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Additive and multiplicative generators in interval-valued fuzzy set theory

Author
Organization
Abstract
In this paper, we introduce the notion of additive and multiplicative generator on L^I, which is the underlying lattice of interval-valued fuzzy set theory. A special class of generators on L^I is the class of representable generators which can be represented using generators on the unit interval. A representation of involutive negators on L^I by means of continuous additive generators which is similar to the representation of involutive negators on the unit interval is given. We also investigate additive and multiplicative generators of t-norms on L^I.
Keywords
additive generator, addition on L^I, involutive negator, multiplication on L^I, multiplicative generator, representable generator, t-norm

Citation

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Chicago
Deschrijver, Glad. 2007. “Additive and Multiplicative Generators in Interval-valued Fuzzy Set Theory.” IEEE Transactions on Fuzzy Systems 15 (2): 222–237.
APA
Deschrijver, Glad. (2007). Additive and multiplicative generators in interval-valued fuzzy set theory. IEEE Transactions on Fuzzy Systems, 15(2), 222–237.
Vancouver
1.
Deschrijver G. Additive and multiplicative generators in interval-valued fuzzy set theory. IEEE Transactions on Fuzzy Systems. IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC; 2007;15(2):222–37.
MLA
Deschrijver, Glad. “Additive and Multiplicative Generators in Interval-valued Fuzzy Set Theory.” IEEE Transactions on Fuzzy Systems 15.2 (2007): 222–237. Print.
@article{368181,
  abstract     = {In this paper, we introduce the notion of additive and multiplicative generator on L\^{ }I, which is the underlying lattice of interval-valued fuzzy set theory. A special class of generators on L\^{ }I is the class of representable generators which can be represented using generators on the unit interval. A representation of involutive negators on L\^{ }I by means of continuous additive generators which is similar to the representation of involutive negators on the unit interval is given. We also investigate additive and multiplicative generators of t-norms on L\^{ }I.},
  author       = {Deschrijver, Glad},
  issn         = {1063-6706},
  journal      = {IEEE Transactions on Fuzzy Systems},
  language     = {eng},
  number       = {2},
  pages        = {222--237},
  publisher    = {IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC},
  title        = {Additive and multiplicative generators in interval-valued fuzzy set theory},
  volume       = {15},
  year         = {2007},
}

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