TY - JOUR UR - http://lib.ugent.be/catalog/pug01:610419 ID - pug01:610419 LA - eng TI - A characterization of interval-valued residuated lattices PY - 2008 JO - (2008) 3rd European Workshop on Probabilistic Graphical Models SN - 0888-613X PB - Elsevier 2008 AU - Van Gasse, Bart UGent 002001345426 801002035946 972684868151 0000-0002-2152-1441 AU - Cornelis, Chris AU - Deschrijver, Glad UGent 001995006575 801001452431 AU - Kerre, Etienne AB - As is well-known, residuated lattices (RLs) on the unit interval correspond to left-continuous t-norms. Thus far, a similar characterization has not been found for RLs on the set of intervals of [0, 1], or more generally, of a bounded lattice L. In this paper, we show that the open problem can be solved if it is restricted, making only a few simple and intuitive assumptions, to the class of interval-valued residuated lattices (IVRLs).More specifically, we derive a full characterization of product and implication in IVRLs in terms of their counterparts on the base RL To this aim, we use triangle algebras, a recently introduced variety of RLs that serves as an equational representation of IVRLs. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 610419 | ||
005 | 20161219154122.0 | ||
008 | 090508s2008------------------------eng-- | ||
022 | a 0888-613X | ||
024 | a 000260754900018 2 wos | ||
024 | a 1854/LU-610419 2 handle | ||
024 | a 10.1016/j.ijar.2008.04.006 2 doi | ||
040 | a UGent | ||
245 | a A characterization of interval-valued residuated lattices | ||
260 | b Elsevier c 2008 | ||
520 | a As is well-known, residuated lattices (RLs) on the unit interval correspond to left-continuous t-norms. Thus far, a similar characterization has not been found for RLs on the set of intervals of [0, 1], or more generally, of a bounded lattice L. In this paper, we show that the open problem can be solved if it is restricted, making only a few simple and intuitive assumptions, to the class of interval-valued residuated lattices (IVRLs).More specifically, we derive a full characterization of product and implication in IVRLs in terms of their counterparts on the base RL To this aim, we use triangle algebras, a recently introduced variety of RLs that serves as an equational representation of IVRLs. | ||
598 | a A1 | ||
700 | a Van Gasse, Bart u UGent 0 002001345426 0 801002035946 0 972684868151 0 0000-0002-2152-1441 9 F7DF50B6-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Cornelis, Chris u WE02 0 801001465969 9 F607B454-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Deschrijver, Glad u UGent 0 001995006575 0 801001452431 0 975407443034 9 F5FEAC1A-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Kerre, Etienne u WE02 0 801000205272 9 F358CFA4-F0ED-11E1-A9DE-61C894A0A6B4 | ||
650 | a Mathematics and Statistics | ||
653 | a triangle algebras | ||
653 | a interval-valued fuzzy set theory | ||
653 | a residuated lattices | ||
773 | t 3rd European Workshop on Probabilistic Graphical Models g Int. J. Approx. Reasoning. 2008. Elsevier. 49 (2) p.478-487 q 49:2<478 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/610419/file/627034 z [ugent] y VanGasse.pdf | ||
920 | a article | ||
Z30 | x WE 1 WE02 | ||
922 | a UGENT-WE |
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