Axiomatic characterizations of L-valued rough sets using a single axiom
Axiomatic characterizations of L-valued rough sets using a single axiom
复制标题
DOI：
10.1016/j.ins.2021.08.078
复制
发表时间：
2021-08
期刊：
影响因子：
--
通讯作者：
X. Wei;B. Pang;Jusheng Mi
中科院分区：
文献类型：
--
作者：
X. Wei;B. Pang;Jusheng Mi
模糊粗糙近似算子是模糊粗糙集理论的基础概念。至少有两种方法来发展这些基本概念，即，建设性的方法和公理化的方法。模糊粗糙近似算子的单公理化刻画得到了广泛的关注。本文考虑L是GL-Quantale，以L-集作为定义L-值粗糙近似算子的基本论域，发展了L-值粗糙集理论。采用模糊粗糙集的单公理化刻画的思想，给出了L-集上的L-值上、下粗糙近似算子关于L-集上的自反、对称、传递L-值关系及其组合的公理化刻画.选择一个L-集作为论域将打破采用Zadeh模糊集作为论域的规则。这些结果将进一步为模糊粗糙集理论的公理化研究提供一个新的框架。
Fuzzy rough approximation operators are the underlying concepts in fuzzy rough set theory. There are at least two approaches to develop these primary concepts, ie, the constructive approach and the axiomatic approach. Single axiomatic characterizations of fuzzy rough approximation operators have got tons of attention. In this paper, considering L being a GL-quantale, we will develop the theory of L-valued rough sets with an L-set as the basic universe of defining L-valued rough approximation operators. Adopting the idea of single axiomatic characterizations of fuzzy rough sets, we will present the axiomatic characterizations of L-valued upper and lower rough approximation operators on an L-set with respect to reflexive, symmetric, transitive L-valued relations on an L-set as well as their compositions. Choosing an L-set as the universe will break the rules that adopting Zadeh’s fuzzy sets as the universe. By these results, we will further provide a new framework of axiomatic research of fuzzy rough set theory.