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Convolution on bounded lattices

Laura De Miguel, Humberto Bustince and Bernard De Baets (UGent)
(2018) ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1. In Advances in Intelligent Systems and Computing 641. p.585-596
Author
Organization
Abstract
The union and intersection of two membership degrees of type-2 fuzzy sets are defined using a generalization of the mathematical operation of convolution. In the literature, it has been deeply studied when these convolution operations constitute a bounded distributive lattice. In this paper, we generalize the union and intersection convolution operations by replacing the functions from [0, 1] to itself with functions from a bounded lattice L-1 to a frame L-2, a particular type of bounded lattice. Similarly to some previous studies in the literature, we analyze when these new convolution operations constitute a bounded distributive lattice.
Keywords
FUZZY SETS, FINITE, TYPE-2, Convolution operation, Bounded lattice, Fuzzy logic

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MLA
De Miguel, Laura, et al. “Convolution on Bounded Lattices.” ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1, vol. 641, Springer, 2018, pp. 585–96, doi:10.1007/978-3-319-66830-7_52.
APA
De Miguel, L., Bustince, H., & De Baets, B. (2018). Convolution on bounded lattices. ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1, 641, 585–596. https://doi.org/10.1007/978-3-319-66830-7_52
Chicago author-date
De Miguel, Laura, Humberto Bustince, and Bernard De Baets. 2018. “Convolution on Bounded Lattices.” In ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1, 641:585–96. Cham: Springer. https://doi.org/10.1007/978-3-319-66830-7_52.
Chicago author-date (all authors)
De Miguel, Laura, Humberto Bustince, and Bernard De Baets. 2018. “Convolution on Bounded Lattices.” In ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1, 641:585–596. Cham: Springer. doi:10.1007/978-3-319-66830-7_52.
Vancouver
1.
De Miguel L, Bustince H, De Baets B. Convolution on bounded lattices. In: ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1. Cham: Springer; 2018. p. 585–96.
IEEE
[1]
L. De Miguel, H. Bustince, and B. De Baets, “Convolution on bounded lattices,” in ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1, Warsaw, POLAND, 2018, vol. 641, pp. 585–596.
@inproceedings{8669401,
  abstract     = {{The union and intersection of two membership degrees of type-2 fuzzy sets are defined using a generalization of the mathematical operation of convolution. In the literature, it has been deeply studied when these convolution operations constitute a bounded distributive lattice. In this paper, we generalize the union and intersection convolution operations by replacing the functions from [0, 1] to itself with functions from a bounded lattice L-1 to a frame L-2, a particular type of bounded lattice. Similarly to some previous studies in the literature, we analyze when these new convolution operations constitute a bounded distributive lattice.}},
  author       = {{De Miguel, Laura and Bustince, Humberto and De Baets, Bernard}},
  booktitle    = {{ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 1}},
  isbn         = {{9783319668291}},
  issn         = {{2194-5357}},
  keywords     = {{FUZZY SETS,FINITE,TYPE-2,Convolution operation,Bounded lattice,Fuzzy logic}},
  language     = {{eng}},
  location     = {{Warsaw, POLAND}},
  pages        = {{585--596}},
  publisher    = {{Springer}},
  title        = {{Convolution on bounded lattices}},
  url          = {{http://doi.org/10.1007/978-3-319-66830-7_52}},
  volume       = {{641}},
  year         = {{2018}},
}
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