粗糙模糊集的格论性质

Lattice Theory Properties of Fuzzy Rough Sets

由Pawlak于1982年提出来的粗糙集(rough set)理论是一种处理不完全和不充分信息的数学工具,是传统集合论的拓展,近年来由于在机器学习、知识发现、模式识别、决策支持等领域获得成功的应用引起广大研究人员的关注,经过近20年来计算机科学领域和数学领域的学者的努力,粗糙集理论和应用都得到迅速的发展.

Let U denote a finite and nonempty set called the universe, and P(U) a power set. Suppose R is an equivalence relation on U. Consider the equivalence relation ≈(X≈<=>YRX= RY and RX = RY, X,Y,∈(U)) on F(U), the quotient set denoted by F(U)/#. In this paper we show that F(U)/≈ is a distributive lattice.