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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

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Chicago
Deschrijver, Glad. 2007. “Arithmetic Operators in Interval-valued Fuzzy Set Theory.” Information Sciences 177 (14): 2906–2924.
APA
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. ELSEVIER SCIENCE INC; 2007;177(14):2906–24.
MLA
Deschrijver, Glad. “Arithmetic Operators in Interval-valued Fuzzy Set Theory.” Information Sciences 177.14 (2007): 2906–2924. Print.
@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 \unmatched{0141}ukasiewicz 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},
  language     = {eng},
  number       = {14},
  pages        = {2906--2924},
  publisher    = {ELSEVIER SCIENCE INC},
  title        = {Arithmetic operators in interval-valued fuzzy set theory},
  volume       = {177},
  year         = {2007},
}

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