ON THE PROPERTIES OF A GENERALIZED CLASS OF T-NORMS IN INTERVAL-VALUED FUZZY LOGICS

被引:12
|
作者
Van Gasse, Bart [1 ]
Cornelis, Chris [1 ]
Deschrijver, Glad [1 ]
Kerre, Etienne E. [1 ]
机构
[1] Univ Ghent, Fuzziness & Uncertainty Modelling Res Unit, Dept Appl Math & Comp Sci, Krijgslaan 281,S9, B-9000 Ghent, Belgium
关键词
Formal fuzzy logic; interval-valued fuzzy sets; triangular norms; residuated lattices;
D O I
10.1142/S1793005706000361
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Since it does not generate any MTL-algebra (prelinear residuated lattice), the lattice L-I of closed subintervals of [0, 1] falls outside the mainstream of research on formal fuzzy logics. However, due to the intimate connection between logical connectives on L-I and those on [0, 1], many relevant logical properties can still be maintained, sometimes in a slightly weaker form. In this paper, we focus on a broad class of parametrized t-norms on L-I. We derive their corresponding residual implicators, and examine commonly imposed logical properties. Importantly, we formally establish one-to-one correspondences between.-definability (respectively, weak divisibility) for t-norms of this class and strong.-definability (resp., divisibility) for their counterparts on [0, 1].
引用
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页码:29 / 41
页数:13
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