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  • Book
  • Open Access
  • © 2017

Theory and Applications of Ordered Fuzzy Numbers

A Tribute to Professor Witold Kosiński

  • Offers a comprehensive introduction to ordered fuzzy numbers

  • Demonstrates how to use ordered fuzzy numbers in real-world applications

  • Presents methods for trend modeling when only imprecise data is available

  • Includes supplementary material:

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 356)

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xviii
  2. Background of Fuzzy Set Theory

    1. Front Matter

      Pages 1-1
    2. Introduction to Fuzzy Sets

      • Michal Jezewski, Robert Czabanski, Jacek Leski
      Pages 3-22Open Access
    3. Introduction to Fuzzy Systems

      • Robert Czabanski, Michal Jezewski, Jacek Leski
      Pages 23-43Open Access
  3. Theory of Ordered Fuzzy Numbers

    1. Front Matter

      Pages 45-45
    2. Ordered Fuzzy Numbers: Sources and Intuitions

      • Piotr Prokopowicz, Dominik Ślȩzak
      Pages 47-56Open Access
    3. Ordered Fuzzy Numbers: Definitions and Operations

      • Piotr Prokopowicz, Dominik Ślȩzak
      Pages 57-79Open Access
    4. Processing Direction with Ordered Fuzzy Numbers

      • Piotr Prokopowicz
      Pages 81-98Open Access
    5. Comparing Fuzzy Numbers Using Defuzzificators on OFN Shapes

      • Jacek M. Czerniak, Wojciech T. Dobrosielski, Iwona Filipowicz
      Pages 99-132Open Access
    6. Two Approaches to Fuzzy Implication

      • Magdalena Kacprzak, Bartłomiej Starosta
      Pages 133-154Open Access
  4. Examples of Applications

    1. Front Matter

      Pages 155-155
    2. OFN Capital Budgeting Under Uncertainty and Risk

      • Anna Chwastyk, Iwona Pisz
      Pages 157-169Open Access
    3. Input-Output Model Based on Ordered Fuzzy Numbers

      • Dariusz Kacprzak
      Pages 171-182Open Access
    4. Ordered Fuzzy Candlesticks

      • Adam Marszałek, Tadeusz Burczyński
      Pages 183-194Open Access
    5. Detecting Nasdaq Composite Index Trends with OFNs

      • Hubert Zarzycki, Jacek M. Czerniak, Wojciech T. Dobrosielski
      Pages 195-205Open Access
    6. OFNAnt Method Based on TSP Ant Colony Optimization

      • Jacek M. Czerniak
      Pages 207-222Open Access
    7. A New OFNBee Method as an Example of Fuzzy Observance Applied for ABC Optimization

      • Dawid Ewald, Jacek M. Czerniak, Marcin Paprzycki
      Pages 223-237Open Access
    8. Fuzzy Observation of DDoS Attack

      • Łukasz Apiecionek
      Pages 239-252Open Access
    9. Fuzzy Control for Secure TCP Transfer

      • Łukasz Apiecionek
      Pages 253-268Open Access
    10. Fuzzy Numbers Applied to a Heat Furnace Control

      • Wojciech T. Dobrosielski, Jacek M. Czerniak, Hubert Zarzycki, Janusz Szczepański
      Pages 269-288Open Access

About this book

This book is open access under a CC BY 4.0 license.

This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike.


  • Fuzzy Numbers with Direction
  • Fuzzy Arithmetic
  • Defuzzyfication
  • Fuzzy Controllers
  • OFN Controllers
  • Fuzzy Prediction Models
  • Fuzzy Number Models
  • Trend Analysis
  • Trend processing
  • Uncertainty modeling
  • Propagation of uncertainty
  • Comparison of fuzzy models
  • Kosinski’s fuzzy numbers
  • Open Access

Editors and Affiliations

  • Faculty of Mathematics, Physics and Technical Science, Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, Bydgoszcz, Poland

    Piotr Prokopowicz, Dariusz Mikołajewski

  • Faculty of Mathematics, Physics and Technical Science, Institute of Technology, Kazimierz Wielki University, Bydgoszcz, Poland

    Jacek Czerniak, Łukasz Apiecionek

  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Dominik Ślȩzak

Bibliographic Information

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)