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Interval-valued algebras and fuzzy logics

Bart Van Gasse UGent, Chris Cornelis UGent and Glad Deschrijver UGent (2011) 35 Years of fuzzy set theory : celebratory volume dedicated to the retirement of Etienne E. Kerre. In Studies in Fuzziness and Soft Computing 261. p.57-82
abstract
In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter.
Please use this url to cite or link to this publication:
author
organization
year
type
bookChapter
publication status
published
subject
book title
35 Years of fuzzy set theory : celebratory volume dedicated to the retirement of Etienne E. Kerre
editor
Chris Cornelis UGent, Glad Deschrijver UGent, Mike Nachtegael UGent, Steven Schockaert UGent and Yun Shi UGent
series title
Studies in Fuzziness and Soft Computing
volume
261
pages
57 - 82
publisher
Springer
place of publication
Berlin, Germany
ISBN
9783642166280
DOI
10.1007/978-3-642-16629-7_4
language
English
UGent publication?
yes
classification
B2
copyright statement
I have transferred the copyright for this publication to the publisher
VABB id
c:vabb:339772
VABB type
VABB-4
id
1224869
handle
http://hdl.handle.net/1854/LU-1224869
date created
2011-05-16 17:04:34
date last changed
2011-06-08 17:20:53
@incollection{1224869,
  abstract     = {In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of {\textquoteleft}p implies q{\textquoteright} and {\textquoteleft}p and q{\textquoteright}, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter.},
  author       = {Van Gasse, Bart and Cornelis, Chris and Deschrijver, Glad},
  booktitle    = {35 Years of fuzzy set theory : celebratory volume dedicated to the retirement of Etienne E. Kerre},
  editor       = {Cornelis, Chris and Deschrijver, Glad and Nachtegael, Mike and Schockaert, Steven and Shi, Yun},
  isbn         = {9783642166280},
  language     = {eng},
  pages        = {57--82},
  publisher    = {Springer},
  series       = {Studies in Fuzziness and Soft Computing},
  title        = {Interval-valued algebras and fuzzy logics},
  url          = {http://dx.doi.org/10.1007/978-3-642-16629-7\_4},
  volume       = {261},
  year         = {2011},
}

Chicago
Van Gasse, Bart, Chris Cornelis, and Glad Deschrijver. 2011. “Interval-valued Algebras and Fuzzy Logics.” In 35 Years of Fuzzy Set Theory : Celebratory Volume Dedicated to the Retirement of Etienne E. Kerre, ed. Chris Cornelis, Glad Deschrijver, Mike Nachtegael, Steven Schockaert, and Yun Shi, 261:57–82. Berlin, Germany: Springer.
APA
Van Gasse, Bart, Cornelis, C., & Deschrijver, G. (2011). Interval-valued algebras and fuzzy logics. In C. Cornelis, G. Deschrijver, M. Nachtegael, S. Schockaert, & Y. Shi (Eds.), 35 Years of fuzzy set theory : celebratory volume dedicated to the retirement of Etienne E. Kerre (Vol. 261, pp. 57–82). Berlin, Germany: Springer.
Vancouver
1.
Van Gasse B, Cornelis C, Deschrijver G. Interval-valued algebras and fuzzy logics. In: Cornelis C, Deschrijver G, Nachtegael M, Schockaert S, Shi Y, editors. 35 Years of fuzzy set theory : celebratory volume dedicated to the retirement of Etienne E. Kerre. Berlin, Germany: Springer; 2011. p. 57–82.
MLA
Van Gasse, Bart, Chris Cornelis, and Glad Deschrijver. “Interval-valued Algebras and Fuzzy Logics.” 35 Years of Fuzzy Set Theory : Celebratory Volume Dedicated to the Retirement of Etienne E. Kerre. Ed. Chris Cornelis et al. Vol. 261. Berlin, Germany: Springer, 2011. 57–82. Print.