第四章 結果與分析
第一節 比較不同模糊分群演算法之正確率
童之表現情形。
第一節 比較不同模糊分群演算法之正確率
以網路上公認的蝴蝶花、葡萄酒等資料，以新的模糊分群演算法計算正確 率，再與傳統的 FCM 分群演算法、GK 分群演算法、GG 分群演算法比較其 正確百分率。
壹、以 150 筆蝴蝶花的資料（Fisher, 1936）為例
蝴蝶花（Iris）（或稱鳶尾花）的資料特徵包括花萼萼片的長、萼片的寬、
花瓣瓣片的長及瓣片的寬共 4 種，依蝴蝶花的資料特徵可分成 3 群，參見表 4-1-1。FCM 程式係來自 MATLAB 軟體所提供，GK 及 GG 程式分別由文獻 提供，FCM-M 及 FCM-CM 則使用 MATLAB 軟體撰寫，為避免因初值隸屬 度影響分類結果，因此選用相同之初值隸屬度進行比較不同模糊分群演算法 之正確率，模糊程度以預設值為 m=2，收斂閥值
ε
>0，取預設值為ε =0.001， 正確率係以演算法執行 100 次的平均值計算，詳如表 4-1-2 所示，分類結果 發現以 FCM-CM 分群演算法之正確率最高。表 4-1 蝴蝶花資料依特徵共分成 3 群
組別 樣本個數 特徵
1 50 花萼萼片及花瓣瓣片較長
2 50 花色較多變化
3 50 維吉尼亞品種
表 4-2 150 筆蝴蝶花比較模糊分群演算法之正確率
模糊分群演算法 正確率
FCM 89.33％
GG 76.49％
GK 90.00％
FCM-M 90.00％
FCM-CM 92.79％
表 4-3 隨機產生 100 組隸屬度初值分群演算法之正確率
FCM GK GG FCMM FCMCM
89.33% 90.00% 76.49% 90.00% 92.67%
89.33% 90.00% 63.33% 90.00% 96.67%
89.33% 90.00% 74.00% 90.00% 91.33%
89.33% 90.00% 73.33% 90.00% 92.67%
89.33% 90.00% 70.00% 90.00% 96.67%
89.33% 90.00% 66.67% 90.00% 89.33%
89.33% 90.00% 72.00% 90.00% 96.67%
89.33% 90.00% 88.67% 90.00% 91.33%
89.33% 90.00% 76.49% 90.00% 96.67%
89.33% 90.00% 88.67% 90.00% 92.00%
89.33% 90.00% 74.00% 90.00% 89.33%
89.33% 90.00% 96.67% 90.00% 92.67%
89.33% 90.00% 74.00% 90.00% 91.33%
89.33% 90.00% 96.67% 90.00% 91.33%
89.33% 90.00% 66.67% 90.00% 92.67%
89.33% 90.00% 74.00% 90.00% 91.33%
89.33% 90.00% 72.67% 90.00% 92.67%
89.33% 90.00% 72.67% 90.00% 92.00%
89.33% 90.00% 66.67% 90.00% 96.67%
89.33% 90.00% 76.49% 90.00% 96.67%
89.33% 90.00% 66.67% 90.00% 91.33%
89.33% 90.00% 76.00% 90.00% 92.00%
89.33% 90.00% 96.67% 90.00% 91.33%
89.33% 90.00% 88.67% 90.00% 92.67%
表 4-3 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
89.33% 90.00% 72.67% 90.00% 91.33%
89.33% 90.00% 76.00% 90.00% 96.67%
89.33% 90.00% 71.33% 90.00% 96.67%
89.33% 90.00% 96.67% 90.00% 91.33%
89.33% 90.00% 76.49% 90.00% 91.33%
89.33% 90.00% 74.00% 90.00% 92.67%
89.33% 90.00% 72.67% 90.00% 92.00%
89.33% 90.00% 96.67% 90.00% 91.33%
89.33% 90.00% 96.67% 90.00% 91.33%
89.33% 90.00% 72.67% 90.00% 91.33%
89.33% 90.00% 56.67% 90.00% 92.00%
89.33% 90.00% 75.33% 90.00% 90.00%
89.33% 90.00% 96.67% 90.00% 92.67%
89.33% 90.00% 76.49% 90.00% 92.67%
89.33% 90.00% 73.33% 90.00% 92.00%
89.33% 90.00% 74.67% 90.00% 91.33%
89.33% 90.00% 74.00% 90.00% 92.67%
89.33% 90.00% 96.67% 90.00% 92.67%
89.33% 90.00% 74.00% 90.00% 92.67%
89.33% 90.00% 96.67% 90.00% 92.67%
89.33% 90.00% 72.67% 90.00% 91.33%
89.33% 90.00% 66.67% 90.00% 96.67%
89.33% 90.00% 72.67% 90.00% 92.67%
89.33% 90.00% 72.67% 90.00% 91.33%
89.33% 90.00% 74.67% 90.00% 91.33%
表 4-3 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
