(∈,∈∨_q)-区间值模糊子格

(∈,∈∨_q)-interval Valued Fuzzy Sublattices

将区间值模糊集的概念和运算应用于子格概念的研究,引入(∈,∈∨q)-区间值模糊子格的概念并考察它们的基本性质。给出了格L上区间值模糊集成为L的(∈,∈∨q)-区间值模糊子格的若干等价条件;讨论(∈,∈∨q)-区间值模糊子格与子格及(∈,∈∨q)-模糊子格间的相互关系;获得了(∈,∈∨q)-区间值模糊子格的像与原像成为(∈,∈∨q)-区间值模糊子格的条件。

In this paper,we study the notion of sublattices by using the concept and operations of interval valued fuzzy sets.The notion of（∈,∈∨q）-interval valued fuzzy sublattices is introduced and its essential properties are investigated.Several equivalent conditions of an interval valued fuzzy set to be（∈,∈∨q）-interval valued fuzzy sublattices are given.The relations between（∈,∈∨q）-interval valued fuzzy sublattices and（∈,∈∨q）-fuzzy sublattices and sublattices are discussed.The conditions for images and inverse images of（∈,∈∨q）-interval valued fuzzy sublattices to be（∈,∈∨q）-interval valued fuzzy sublattices are obtained.