Negation and affirmation: the role of involutive negators
Negation and affirmation: the role of involutive negators
复制标题
DOI：
10.1007/s00500-006-0127-x
复制
发表时间：
2007-02
期刊：
影响因子：
4.1
通讯作者：
Koen Maes;B. Baets
中科院分区：
文献类型：
--
作者：
Koen Maes;B. Baets
严格否定和自同构普遍用于模糊布尔否定和肯定。内卷否定者特别令人感兴趣。每个单调 [0,1] → [0,1] 双射最多由四个内合否定组成。内卷否定在几何上可以通过其图形的对称性来识别。第一个平分线。如果自同构图具有交替行为，我们可以通过一对内合否定来生成自同构。
Strict negators and automorphisms are prevalently used to fuzzify the Boolean negation and affirmation. Involutive negators are of particular interest. Every monotone [0,1] → [0,1] bijection is a composition of at most four involutive negators. Involutive negators are geometrically recognized by the symmetry of their graph w.r.t. the first bisector. If the graph of an automorphism has an alternating behavior, we can generate the automorphism by a pair of involutive negators.