89.33% 90.00% 46.00% 90.00% 91.33%
89.33% 90.00% 73.33% 90.00% 96.67%
89.33% 90.00% 70.00% 90.00% 92.00%
89.33% 90.00% 33.33% 90.00% 92.67%
89.33% 90.00% 68.00% 90.00% 90.00%
89.33% 90.00% 96.67% 90.00% 92.67%
89.33% 90.00% 65.33% 90.00% 92.00%
89.33% 90.00% 66.00% 90.00% 92.67%
89.33% 90.00% 76.49% 90.00% 92.67%
89.33% 90.00% 96.67% 90.00% 91.33%
89.33% 90.00% 72.67% 90.00% 92.00%
89.33% 90.00% 76.49% 90.00% 96.67%
89.33% 90.00% 72.67% 90.00% 92.67%
89.33% 90.00% 84.67% 90.00% 91.33%
89.33% 90.00% 72.67% 90.00% 92.67%
89.33% 90.00% 76.49% 90.00% 90.67%
89.33% 90.00% 74.67% 90.00% 96.67%
89.33% 90.00% 76.49% 90.00% 92.00%
89.33% 90.00% 69.33% 90.00% 96.67%
89.33% 90.00% 96.67% 90.00% 92.00%
89.33% 90.00% 50.67% 90.00% 91.33%
89.33% 90.00% 76.49% 90.00% 91.33%
89.33% 90.00% 76.49% 90.00% 92.00%
89.33% 90.00% 71.33% 90.00% 96.67%
89.33% 90.00% 73.33% 90.00% 88.67%
表 4-3 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
89.33% 90.00% 76.49% 90.00% 96.67%
89.33% 90.00% 76.49% 90.00% 90.67%
89.33% 90.00% 96.67% 90.00% 96.67%
89.33% 90.00% 96.67% 90.00% 91.33%
89.33% 90.00% 76.49% 90.00% 96.67%
89.33% 90.00% 96.67% 90.00% 91.33%
89.33% 90.00% 76.49% 90.00% 91.33%
89.33% 90.00% 66.67% 90.00% 92.00%
89.33% 90.00% 74.67% 90.00% 96.67%
89.33% 90.00% 66.67% 90.00% 91.33%
89.33% 90.00% 63.33% 90.00% 91.33%
89.33% 90.00% 96.67% 90.00% 92.67%
89.33% 90.00% 76.49% 90.00% 92.67%
89.33% 90.00% 72.67% 90.00% 91.33%
89.33% 90.00% 84.67% 90.00% 92.00%
89.33% 90.00% 72.67% 90.00% 92.00%
89.33% 90.00% 66.67% 90.00% 96.67%
89.33% 90.00% 78.67% 90.00% 92.00%
89.33% 90.00% 76.49% 90.00% 96.67%
89.33% 90.00% 66.67% 90.00% 92.00%
89.33% 90.00% 76.00% 90.00% 91.33%
89.33% 90.00% 96.67% 90.00% 96.67%
89.33% 90.00% 72.67% 90.00% 92.00%
89.33% 90.00% 71.33% 90.00% 92.67%
89.33% 90.00% 80.00% 90.00% 91.33%
表 4-3 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
89.33% 90.00% 72.67% 90.00% 92.67%
貳、以 120 筆蝴蝶花的資料（Fisher, 1936）為例
為確認當各群的樣本個數不同時，對不同模糊分群演算法之正確率是否 有影響，隨機產生分別為 30、40、50 之 120 筆蝴蝶花（Iris）的資料。分類 結果由表 4-1-3 發現仍以 FCM-CM 之分群演算法之正確率 88.52％最高。
表 4-4 120 筆蝴蝶花比較模糊分群演算法之正確率
模糊分群演算法 正確率
FCM 87.50％
GG 73.13％
GK 88.30％
FCM-M 87.50％
FCM-CM 88.23％
表 4-5 隨機產生 100 組隸屬度初值分群演算法之正確率
FCM GK GG FCMM FCMIM
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 87.50% 42.50% 87.50% 87.50%
79.78% 87.50% 74.17% 87.50% 87.50%
79.78% 88.33% 81.67% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 87.50% 81.67% 87.50% 87.50%
表 4-5 隨機產生 100 組隸屬度初值之不同分群演算法之正確率（續）
79.78% 87.50% 67.50% 87.50% 87.50%
