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Generalized arithmetic operations in interval-valued fuzzy set theory

Glad Deschrijver (UGent) and Annelies Vroman
(2005) Journal of Intelligent and Fuzzy Systems. 16(4). p.265-271
Author
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:

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}},
}
Web of Science
Times cited: