Conjunctors and their Residual Implicators: Characterizations and Construction Methods
Conjunctors and their Residual Implicators: Characterizations and Construction Methods
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DOI：
10.1007/s00009-007-0122-1
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发表时间：
2007-10
影响因子：
1.1
通讯作者：
F. Durante;E. Klement;R. Mesiar;C. Sempi
中科院分区：
文献类型：
--
作者：
F. Durante;E. Klement;R. Mesiar;C. Sempi
在模糊逻辑的许多实际应用中，似乎很明显，在选择合取时需要更大的灵活性：特别是，合取的结合性和交换性可以被去除。出于这些考虑，我们提出了几类合取，即[0，1]上的二元运算，用于将布尔合取从{0，1}扩展到[0，1]，并描述了它们各自的剩余蕴涵。因此，我们建立了一个一对一的对应关系的构造方法之间的连接符和剩余蕴涵的构造方法。此外，我们直接在剩余蕴涵算子类中引入了一些构造方法，并通过一个去剩余过程得到了新的合取算子。
In many practical applications of fuzzy logic it seems clear that one needs more flexibility in the choice of the conjunction: in particular, the associativity and the commutativity of a conjunction may be removed. Motivated by these considerations, we present several classes of conjunctors, i.e. binary operations on [0, 1] that are used to extend the boolean conjunction from {0, 1} to [0, 1], and characterize their respective residual implicators. We establish hence a one-to-one correspondence between construction methods for conjunctors and construction methods for residual implicators. Moreover, we introduce some construction methods directly in the class of residual implicators, and, by using a deresiduation procedure, we obtain new conjunctors.