79.78% 88.33% 66.67% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 57.50% 87.50% 88.33%
79.78% 88.33% 65.00% 87.50% 88.33%
79.78% 88.33% 67.50% 87.50% 88.33%
79.78% 88.33% 65.83% 87.50% 88.33%
79.78% 88.33% 81.67% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 87.50% 73.33% 87.50% 87.50%
79.78% 88.33% 66.67% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 74.17% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 81.67% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 65.83% 87.50% 88.33%
79.78% 88.33% 67.50% 87.50% 88.33%
79.78% 88.33% 55.00% 87.50% 88.33%
79.78% 88.33% 43.33% 87.50% 88.33%
79.78% 87.50% 67.50% 87.50% 87.50%
79.78% 88.33% 66.67% 87.50% 88.33%
79.78% 88.33% 86.67% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
表 4-5 隨機產生 100 組隸屬度初值之不同分群演算法之正確率（續）
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 70.83% 87.50% 88.33%
79.78% 88.33% 72.50% 87.50% 88.33%
79.78% 88.33% 66.67% 87.50% 88.33%
79.78% 88.33% 71.67% 87.50% 88.33%
79.78% 88.33% 83.33% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 64.17% 87.50% 88.33%
79.78% 87.50% 73.33% 87.50% 87.50%
79.78% 87.50% 73.33% 87.50% 87.50%
79.78% 88.33% 69.17% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 65.00% 87.50% 88.33%
79.78% 87.50% 95.83% 87.50% 87.50%
79.78% 88.33% 62.50% 87.50% 88.33%
79.78% 88.33% 70.00% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 88.33% 68.33% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 62.50% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 89.17% 87.50% 88.33%
表 4-5 隨機產生 100 組隸屬度初值之不同分群演算法之正確率（續）
79.78% 88.33% 56.67% 87.50% 88.33%
79.78% 88.33% 73.33% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 87.50% 84.17% 87.50% 87.50%
79.78% 88.33% 65.00% 87.50% 88.33%
79.78% 88.33% 74.17% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 51.67% 87.50% 88.33%
79.78% 88.33% 69.17% 87.50% 88.33%
79.78% 88.33% 57.50% 87.50% 88.33%
79.78% 87.50% 73.33% 87.50% 87.50%
79.78% 88.33% 77.50% 87.50% 88.33%
79.78% 88.33% 75.00% 87.50% 88.33%
79.78% 88.33% 77.50% 87.50% 88.33%
79.78% 88.33% 66.67% 87.50% 88.33%
79.78% 88.33% 56.67% 87.50% 88.33%
79.78% 88.33% 66.67% 87.50% 88.33%
79.78% 88.33% 54.17% 87.50% 88.33%
79.78% 87.50% 74.17% 87.50% 87.50%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 88.33% 63.33% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
表 4-5 隨機產生 100 組隸屬度初值之不同分群演算法之正確率（續）
79.78% 88.33% 75.00% 87.50% 88.33%
79.78% 88.33% 65.00% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 88.33% 73.13% 87.50% 88.33%
