论文标题
图片模糊拓扑空间的分类和构建
Classification and construction of picture fuzzy topological spaces
论文作者
论文摘要
本文启动了图片模糊拓扑空间的研究。为了开发一种构建图片模糊拓扑空间的机制，我们证明了与图片模糊集有关的一些基本结果，以及引入许多新概念（例如平衡和\ r {ho} - 等效关系）的基本结果。我们还定义了图片模糊拓扑空间的等级，图片模糊基础和图片模糊子基础。在这些概念的帮助下，我们提出了一种设计图片模糊拓扑空间的方法，这是这项工作的主要结果。据我们所知，这是研究图片模糊拓扑空间的第一次认真尝试。希望这项研究将为进一步开发图片模糊拓扑空间及其在决策理论中的应用提供一个体面的平台。
This paper initiates the study of picture fuzzy topological spaces. In order to develop a mechanism to construct picture fuzzy topological spaces, we prove some basic results related to picture fuzzy sets together with the introduction of many new notions such as balanced and \r{ho}-equivalent relations on picture fuzzy sets. We also define the rank, picture fuzzy base and picture fuzzy sub-base of picture fuzzy topological spaces. With the help of these notions, we present a method to design picture fuzzy topological spaces, which is the main outcome of this work. To the best of our knowledge, this is the first serious attempt to study picture fuzzy topological spaces. It is hoped that, this study will provide a decent platform for further development of picture fuzzy topological spaces and their applications in decision making theory.
