresponding probabilities: in measurements, we often only know the upper bound on the measurement errors; this is known as interval uncertainty. In turn, expert estimates often include imprecise (fuzzy) words from natural language such as "small"; this is known as fuzzy uncertainty. 
In this book, leading specialists on interval, fuzzy, probabilistic uncertainty and their combination describe state-of-the-art developments in their research areas. Accordingly, the book offers a valuable guide for researchers and practitioners interested in data processing under uncertainty, and an introduction to the latest trends and techniques in this area, suitablefor graduate students. 


Editors and Affiliations

  • Department of Teacher Education, University of Texas at El Paso, El Paso, USA

    Olga Kosheleva

  • Institute of Computational Technologies SB RAS, Novosibirsk, Russia

    Sergey P. Shary

  • Johns Creek, USA

    Gang Xiang

  • Deptartment of Informatics, The State Russian Museum, Saint Petersburg, Russia

    Roman Zapatrin

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