79.78% 88.33% 66.67% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 88.33% 65.00% 87.50% 88.33%
79.78% 88.33% 63.33% 87.50% 88.33%
79.78% 87.50% 86.67% 87.50% 87.50%
79.78% 88.33% 67.50% 87.50% 88.33%
79.78% 88.33% 70.83% 87.50% 88.33%
79.78% 88.33% 95.83% 87.50% 88.33%
79.78% 88.33% 66.67% 87.50% 88.33%
參、使用 241 名受測學童在「扇形」測驗為例
「扇形」單元教材知識結構依據康軒文教事業（2001），「扇形」單元 之教學目標為：1、複習圓面積的求法。2、認識扇形及其構成要素 。3、認 識 12 圓、14 圓、16 圓、18 圓等扇形，及了解其面積的求法。4、利用 12 圓、14 圓等扇形繪製圖形。5.透過分析、綜合，求算利用 12 圓、14 圓所繪 製成的圖形面積（郭伯臣，2005）。
「扇形」單元樣本數總計828人，分為8群補救教學類型.尋找各縣市願 意配合的學校進行施測，進行「扇形」單元的施測學校有4所，計23個班級，
828位學生，本研究取人數相近的六群資料進行分群演算法之檢驗，刪除人 數 高 於 200人 以 上 之 第 四 與 第 八 群 ， 因 此 選 取 之 樣 本 數 為 241人 ， 詳 如 表 4-1-6。
表4-6「扇形」測驗的六種需進行補救教學概念之類型
組別 人數 需進行補救教學之概念
1 50 加強練習（粗心犯錯）
2 36 「複合扇形面積」
3 47 「複合扇形面積」、「基本扇形面積」
5 53 「圖形繪製」
6 30 「複合扇形面積」、「圖形繪製」
7 25 「複合扇形面積」、「基本扇形面積」、「圖形繪製」
比較不同模糊分群演算法之正確率，分類結果詳如表 4-1-7，仍以 FCM-CM 之分群演算法之正確率 45.24％最高。
表 4-7 學童 241 名比較不同模糊分群演算法之正確率
模糊分群演算法 正確率
FCM 43.39％
GG 41.06％
GK 37.03％
FCM-M 43.79％
FCM-CM 45.24％
表 4-8 隨機產生 100 組隸屬度初值分群演算法之正確率
FCM GG GK FCM-M FCM-CM
0.443983402 0.43153527 0.414937759 0.456431535 0.481327801 0.423236515 0.390041494 0.439834025 0.468879668 0.477178423 0.456431535 0.352697095 0.331950207 0.410788382 0.419087137 0.443983402 0.365145228 0.356846473 0.456431535 0.456431535 0.423236515 0.373443983 0.44813278 0.410788382 0.456431535 0.423236515 37.03000000 0.360995851 0.423236515 0.406639004 0.443983402 0.439834025 0.398340249 0.410788382 0.427385892 0.443983402 0.365145228 0.369294606 0.493775934 0.493775934 0.423236515 0.323651452 0.390041494 0.477178423 0.473029046 0.456431535 0.356846473 0.477178423 0.410788382 0.456431535 0.423236515 0.294605809 0.414937759 0.410788382 0.477178423 0.423236515 0.360995851 0.369294606 0.497925311 0.506224066 0.423236515 0.278008299 0.406639004 0.410788382 0.44813278 0.443983402 0.473029046 0.331950207 0.410788382 0.493775934 0.414937759 37.03000000 0.365145228 0.510373444 0.506224066 0.423236515 0.356846473 0.435684647 0.46473029 0.481327801 0.423236515 0.2406639 0.377593361 0.406639004 0.460580913 0.448132780 0.369294606 0.381742739 0.398340249 0.419087137 0.423236515 0.390041494 0.402489627 0.477178423 0.477178423 0.423236515 0.410788382 0.377593361 0.419087137 0.410788382 0.456431535 0.414937759 0.477178423 0.410788382 0.414937759 0.456431535 0.402489627 0.369294606 0.410788382 0.419087137 0.423236515 0.307053942 0.377593361 0.410788382 0.414937759 0.456431535 0.331950207 0.43153527 0.473029046 0.44813278
