Studies in Fuzziness and Soft Computing

Advances in Fuzzy Implication Functions

Editors: Baczyński, M., Beliakov, G., Bustince Sola, H., Pradera, A. (Eds.)

  • Recent research in Fuzzy Implication Operators
  • Timely collection of the most recent works in the area of Fuzzy Implications
  • Written by leading experts in the field
see more benefits

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-642-35677-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-3-642-35676-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-3-642-43779-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

Fuzzy implication functions are one of the main operations in fuzzy logic. They generalize the classical implication, which takes values in the set {0,1}, to fuzzy logic, where the truth values belong to the unit interval [0,1]. These functions are not only fundamental for fuzzy logic systems, fuzzy control, approximate reasoning and expert systems, but they also play a significant role in mathematical fuzzy logic, in fuzzy mathematical morphology and image processing, in defining fuzzy subsethood measures and in solving fuzzy relational equations.

 

This volume collects 8 research papers on fuzzy implication functions.

Three articles focus on the construction methods, on different ways of generating new classes and on the common properties of implications and their dependencies. Two articles discuss implications defined on lattices, in particular implication functions in interval-valued fuzzy set theories. One paper summarizes the sufficient and necessary conditions of solutions for one distributivity equation of implication. The following paper analyzes compositions based on a binary operation * and discusses the dependencies between the algebraic properties of this operation and the induced sup-* composition. The last article discusses some open problems related to fuzzy implications, which have either been completely solved or those for which partial answers are known. These papers aim to present today’s state-of-the-art in this area.

Reviews

From the reviews:

“The editors of this book have assembled a collection of eight papers from a select group of researchers. … they provide relevant and useful information on the latest advances in the research area of fuzzy implication functions. … The information in the papers requires experience with fuzzy logic, targeted at either the serious researcher or the expert practitioner well versed in fuzzy logic. For those readers, I highly recommend this book to augment their current study of fuzziness and soft computing.” (Eric W. Yocam, Computing Reviews, September, 2013)

Table of contents (8 chapters)

  • An Overview of Construction Methods of Fuzzy Implications

    Massanet, Sebastià (et al.)

    Pages 1-30

  • Fuzzy Implications: Classification and a New Class

    Shi, Yun (et al.)

    Pages 31-51

  • A Survey of the Distributivity of Implications over Continuous T-norms and the Simultaneous Satisfaction of the Contrapositive Symmetry

    Qin, Feng (et al.)

    Pages 53-72

  • Implication Functions in Interval-Valued Fuzzy Set Theory

    Deschrijver, Glad

    Pages 73-99

  • (S,N)-Implications on Bounded Lattices

    Bedregal, Benjamín (et al.)

    Pages 101-124

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-642-35677-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-3-642-35676-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-3-642-43779-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Advances in Fuzzy Implication Functions
Editors
  • Michał Baczyński
  • Gleb Beliakov
  • Humberto Bustince Sola
  • Ana Pradera
Series Title
Studies in Fuzziness and Soft Computing
Series Volume
300
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-35677-3
DOI
10.1007/978-3-642-35677-3
Hardcover ISBN
978-3-642-35676-6
Softcover ISBN
978-3-642-43779-3
Series ISSN
1434-9922
Edition Number
1
Number of Pages
VII, 209
Topics