知識結構有向圖形類似度之改進指標

Improving Indexes for Similarity Measure between the Directed Graphs of Knowledge Structures

劉湘川(Hsiang-Chuan Liu)

《測驗統計年刊》 12期_下 (2004/12) Pp. 193-210

https://doi.org/10.6773/JRMS.200412.0193

摘要

竹谷誠(1997)之LFT分析法中，定義之知識結構圖形之類似度指標，即竹谷誠類似度指標，其「兩圖形邊之連結集之交集與聯集」之求取非常繁瑣不便，本文首先改以「兩圖形交集與聯集之邊之連結集」之求取則甚為方便，而得計算簡便之「第一種改進類似度指標」，又竹谷誠類似度指標僅考慮「邊之不同經由路徑之存在數量」及「邊之不同位序值」，提出計算簡便，且靈敏有效更具鑑別力之「第二種及第三種改進圖形類似度指標」。

關鍵字

LFT ； 有向圖形 ； 有向路程 ； 圖形之類似度

並列摘要

The calculating of Takeya similarity indexes based on the intersections and unions between two connected sets of the edge of directed graphs as the formula (1) was too complicated (The equation is abbreviated) where C(vk, vl|G) is the connected set of edge (vk, vl) in graph G. This study provided an easy calculating improved similarity indexes as the formula (2): (The equation is abbreviated) Furthermore, replacing the connected set by path set and ranking position path set, This study provided two improved similarity indexes as the formula (3) and (4): (The equation is abbreviated) (The equation is abbreviated).

並列關鍵字

LFT ； directed graph ； directed path ； similarity between two graphs

參考文獻

竹谷誠、佐佐木整(1997)。學習者描畫の認知マツプによる理解度評價法。電子情報學會論文誌。80(1)，336-347。

佐伯卓也(1981)。「數學的構造の學習」の評價法。日本數學教育學會誌。63(1)，31-36。

廖寶貴、曾智鈿、胡豐榮、許天維(2004)。LFT之計分理論分析。測驗統計簡訊。58，14-21。

Shavelson, R. J.(1972).Some aspects of the correspondence between content structure and cognitive structure in physics instruction.Journal of Educational Psychology.33,225-234.

Shavelson, R. J.,Stanton, G. C.(1975).Construct validation: Methodology and application to three measure of cognitive structure.Journal of Educational Measurement.12,67-85.