表 4-8 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
0.423236515 0.394190871 0.410788382 0.481327801 0.46473029 0.423236515 0.414937759 0.365145228 0.410788382 0.410788382 0.443983402 0.228215768 0.385892116 0.439834025 0.468879668 0.456431535 0.360995851 0.427385892 0.410788382 0.435684647 0.443983402 0.360995851 0.394190871 0.394190871 0.410788382 0.423236515 0.302904564 0.414937759 0.414937759 0.414937759 0.423236515 37.03000000 0.410788382 0.410788382 0.410788382 0.44813278 0.423236515 0.398340249 0.406639004 0.402489627 0.443983402 0.473029046 0.377593361 0.410788382 0.419087137
表 4-8 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
0.423236515 0.352697095 0.460580913 0.473029046 0.485477178 0.406639004 0.360995851 0.398340249 0.473029046 0.506224066 0.443983402 0.423236515 0.385892116 0.46473029 0.435684647 0.423236515 0.340248963 0.394190871 0.443983402 0.44813278 0.423236515 0.319502075 0.323651452 0.522821577 0.514522822 0.443983402 0.356846473 0.381742739 0.406639004 0.473029046 0.423236515 0.278008299 0.348547718 0.410788382 0.427385892 0.443983402 0.456431535 0.44813278 0.44813278 0.460580913 0.443983402 0.406639004 0.398340249 0.473029046 0.489626556 0.443983402 0.336099585 0.452282158 0.460580913 0.456431535 0.406639004 0.398340249 0.473029046 0.456431535 0.460580913 0.423236515 0.402489627 0.365145228 0.452282158 0.460580913 0.414937759 0.32780083 0.356846473 0.468879668 0.46473029 0.423236515 0.427385892 0.477178423 0.473029046 0.481327801 0.423236515 0.352697095 0.385892116 0.410788382 0.419087137 0.456431535 0.356846473 0.419087137 0.410788382 0.410788382 0.443983402 0.336099585 0.460580913 0.460580913 0.46473029 0.443983402 0.31120332 0.385892116 0.468879668 0.456431535 0.423236515 0.410788382 0.452282158 0.410788382 0.514522822 0.423236515 0.369294606 0.369294606 0.419087137 0.423236515 0.456431535 0.390041494 0.385892116 0.410788382 0.410788382 0.427385892 0.34439834 0.44813278 0.423236515 0.406639004 0.423236515 0.31120332 0.398340249 0.406639004 0.402489627 0.423236515 0.481327801 0.402489627 0.419087137 0.419087137 0.410788382 0.360995851 0.360995851 0.410788382 0.452282158 0.443983402 0.398340249 0.497925311 0.410788382 0.477178423
表 4-8 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
