Arithmetic operators in interval-valued fuzzy set theory
- Author
- Glad Deschrijver (UGent)
- 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: http://hdl.handle.net/1854/LU-376995
- 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}}, }