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Pseudo-chain completeness of formal interval-valued fuzzy logic

Bart Van Gasse (UGent) , Chris Cornelis (UGent) , Glad Deschrijver (UGent) and Etienne Kerre (UGent)
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Organization
Abstract
Triangle Logic is a formal fuzzy logic with intervals as truth values. Its construction is based on triangle algebras: equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which were called interval-valued residuated lattices (IVRLs). We prove that the so-called pseudo-prelinear triangle algebras are subdirect products of pseudo-linear triangle algebras. This can be compared with MTL-algebras (prelinear residuated lattices) being subdirect products of linear residuated lattices. Using this result, we prove an analogue of the chain completeness of MTL for Pseudo-prelinear Triangle Logic. It also enables us to prove properties of pseudo-prelinear triangle algebras more easily. We give some examples.
Keywords
interval-valued fuzzy set theory, residuated lattices, formal logic

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Chicago
Van Gasse, Bart, Chris Cornelis, Glad Deschrijver, and Etienne Kerre. 2008. “Pseudo-chain Completeness of Formal Interval-valued Fuzzy Logic.” In World Scientific Proceedings Series on Computer Engineering and Information Science, ed. Da Ruan, Javier Montero, Jie Lu, Luis Martínez, Pierre D’Hondt, and Etienne Kerre, 1:223–228. Singapore, Singapore: World Scientific.
APA
Van Gasse, Bart, Cornelis, C., Deschrijver, G., & Kerre, E. (2008). Pseudo-chain completeness of formal interval-valued fuzzy logic. In Da Ruan, J. Montero, J. Lu, L. Martínez, P. D’Hondt, & E. Kerre (Eds.), World Scientific Proceedings Series on Computer Engineering and Information Science (Vol. 1, pp. 223–228). Presented at the 8th International FLINS conference on Computational Intelligence in Decision and Control (FLINS 2008), Singapore, Singapore: World Scientific.
Vancouver
1.
Van Gasse B, Cornelis C, Deschrijver G, Kerre E. Pseudo-chain completeness of formal interval-valued fuzzy logic. In: Ruan D, Montero J, Lu J, Martínez L, D’Hondt P, Kerre E, editors. World Scientific Proceedings Series on Computer Engineering and Information Science. Singapore, Singapore: World Scientific; 2008. p. 223–8.
MLA
Van Gasse, Bart, Chris Cornelis, Glad Deschrijver, et al. “Pseudo-chain Completeness of Formal Interval-valued Fuzzy Logic.” World Scientific Proceedings Series on Computer Engineering and Information Science. Ed. Da Ruan et al. Vol. 1. Singapore, Singapore: World Scientific, 2008. 223–228. Print.
@inproceedings{431047,
  abstract     = {Triangle Logic is a formal fuzzy logic with intervals as truth values. Its construction is based on triangle algebras: equationally de\unmatched{fb01}ned structures that are equivalent with certain residuated lattices on a set of intervals, which were called interval-valued residuated lattices (IVRLs). We prove that the so-called pseudo-prelinear triangle algebras are subdirect products of pseudo-linear triangle algebras. This can be compared with MTL-algebras (prelinear residuated lattices) being subdirect products of linear residuated lattices. Using this result, we prove an analogue of the chain completeness of MTL for Pseudo-prelinear Triangle Logic. It also enables us to prove properties of pseudo-prelinear triangle algebras more easily. We give some examples.},
  author       = {Van Gasse, Bart and Cornelis, Chris and Deschrijver, Glad and Kerre, Etienne},
  booktitle    = {World Scientific Proceedings Series on Computer Engineering and Information Science},
  editor       = {Ruan, Da and Montero, Javier and Lu, Jie and Mart{\'i}nez, Luis and D'Hondt, Pierre and Kerre, Etienne},
  isbn         = {9789812799463},
  language     = {eng},
  location     = {Madrid, Spain},
  pages        = {223--228},
  publisher    = {World Scientific},
  title        = {Pseudo-chain completeness of formal interval-valued fuzzy logic},
  volume       = {1},
  year         = {2008},
}

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