0.423236515 0.381742739 0.377593361 0.410788382 0.414937759 0.443983402 0.385892116 0.439834025 0.473029046 0.477178423 0.423236515 0.265560166 0.43153527 0.477178423 0.485477178 0.423236515 0.390041494 0.439834025 0.502074689 0.502074689 0.423236515 0.398340249 0.377593361 0.460580913 0.460580913 0.456431535 0.365145228 0.352697095 0.410788382 0.414937759 0.443983402 0.419087137 0.43153527 0.443983402 0.460580913 0.423236515 0.402489627 0.423236515 0.423236515 0.410788382 0.414937759 37.03000000 0.43153527 0.410788382 0.423236515 0.410788382 0.369294606 0.427385892 0.406639004 0.410788382 0.456431535 0.34439834 0.414937759 0.410788382 0.419087137 0.443983402 0.410788382 0.410788382 0.410788382 0.410788382 0.423236515 0.373443983 0.44813278 0.468879668 0.485477178 0.423236515 0.323651452 0.360995851 0.485477178 0.514522822 0.443983402 0.423236515 0.423236515 0.473029046 0.468879668 0.456431535 0.402489627 0.414937759 0.468879668 0.46473029 0.456431535 0.390041494 0.468879668 0.410788382 0.493775934 0.456431535 0.402489627 0.452282158 0.410788382 0.419087137 0.423236515 0.294605809 0.419087137 0.477178423 0.497925311 0.443983402 0.369294606 0.439834025 0.419087137 0.406639004 0.414937759 0.315352697 0.485477178 0.410788382 0.419087137 0.456431535 0.356846473 0.402489627 0.423236515 0.414937759 0.423236515 0.356846473 0.360995851 0.410788382 0.477178423 0.456431535 0.373000000 0.456431535 0.406639004 0.485477178 0.456431535 0.369294606 0.531120332 0.502074689 0.518672199 0.456431535 0.323651452 0.493775934 0.410788382 0.394190871
表 4-8 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
0.423236515 0.493775934 0.468879668 0.410788382 0.481327801 0.443983402 0.402489627 0.414937759 0.456431535 0.46473029 0.423236515 0.381742739 0.356846473 0.46473029 0.443983402 0.423236515 0.34439834 0.356846473 0.419087137 0.402489627 0.423236515 37.03000000 0.481327801 0.410788382 0.468879668 0.443983402 0.348547718 0.348547718 0.402489627 0.46473029 0.423236515 37.03000000 0.331950207 0.43153527 0.402489627 0.456431535 0.219917012 0.414937759 0.414937759 0.414937759 0.443983402 0.510373444 0.502074689 0.406639004 0.481327801 0.414937759 0.44813278 0.460580913 0.485477178 0.468879668 0.423236515 0.369294606 0.543568465 0.506224066 0.522821577 0.423236515 0.402489627 0.381742739 0.410788382 0.468879668 0.423236515 0.398340249 0.390041494 0.473029046 0.481327801 0.443983402 0.315352697 0.394190871 0.46473029 0.460580913 0.423236515 37.03000000 0.373443983 0.410788382 0.473029046
肆、使用 178 筆酒資料為例
（Aeberhard, Coomans and deVel, 1992）
178 筆酒原料生長在義大利的相同地區，這些資料係經由化學分析所得 結果，共可分成 3 個群組，原本包括 30 種特徵，但目前由文獻資料有 13 種特徵，詳如表 4-1-9。
表 4-9 酒 178 筆資料 3 群特徵之平均數
酒的特徵 組別=1 組別=2 組別=3
酒精 13.7447 12.2787 13.1538
蘋果酸 2.0107 1.9327 3.3338
碳酸鈉 2.4556 2.2448 2.4371
Alcalinity
