TY - JOUR UR - http://lib.ugent.be/catalog/pug01:610504 ID - pug01:610504 LA - eng TI - The pseudo-linear semantics of interval-valued fuzzy logics PY - 2009 JO - (2009) Information Sciences SN - 0020-0255 PB - Elsevier 2009 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 - Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called interval-valued residuated lattices (IVRLs). Triangle algebras have been used to construct triangle logic (TL), a formal fuzzy logic that is sound and complete w.r.t. the class of IVRIs.In this paper, 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.As a consequence, we are able to prove the pseudo-chain completeness of pseudo-linear triangle logic (PTL), an axiomatic extension of TL introduced in this paper. This kind of completeness is the analogue of the chain completeness of monoidal T-nornn based logic (MTL).This result also provides a better insight in the structure of triangle algebras: it enables us, amongst others, to prove properties of pseudo-prelinear triangle algebras more easily. It is known that there is a one-to-one correspondence between triangle algebras and couples (L, alpha), in which L is a residuated lattice and alpha an element in that residuated lattice. We give a schematic overview of some properties of pseudo-prelinear triangle algebras (and a number of others that can be imposed on a triangle algebra), and the according necessary and sufficient conditions on L and alpha. ER -Download RIS file
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001 | 610504 | ||
005 | 20161219154433.0 | ||
008 | 090508s2009------------------------eng-- | ||
022 | a 0020-0255 | ||
024 | a 000262962100002 2 wos | ||
024 | a 1854/LU-610504 2 handle | ||
024 | a 10.1016/j.ins.2008.11.005 2 doi | ||
040 | a UGent | ||
245 | a The pseudo-linear semantics of interval-valued fuzzy logics | ||
260 | b Elsevier c 2009 | ||
520 | a Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called interval-valued residuated lattices (IVRLs). Triangle algebras have been used to construct triangle logic (TL), a formal fuzzy logic that is sound and complete w.r.t. the class of IVRIs.In this paper, 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.As a consequence, we are able to prove the pseudo-chain completeness of pseudo-linear triangle logic (PTL), an axiomatic extension of TL introduced in this paper. This kind of completeness is the analogue of the chain completeness of monoidal T-nornn based logic (MTL).This result also provides a better insight in the structure of triangle algebras: it enables us, amongst others, to prove properties of pseudo-prelinear triangle algebras more easily. It is known that there is a one-to-one correspondence between triangle algebras and couples (L, alpha), in which L is a residuated lattice and alpha an element in that residuated lattice. We give a schematic overview of some properties of pseudo-prelinear triangle algebras (and a number of others that can be imposed on a triangle algebra), and the according necessary and sufficient conditions on L and alpha. | ||
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 Residuated lattices | ||
653 | a Interval-valued fuzzy set theory | ||
653 | a Formal logic | ||
773 | t Information Sciences g Inf. Sci. 2009. Elsevier. 179 (6) p.717-728 q 179:6<717 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/610504/file/627042 z [ugent] y sdarticle-2.pdf | ||
920 | a article | ||
Z30 | x WE 1 WE02 | ||
922 | a UGENT-WE |
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