
Generalized arithmetic operations in interval-valued fuzzy set theory
- Author
- Glad Deschrijver (UGent) and Annelies Vroman
- Organization
- Abstract
- We generalize the addition, subtraction, multiplication and division on L^I defined in a previous paper, where L^I is the underlying lattice of both interval-valued fuzzy set theory and intuitionistic fuzzy set theory. We investigate some algebraic properties of these operations. We show that using these operations some important t-norms on L^I and some related operations can be written in a similar way as their counterparts on the unit interval.
- Keywords
- t-norm on L^I, arithmetic operations on L^I, addition, subtraction, multiplication, division
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-325931
- MLA
- Deschrijver, Glad, and Annelies Vroman. “Generalized Arithmetic Operations in Interval-Valued Fuzzy Set Theory.” Journal of Intelligent and Fuzzy Systems, vol. 16, no. 4, IOS Press, 2005, pp. 265–71.
- APA
- Deschrijver, G., & Vroman, A. (2005). Generalized arithmetic operations in interval-valued fuzzy set theory. Journal of Intelligent and Fuzzy Systems, 16(4), 265–271.
- Chicago author-date
- Deschrijver, Glad, and Annelies Vroman. 2005. “Generalized Arithmetic Operations in Interval-Valued Fuzzy Set Theory.” Journal of Intelligent and Fuzzy Systems 16 (4): 265–71.
- Chicago author-date (all authors)
- Deschrijver, Glad, and Annelies Vroman. 2005. “Generalized Arithmetic Operations in Interval-Valued Fuzzy Set Theory.” Journal of Intelligent and Fuzzy Systems 16 (4): 265–271.
- Vancouver
- 1.Deschrijver G, Vroman A. Generalized arithmetic operations in interval-valued fuzzy set theory. Journal of Intelligent and Fuzzy Systems. 2005;16(4):265–71.
- IEEE
- [1]G. Deschrijver and A. Vroman, “Generalized arithmetic operations in interval-valued fuzzy set theory,” Journal of Intelligent and Fuzzy Systems, vol. 16, no. 4, pp. 265–271, 2005.
@article{325931, abstract = {{We generalize the addition, subtraction, multiplication and division on L^I defined in a previous paper, where L^I is the underlying lattice of both interval-valued fuzzy set theory and intuitionistic fuzzy set theory. We investigate some algebraic properties of these operations. We show that using these operations some important t-norms on L^I and some related operations can be written in a similar way as their counterparts on the unit interval.}}, author = {{Deschrijver, Glad and Vroman, Annelies}}, issn = {{1064-1246}}, journal = {{Journal of Intelligent and Fuzzy Systems}}, keywords = {{t-norm on L^I,arithmetic operations on L^I,addition,subtraction,multiplication,division}}, language = {{eng}}, number = {{4}}, pages = {{265--271}}, publisher = {{IOS Press}}, title = {{Generalized arithmetic operations in interval-valued fuzzy set theory}}, volume = {{16}}, year = {{2005}}, }