碳酸鈉 17.0373 20.2380 21.4167 鎂 106.3390 94.5493 99.3125
總酚 2.8402 2.2589 1.6787
類黃酮素 2.9824 2.0808 .7815
Nonflavanoid 酚 .2900 .3637 .4475 Proanthocyanins 1.8993 1.6303 1.1535
烈性 5.5283 3.0866 7.3962
特色 1.0620 1.0563 .6827
OD280/OD315 稀釋酒 3.1578 2.7854 1.6835 氨基酸 1115.7119 519.5070 629.8958
由上表 4-1-9 知，酒 178 筆資料中包括 13 種特徵分別為：酒精、蘋果 酸、Alcalinity 碳酸鈉、鎂、總酚、類黃酮素、Nonflavanoid 酚、Proanthocyanins、
烈性、特色、OD280/OD315 稀釋酒、氨基酸，其中鎂及氨基酸之各組平均 數分別為 100 至 1000 之間，為避免過大之數值對其他變項之干擾，因此刪
除變項鎂及氨基酸。
酒 178 筆資料分成 3 群，組別＝1 之特徵為酒烈性屬中等，組別＝2 之 特徵為酒烈性最弱，組別＝3 之特徵為酒烈性最強，參見表 4-1-10。
表 4-10 酒 178 筆資料 3 群得的樣本個數及命名
組別 樣本個數 特徵
1 59 烈性中等
2 71 烈性最弱
3 48 烈性最強
比較不同模糊分群演算法之正確率，分類結果詳如表 4-1-11，以 FCM、
FCM-M 及 FCM-CM 之分群演算法之正確率 79.78％較高。
表 4-11 酒 178 筆資料比較模糊分群演算法之正確率
模糊分群演算法 正確率
FCM 79.78％
GG 70.40％
GK 60.67％
FCM-M 79.78％
FCM-CM 79.78％
表 4-12 隨機產生 100 組隸屬度初值分群演算法之正確率
FCM GK GG FCM-M FCM-CM
79.78% 60.67% 56.74% 79.78% 79.78%
79.78% 60.67% 88.76% 79.78% 79.78%
79.78% 60.67% 67.98% 79.78% 79.78%
79.78% 60.67% 67.98% 79.78% 79.78%
79.78% 60.67% 70.22% 79.78% 79.78%
79.78% 60.67% 69.66% 79.78% 79.78%
79.78% 60.67% 67.42% 79.78% 79.78%
79.78% 60.67% 78.09% 79.78% 79.78%
79.78% 60.67% 76.40% 79.78% 79.78%
表 4-12 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
79.78% 60.67% 86.52% 79.78% 79.78%
79.78% 60.67% 93.82% 79.78% 79.78%
79.78% 60.67% 87.64% 79.78% 79.78%
79.78% 60.67% 69.10% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 52.81% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 72.47% 79.78% 79.78%
79.78% 60.67% 42.13% 79.78% 79.78%
79.78% 60.67% 67.42% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 55.06% 79.78% 79.78%
79.78% 60.67% 67.42% 79.78% 79.78%
79.78% 60.67% 88.76% 79.78% 79.78%
79.78% 60.67% 82.58% 79.78% 79.78%
79.78% 60.67% 85.39% 79.78% 79.78%
79.78% 60.67% 71.91% 79.78% 79.78%
79.78% 60.67% 80.90% 79.78% 79.78%
79.78% 60.67% 76.40% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 85.96% 79.78% 79.78%
79.78% 60.67% 73.60% 79.78% 79.78%
79.78% 62.36% 70.40% 79.78% 79.78%
表 4-12 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
79.78% 60.67% 74.72% 79.78% 79.78%
79.78% 60.67% 70.79% 79.78% 79.78%
79.78% 60.67% 78.09% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 71.91% 79.78% 79.78%
79.78% 60.67% 76.40% 79.78% 79.78%
79.78% 60.67% 70.79% 79.78% 79.78%
79.78% 60.67% 41.57% 79.78% 79.78%
79.78% 60.67% 55.06% 79.78% 79.78%
79.78% 60.67% 58.43% 79.78% 79.78%
79.78% 60.67% 69.66% 79.78% 79.78%
79.78% 60.67% 88.76% 79.78% 79.78%
79.78% 60.67% 73.60% 79.78% 79.78%
