在張宜武教授的博士論文中研究到視線表示法和視線數。我們以類似的方法定義有向圖的表示法和有向圖的視線數。 首先，我們定義有向圖的視線數為b(Ｄ) ，Ｄ為有方向性的圖，在論文中可得b(Ｄ)≦┌1/2max｛△﹢(Ｄ),△﹣(Ｄ)｝┐。另一個重要的結論為考慮一個平面有向圖Ｄ，對圖形Ｄ上所有的點v，離開點v的邊（進入的邊）是緊鄰在一起時，則可得有向圖的視線數在這圖形上是１（即 b(Ｄ)=1）。 另外對特殊的圖形也有其不同的視線數，即對有向完全偶圖Ｄm,n ，b(Ｄm,n)≦┌1/2min｛m,n｝┐ ，而對競賽圖Ｄn ，可得b(Ｄn)≦┌n/3┐+1。 / In [2], Chang stuidied the bar visibility representations and defined bar visibility number.We defined analogously the bar visibility representation and the bar visibility number of a directed graph Ｄ. First we show that the bar visibility number, denoted by b(Ｄ),is at most ┌1/2max｛△﹢(Ｄ),△﹣(Ｄ)｝┐ if D is an oriented graph.And we show that b(Ｄ)=1 for the oriented planar graphs in which all outgoing (incoming) edges of any vertex v of Ｄ appear consecutively around v.For any complete bipartite digraph Ｄm,n ，b(Ｄm,n)≦┌1/2min｛m,n｝┐.For any tournament Ｄn,b(Ｄn)≦┌n/3┐+1.

本文以人對事物現象認識的感覺與模糊性作為切入點，闡述模糊性是人對事物認識的一種表徵及反應。然後，引入模糊集合的定義及刻劃模糊集合的表示函數—隸屬度，對模糊集合的各種運算、模糊矩陣、模糊差集以及宇集等內容進行較詳細的討論，並以各種事例說明一些相關概念和運算。 最後，再深入探討如何以模糊矩陣表示圖學中有向圖的問題。 / This article is to focus on the understanding of human being to the phenomenon of things as well as the fuzziness. Then, by applying the definition of the fuzzy set and explaining the membership of fuzzy set, we are going to have a detailed discussion of the operation of fuzzy set, fuzzy matrix, fuzzy subtraction and universal set. Examples are given to demonstrate some of the related concepts and expression. Next, further questions about how to display directed graph in the graph theory with fuzzy matrix will be discussed .