正規階層圖在IM法下的研究

應用日本學者佐佐木整、竹谷誠(1998)所提出illustrative mapping method （簡稱IM法）於階層概念圖(hierarchical concept map)，不僅可以減少階層概念圖中的交錯邊數，同時階層概念圖的實際應用中，IM法具有其它減少交錯邊方法所沒有的特性，可以群聚同性質的概念。但是，目前並無相關文獻探討IM法在減少交錯邊數的成效。因此，本研究主要目的是採用Matlab程式去模擬IM法在減少交錯邊數的成效，同時為了能廣泛用在實際之階層概念圖的應用中，特別針對正規階層圖的模式去模擬。所以，分別隨機產生代表30個頂點6階層、60個頂點6階層和60個頂點12個階層的正規階層圖之連接矩陣，統計連接矩陣在經IM法後，所能減少交錯邊數之比率，同時反覆執行這樣的模擬實驗100次，並求平均減少交錯邊數的比率。本研究的結果如下：一、IM法對於正規階層圖，在平均減少交錯邊數的成效約30%至70%，平均減少的比率受正規階層圖中連邊發生的機率影響，當連邊發生的機率越高，平均減少的比率就越低，當連邊發生的機率越低，平均減少的比率就越高。二、雖然平均減少交錯邊數的成效，受連邊發生的機率所影響，但是實際可以減少正規階層圖中交錯邊數的多寡，取決於正規階層圖的結構。三、在模擬的過程中，發現IM法如同其它減少交錯邊數的方法，亦有不穩定的狀況，其不穩定的狀況多半發生在同一階層中相鄰的兩頂點，若這些相鄰的頂點能左右對調，可以進一步改善減少交錯邊數的成效。

關鍵字

減少交錯邊數；階層概念圖； Illustrative mapping method

並列摘要

Use Japanese scholar H. Sasaki (1998) puts forward illustrative mapping method (abbreviated as IM law) in stratum's concept picture (hierarchical concept map), the ones that can not merely be reduced in stratum's concept picture interlock and counting, at the same time in the practical application of stratum's concept picture, IM law has other reduction to interlock the unexistent characteristic of method, all right clustering and concept of nature. However, there are not relevant documents that probe into IM law and reduce and mixed with the effect counted at present. So, the main purpose of this research department is to adopt Matlab procedure to imitate IM law and reduce and mixed with the effect counted, at the same time in order to use it in the application of the real stratum concept picture extensively, especially imitate to the way of the regular stratum's picture. So, it represents 30 summit pinnacle 6 strata, 60 summit pinnacle 6 strata and connection matrix of the regular stratum's pictures of 60 summit pinnacles and 12 strata to produce at random separately, count the matrix of connecting after IM law, can reduce and mixed with the rate counted, carry out such 100 times of simulation experiment repeatedly at the same time, and ask and reduce and mixed with the rate counted equally. Result of this research: 1. IM law, to the regular stratum's picture, reducing and mixed with about 30% effects counted to 70% equally, the rate reduced equally is being connected with the probability happenning in the regular stratum's picture and sounded, it is the higher to act as and connect with the probability that happens, the lower the rate reduced equally is, act as and connect with the probability happenning is the lower, the higher the rate reduced equally is. 2. Though reduce and mixed with the effect counted equally, connected with the probability happenning and sounded, but reality can be reduced regularly mixed with the number counted in stratum's picture, depend on the structure of the regular stratum's picture. 3. During the process of imitating, find that IM law is mixed with the method to count like other reduction, also have unstable states, two adjoint summit pinnacles in the same stratum take place mostly in its unstable state, summit pinnacle that with adjoint these Yes about rightadjust, can be improving and reducing and mixed with the effect counted further.