79.78% 60.67% 58.43% 79.78% 79.78%
79.78% 60.11% 89.89% 79.78% 79.78%
79.78% 60.67% 64.61% 79.78% 79.78%
79.78% 60.67% 41.01% 79.78% 79.78%
79.78% 60.67% 67.98% 79.78% 79.78%
79.78% 60.67% 80.90% 79.78% 79.78%
79.78% 60.67% 53.93% 79.78% 79.78%
79.78% 60.67% 55.06% 79.78% 79.78%
79.78% 60.67% 61.24% 79.78% 79.78%
79.78% 60.67% 67.42% 79.78% 79.78%
79.78% 60.67% 44.94% 79.78% 79.78%
79.78% 60.67% 62.36% 79.78% 79.78%
表 4-12 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
79.78% 60.67% 84.27% 79.78% 79.78%
79.78% 60.11% 73.60% 79.78% 79.78%
79.78% 60.67% 56.18% 79.78% 79.78%
79.78% 60.67% 83.15% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.11% 74.72% 79.78% 79.78%
79.78% 60.67% 71.91% 79.78% 79.78%
79.78% 60.67% 61.24% 79.78% 79.78%
79.78% 60.67% 82.02% 79.78% 79.78%
79.78% 60.67% 93.82% 79.78% 79.78%
79.78% 60.67% 66.29% 79.78% 79.78%
79.78% 60.67% 94.94% 79.78% 79.78%
79.78% 60.67% 87.08% 79.78% 79.78%
79.78% 60.67% 70.22% 79.78% 79.78%
79.78% 60.67% 39.89% 79.78% 79.78%
79.78% 60.67% 74.72% 79.78% 79.78%
79.78% 60.67% 93.82% 79.78% 79.78%
79.78% 60.67% 87.08% 79.78% 79.78%
79.78% 60.67% 65.17% 79.78% 79.78%
79.78% 60.67% 57.30% 79.78% 79.78%
79.78% 60.67% 69.66% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 58.43% 79.78% 79.78%
79.78% 60.67% 56.74% 79.78% 79.78%
79.78% 60.67% 72.47% 79.78% 79.78%
表 4-12 隨機產生 100 組隸屬度初值分群演算法之正確率（續）
79.78% 60.67% 39.89% 79.78% 79.78%
79.78% 60.67% 67.42% 79.78% 79.78%
79.78% 60.67% 70.22% 79.78% 79.78%
79.78% 60.67% 87.08% 79.78% 79.78%
79.78% 60.67% 84.27% 79.78% 79.78%
79.78% 60.11% 75.28% 79.78% 79.78%
79.78% 60.67% 69.10% 79.78% 79.78%
79.78% 60.67% 81.46% 79.78% 79.78%
79.78% 60.67% 60.67% 79.78% 79.78%
79.78% 60.67% 74.16% 79.78% 79.78%
79.78% 60.67% 72.47% 79.78% 79.78%
79.78% 60.67% 69.10% 79.78% 79.78%
79.78% 60.67% 70.40% 79.78% 79.78%
79.78% 60.67% 72.47% 79.78% 79.78%
79.78% 60.67% 53.93% 79.78% 79.78%
79.78% 60.67% 52.81% 79.78% 79.78%
伍、透過實證資料的經驗對理論的驗證
就 178 筆酒資料中，如果使用所有的 13 種特徵，發現其中的鎂各群之 群中心約在 100 左右，加上氨基酸各群之群中心約在 500-1000 之間，發現 分群結果將受制於鎂及氨基酸兩特徵影響，無法發揮其他 11 種特徵，導致 分群結果不佳，本研究改以正規化（normalized）對此 13 種特徵處理，目的 可以避免各特徵之大小差異太大所致，研究初步結果非常理想，此種正規化 各特徵值是未來研究的方向，此次先將超大數值之鎂與氨基酸不列入運算，
所得結果與理論相符。
透過觀察各群資料的最小值與分群正確率，發現產生不收斂的演算法所 對應之資料，會與閥值有密切之關係，參見圖 4-5-1、圖 4-5-2。
0 20 40 60 80 100 120 140 0.38
0.4 0.42 0.44 0.46 0.48 0.5
0 20 40 60 80 100 120 140
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
圖 4-1 樣本資料的最小值與分群正確率得參照圖
圖 4-2 樣本資料的最小值與分群正確率得參照圖
本研究透過實證資量料，除驗證所推導之理論正確無誤，並完全吻合文 獻資料之結果，透過仔細分析程式所執行演算法之過程，從中獲得更多啟示 對未來之研究提供更多可行之具體方案。