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Arithmetic operators in interval-valued fuzzy set theory

(2007) Information Sciences. 177(14). p.2906-2924
Author
Organization
Abstract
We introduce the addition, subtraction, multiplication and division on L^I, where L^I is the underlying lattice of both interval-valued fuzzy set theory (R. Sambuc) and intuitionistic fuzzy set theory (K.T. Atanassov). We investigate some algebraic properties of these operators. We show that using these operators the pseudo-t-representable extensions of the Łukasiewicz t-norm and the product t-norm on the unit interval to L^I and some related operators can be written in a similar way as their counterparts on the unit interval.
Keywords
arithmetic operators on L^I, t-norm on L^I, sum, difference, product, quotient, addition, subtraction, multiplication, division

Citation

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

MLA
Deschrijver, Glad. “Arithmetic Operators in Interval-Valued Fuzzy Set Theory.” Information Sciences, vol. 177, no. 14, ELSEVIER SCIENCE INC, 2007, pp. 2906–24.
APA
Deschrijver, G. (2007). Arithmetic operators in interval-valued fuzzy set theory. Information Sciences, 177(14), 2906–2924.
Chicago author-date
Deschrijver, Glad. 2007. “Arithmetic Operators in Interval-Valued Fuzzy Set Theory.” Information Sciences 177 (14): 2906–24.
Chicago author-date (all authors)
Deschrijver, Glad. 2007. “Arithmetic Operators in Interval-Valued Fuzzy Set Theory.” Information Sciences 177 (14): 2906–2924.
Vancouver
1.
Deschrijver G. Arithmetic operators in interval-valued fuzzy set theory. Information Sciences. 2007;177(14):2906–24.
IEEE
[1]
G. Deschrijver, “Arithmetic operators in interval-valued fuzzy set theory,” Information Sciences, vol. 177, no. 14, pp. 2906–2924, 2007.
@article{376995,
  abstract     = {{We introduce the addition, subtraction, multiplication and division on L^I, where L^I is the underlying lattice of both interval-valued fuzzy set theory (R. Sambuc) and intuitionistic fuzzy set theory (K.T. Atanassov). We investigate some algebraic properties of these operators. We show that using these operators the pseudo-t-representable extensions of the Łukasiewicz t-norm and the product t-norm on the unit interval to L^I and some related operators can be written in a similar way as their counterparts on the unit interval.}},
  author       = {{Deschrijver, Glad}},
  issn         = {{0020-0255}},
  journal      = {{Information Sciences}},
  keywords     = {{arithmetic operators on L^I,t-norm on L^I,sum,difference,product,quotient,addition,subtraction,multiplication,division}},
  language     = {{eng}},
  number       = {{14}},
  pages        = {{2906--2924}},
  publisher    = {{ELSEVIER SCIENCE INC}},
  title        = {{Arithmetic operators in interval-valued fuzzy set theory}},
  volume       = {{177}},
  year         = {{2007}},
}

Web of Science
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