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Textural dependency and concept lattices
International Journal of Approximate Reasoning ( IF 3.2 ) Pub Date : 2021-06-05 , DOI: 10.1016/j.ijar.2021.05.007
Sadık Bayhan

In this paper, the dependence spaces are discussed for textural formal concepts considering the method given by Ma et al. A complete congruence on a complete lattice is an equivalence relation if it satisfies the infinite substitution property. More generally, a join-dependence and a meet-dependence space with respect to infinite domain of discourse are presented. Using the duality in textures, the closure and interior operators are defined to obtain the intensions and co-intensions of concept lattices, respectively. The main theorem for dual formal concept lattices given by Chen and Yao is stated. Further, it is shown that the co-intensions of a dual formal concept lattice can be obtained using an interior operator. Finally, the independency notion of Novotný for t-formal concepts is discussed.



中文翻译:

纹理依赖和概念格

在本文中,考虑到 Ma 等人给出的方法,讨论了纹理形式概念的依赖空间。一个完全格上的完全同余是一个等价关系,如果它满足无限代换性质。更一般地,提出了关于无限话语域的连接依赖和相遇依赖空间。利用纹理中的对偶性,定义闭包和内部算子分别获得概念格的内涵和共内涵。陈述了陈和姚给出的对偶形式概念格的主要定理。此外,还表明可以使用内部算子获得对偶形式概念格的共内涵。最后,讨论了 t 形式概念的 Novotný 独立性概念。

更新日期:2021-06-10
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