Fuzzy GP

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1 : 林

2 理論數論 1

3 率 2

4 類,, 金流量金利數益,, 3

5 不異 (Multi- Valued) (Single-Valued) 數數數 (Local Optimum) (Global Optimum) 4

6 (Multi-valued) (Non-linear) (Self-learning) 5

7 (Genetic Programming, GP) GP 1. 亂數 2. (individuals) 3. (Selection), (crossover), (mutation)

8 GP GP 數 (Functional nodes), 林, F={+, -,,, True or False, If Then Else,...} (Terminal nodes) 數參數 T={x, y} x, y 立數 7

9 GP Selection Roulette wheel Rank Tournament Crossover 兩 (parents) 亂數,, (offsprings) Mutation 亂數, 亂數 8

10 數若數, 理不狀, 讀不若 (performance), 降度, 讀, 不易 (building block) 9

11 理不易度 (Depth dependent crossover) 度率, 度, 率 (Island model crossover) 度來年數 (Page-based crossover) GP 串列,,, 不 10

12 理論 (Crisp set) x, 不 (Fuzzy set) x A 隸. 隸度 0 1 連 µa( x) [0,1] x 度, 隸度 1, 0 µa(x) x 隷數 11

13 數數 (Fuzzy Number) 數, 見 (Triangular) 數 b 隸度 µa(x) 1, 兩 a, c 隸度 µa(x) 0. µ A( x) = ( x a ), a x b ( b a ) ( x c ), b x c ( b c ) 0, otherwise µa(x) a b c 12

14 數 ( ) (Trapezoidal) 數落 [b, c] 隸度 µa(x) 1, 兩 a d 隸度 µa(x) 0. µ A( x) = ( x a), a x b ( b a) 1, b x c ( x d ), c x d ( c d ) 0, otherwise µa(x) 1 0 a b c d x 13

15 數數 [a, b] [d, e] 數兩, a b, d e 兩 : [a, b] + [d, e] = [a + d, b + e] [a, b] [d, e] = [a e, b d] [a, b] [d, e] = {min[ad, ae, bd, be], max[ad, ae, bd, be]} [a, b] [d, e] = {min[a/d, a/e, b/d, b/e], max[a/d, a/e, b/d, b/e]} 14

16 理論領易略 GP 易略 GP S&P500 GP 利率率, 15

17 BV = f ( v, v2,... v 1 n ) BV: f(): v: 立數 n: 數數 16

18 數 (Fuzzy number type) 數 (Variable set 數 (Fuzzy operator set) (Fuzzy Tree Crossover) 數 (Fitness function) 參數 (Parameter) 17

19 數數 18

20 GP 狀數 Variables (v i ) 數 Numbers (n j ) 數 Arithmetic Operators (f k ) f 1 f 2 f 3 n 1 v 1 n 2 f 4 v 3 n 3 19

21 GP 數 Variables (v i ) 數 Fuzzy Numbers (n j ) 數數 Fuzzy Arithmetic Operators (f k ) f 1 f 2 f 3 n 1 v 1 n 2 f 4 v 3 n 3 20

22 procedure Fuzzy GP Business Valuation Initialize a population of fuzzy expression trees while (termination condition is false) Select fuzzy expression trees for crossover Crossover selected fuzzy expression trees Mutate fuzzy expression trees endwhile Return the best fuzzy expression tree endprocedure 21

23 數 70 率 r 1 : 率 (return on total assets, %) r 2 : 流率 (current liabilities, %) r 3 : (earning per share) r 70 : (fixed assets per employee) 22

24 數數 Triangular 1 Trapezoidal 易略 0 Z 1 Z 2 Z 3 Z 4 x 23

25 數 {+, -, *} 兩數, X = [x 1, x 2, x 3, x 4 ] and Y = [y 1, y 2, y 3, y 4 ] 24

26 [x 1, x 2, x 3, x 4 ] + [y 1, y 2, y 3, y 4 ] = [x 1 +y 1, x 2 +y 2, x 3 +y 3, x 4 +y 4 ] [x 1, x 2, x 3, x 4 ] - [y 1, y 2, y 3, y 4 ] = [x 1 -y 4, x 2 -y 3, x 3 -y 2, x 4 -y 1 ] [x 1, x 2, x 3, x 4 ] * [y 1, y 2, y 3, y 4 ] = [min (x 1 y 1, x 1 y 4, x 4 y 1, x 4 y 1 ), min (x 2 y 2, x 2 y 3, x 3 y 2, x 3 y 3 ), max (x 2 y 2, x 2 y 3, x 3 y 2, x 3 y 3 ), max (x 1 y 1, x 1 y 4, x 4 y 1, x 4 y 1 )] 25

27 數數若數切 26

28 f 1 T 1 f 2 f 3 n 1 r 2 n 2 f 4 f 1 T 1 f 2 f 3 n 1 r 2 n 2 r 2 r 3 n 3 f 1 T 2 f 1 T 2 f 2 f 3 f 2 f 3 n 1 r 2 n 2 n 1 f 4 n 2 r 3 n 3 27

29 數 ( ) f 1 T 1 T 1 n 1 T 2 n 2 亂數 n 1 n 2 切 f 2 f 3 n 1 r 2 n 2 f r 3 f 1 T 2 f 2 f 3 n 1 r 2 n 2 n

30 數 ( ) f 1 T 1 f 2 f 3 n 1 r 2 n 2 f r 3 n f 1 T 2 數, 率 f 2 f 3 n 1 r 2 n

31 數數狀不易若立數 [z 1, z 2, z 3, z 4 ] 易略 [z 1, z 2 ]: (buying range) [z 3, z 4 ]: (selling range) 隸數 : 數易略率 FV = ROI σ 30

32 Fuzzy GP 參數 Number of generations 500 Population size 5000 Arithmetic operators +, -, Maximum tree depth 5 Crossover rate 0.9 Mutation rate 0.05 Selection Tournament Crossover Mutation Reserved elitists 留 3 31

33 練 9 年, 3 年, 1 年 3 年, 1 年,, 率 32

34 Borland C ++ Builder 6.0 料理 Microsoft SQL Server 2000 料來料 SPSS

35 來 10 年聯,, 34

36 聯金

37 練 9 年 : 練 81~89 年 3 年 : 練 87~89 年 1 年 : 練 89 料練年度年料易行易, 年

38 易略理不易, 金數理易, 金數理易隷數率 1 0 理 x 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x 37

39 料 ~

40 練 9 年 1 年練 81-89, 90, 易 9106/01~ 率 (%)

41 練 3 年 1 年練 87-89, 90, 易 9106/01~ 率 (%)

42 練 1 年 1 年練 89, 90, 易 9106/01~ 率 (%)

43 聯 -3 年率 (%) w w w w w w w 率

44 聯 -1 年率 (%) w w w w w w w w w

45 8-3 年率 (%)

46 8-1 年率 (%)

47 數 - 聯例數數 ( : ) : : : : : :03 46

48 數 - 聯例數數 ( : ) : : : : : :27 47

49 率

50 率 (%) 易

51 率率

53 理論 GP 理論理練練數, 行率率,, 隸度易略行 52

54 理念數易略金 53

55 數料粒度數不 54

56 來良易略率 55

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