Advanced search
1 file | 1.10 MB

Additive generators based on generalized arithmetic operators in interval-valued fuzzy and Atanassov's intuitionistic fuzzy set theory

Glad Deschrijver (UGent) and Etienne Kerre (UGent)
Author
Organization
Abstract
In this paper we investigate additive generators in Atanassov's intuitionistic fuzzy and interval-valued fuzzy set theory. Starting from generalized arithmetic operators satisfying some axioms we define additive generators and we characterize continuous generators which map exact elements to exact elements in terms of generators on the unit interval. We give necessary and sufficient condition under which a generator actually generates a t-nporm and we show that the generated t-norm belongs to particular classes of t-norms depending on the arithmetic operators involved in the defintion of the generator.
Keywords
additive generator, t-norm, Atanassov's intuitionistic fuzzy set, interval-valued fuzzy set

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 1.10 MB

Citation

Please use this url to cite or link to this publication:

Chicago
Deschrijver, Glad, and Etienne Kerre. 2016. “Additive Generators Based on Generalized Arithmetic Operators in Interval-valued Fuzzy and Atanassov’s Intuitionistic Fuzzy Set Theory.” In Imprecision and Uncertainty in Information Representation and Processing : New Tools Based on Intuitionistic Fuzzy Sets and Generalized Nets, ed. Plamen Angelov and Sotir Sotirov, 332:137–157. Cham, Switzerland: Springer.
APA
Deschrijver, Glad, & Kerre, E. (2016). Additive generators based on generalized arithmetic operators in interval-valued fuzzy and Atanassov’s intuitionistic fuzzy set theory. In Plamen Angelov & S. Sotirov (Eds.), Imprecision and uncertainty in information representation and processing : new tools based on intuitionistic fuzzy sets and generalized nets (Vol. 332, pp. 137–157). Cham, Switzerland: Springer.
Vancouver
1.
Deschrijver G, Kerre E. Additive generators based on generalized arithmetic operators in interval-valued fuzzy and Atanassov’s intuitionistic fuzzy set theory. In: Angelov P, Sotirov S, editors. Imprecision and uncertainty in information representation and processing : new tools based on intuitionistic fuzzy sets and generalized nets. Cham, Switzerland: Springer; 2016. p. 137–57.
MLA
Deschrijver, Glad, and Etienne Kerre. “Additive Generators Based on Generalized Arithmetic Operators in Interval-valued Fuzzy and Atanassov’s Intuitionistic Fuzzy Set Theory.” Imprecision and Uncertainty in Information Representation and Processing : New Tools Based on Intuitionistic Fuzzy Sets and Generalized Nets. Ed. Plamen Angelov & Sotir Sotirov. Vol. 332. Cham, Switzerland: Springer, 2016. 137–157. Print.
@incollection{8129549,
  abstract     = {In this paper we investigate additive generators in Atanassov's intuitionistic fuzzy and interval-valued fuzzy set theory. Starting from generalized arithmetic operators satisfying some axioms we define additive generators and we characterize continuous generators which map exact elements to exact elements in terms of generators on the unit interval. We give necessary and sufficient condition under which a generator actually generates a t-nporm and we show that the generated t-norm belongs to particular classes of t-norms depending on the arithmetic operators involved in the defintion of the generator.},
  author       = {Deschrijver, Glad and Kerre, Etienne},
  booktitle    = {Imprecision and uncertainty in information representation and processing : new tools based on intuitionistic fuzzy sets and generalized nets},
  editor       = {Angelov, Plamen and Sotirov, Sotir},
  isbn         = {9783319263021},
  issn         = {1434-9922},
  language     = {eng},
  pages        = {137--157},
  publisher    = {Springer},
  series       = {Studies in Fuzziness and Soft Computing},
  title        = {Additive generators based on generalized arithmetic operators in interval-valued fuzzy and Atanassov's intuitionistic fuzzy set theory},
  url          = {http://dx.doi.org/10.1007/978-3-319-26302-1\_10},
  volume       = {332},
  year         = {2016},
}

Altmetric
View in Altmetric