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3

........................................................................................................... 6 .............................................. 11 1. ....................... 13 ............................................................................................................... 13 1.1. .................................... 14 ......................................................................................... 20 1.2. ............................................................................ 20 ......................................................................................... 26 1.3. .................................................. 27 ......................................................................................... 31 1.4. .................................................................................... 31 ......................................................................................... 34 1.5. .. 35 ......................................................................................... 40 1.6. ............. 41 ......................................................................................... 44 ................................................................................................................. 44 ................................................................................ 45 2. ................................................................. 58 ............................................................................................................... 58 2.1. ..................................................................................... 59 ......................................................................................... 64 2.2. .................................................................... 65 ......................................................................................... 67 2.3. ............................................................................................ 67 ......................................................................................... 70 2.4. ........................................................................ 71 ......................................................................................... 77 2.5. ............................... 77 ......................................................................................... 81 2.6. ............................... 82 ......................................................................................... 95 ................................................................................................................. 96 ................................................................................ 98

4

3. ............................................. 100 .............................................................................................................. 100 3.1. ................ 101 ........................................................................................ 111 ............................................................................... 112 3.2. ................... 113 ........................................................................................ 122 ............................................................................... 122 3.3. ........................... 123 ........................................................................................ 143 ............................................................................... 143 3.4. ...................................................... 145 ........................................................................................ 152 ............................................................................... 152 3.5. ................................................ 154 ........................................................................................ 161 ................................................................................................................ 162 ............................................................................... 165 4. ................................................................ 168 .............................................................................................................. 168 4.1. ACL- . 170 ........................................................................................ 193 4.2. ......................................................... 194 ........................................................................................ 202 4.3. .............. 202 ........................................................................................ 209 4.4. FT- ................................................................................... 209 ........................................................................................ 210 4.5. - ..................................... 210 ........................................................................................ 217 ............................................................................... 217 5. - .............. 219 .............................................................................................................. 219 5.1. - .. 219 ........................................................................................ 224 5.2. ................................ 225 ........................................................................................ 233

5

5.3. ............................. 234 ........................................................................................ 236 5.4. ........................................................................................ 236 ........................................................................................ 238 5.5. ............................ 239 ........................................................................................ 246 5.6. ...................................................................................... 246 ........................................................................................ 249 5.7. ................................ 250 ........................................................................................ 270 5.8. ....................................................... 270 ........................................................................................ 277 5.9. ............................................ 278 ........................................................................................ 279 5.10. ............................... 279 ........................................................................................ 285 ................................................................................................................ 285 ............................................................................... 286 6. ....................................................... 289 .............................................................................................................. 289 6.1. FuzzyTend ............................................... 289 6.2. .................................................................. 300 ........................................................................................ 313 ................................................................................................................ 313 ............................................................................... 314 .................................................................................................. 316 ...................................................................................................... 317

6

, ...

.

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7

, , - - -, , - - .

, - , - Data Mining, Time Series Data Mining (TSDM). - Time Series Data Mining , -, , , , -, - , , -, .

Time Series Data Mining , (), - . - , , , - - - -. . , . , , Data Mining : , , , , -, , , , - .

8

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9

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- - - (Time Series Data Minig): , , , , , , . - , -

10

, , - . -, - .

- . - - , - - .

11

ACL- (Absolute&Comparative Linguistic) -

. CICO CICO (Crisp-Input and

CrispOutput).

CiFo CIFO (Crisp-Inputs and Fuzzy-Outputs). CWP (computing with words and perceptions

CWP).

DM Data Mining (DM) .

FARIMA - (FARIMA)

FAT Fuzzy Approximation Theorem, - , - .

FiFo FIFO (Fuzzy-Inputs and Fuzzy-Outputs).

FLSRA , FLSRA (Fuzzy least-square regression analysis).

GCL : Generalized Constraint Language. GTU (Generalized Theory

of Uncertainty.

IFSA , , Interna-tional Fuzzy Systems Association.

NL , .

TPM Theory of Precisiation of Meaning (TPM). TSDM Time Series Data

Mining (TSDM).

.

12

. (ARIMA) -

. . . . . . . . . . , . . . . . . . . . . (MSE) . . .

13

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18

[, 2009], [

., 2008; ., 2007].

: [, 1997;

, 2004], [, 2008], -

[ ., 2008; , 2007], CAD/CAM/CAE- [-

, 2008], [

., 2008],

[, 2008], -

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[ ., 2008 ].

. -, -

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19

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20

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1.2.

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- , - (, , ), - . X - . -, .

, - S. - VK. Mr, - VK,

),,,,,( MKSVKYXMarkMr

21

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); S ; MK . MK -

. - - - . , .

- [, 2006].

, , . , - , , -, , , - , -, . - . .

[, 2006].

Y, . . , , - . - VK, .

22

-. ( ), (Human Development Index), . - . - S. , , () , .

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: 1. -

, : , - , , .

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23

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, - S -, , .

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) pr-, -, , , ; ) post-, , - , -; ) cur-, , . (pr-), -

(post-) (cur-) -

24

. r- , -, post- cur-.

- , - , . - , .

, : , ; ; , -

. -

, - , , - , , .

- . [, 1974]. , () , . , - , .

),,,,,(__ MKSVKYXMarkFMrF

25

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); S , -

. - (), , Name - ( ), W ( - -), MF , W, - W [0,1];

MK ().

-:

1. - , .

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26

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9. . ? 10. Mr. 11. -

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? . 14.

? .

15. () ? .

16. Mr. 17.

. 18.

. 19.

? 20. , -

? 21. : ,

, pr-, post-, cur-.

27

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23. .

1.3.

- . - , - , , , .

() , [ ., 2007 ]: : ( ),

( ), - ( );

( , ); ( , ); , , (

); , ( -

); (,

). , -

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28

. :

1) , ;

2) - ;

3) ; 4) .

, . , -

, , , , -. . - -, , [, 2004]. - , , -, .

- - . , - . - , -. : , , , , -

29

, . . , - (), - . , - . - . , - , , - - .

, , n .

, - },{ ii tx , , ].,1[,,, 1 niNtRXXx ii

ix . 1.1. () -

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i~ - .

. Fuzzy,

)),((~ ~ ixi xwFuzzyx i , i~ X~ , X~ ; w ( X) i~ , wxi ;

30

]1,0[)(~ wix

i~ ix , .

1.2. i~ wB wxi , 0)(~ wix , B - X~ .

, - . - , , -. ]1,0[)(~ w

ix .

. 1.1 , - i~ , -.

. 1.1.

1. - ?

2. , - .

31

3. . 4. . 5. i~ .

1.4.

, . [, 1984]:

, ;

- ;

- -, - ;

.

cur- , - , , . , . - .

[ ., 2003], - , , . - .

32

, . - :

, - , ;

, - ;

, - .

, , . - , , - .

, , , - , , . : 1. i- 2. - 3. 4. - 5. . - , - .

, - - . . -

33

[, 2007; , 1999; ., 2006]. : 1. i- 2. 3. - . - , - [, 2008; -, 2008; , 1989; ., 1976; , 1990].

pre- , - [, 2008 ; ., 2007 ]. - ( ), , , . , .

, - - - :

- , - ;

- ;

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34

, - .

1. . 2.

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, .

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.

1.5.

-, - . - , , , -, , . , . , , - . , - , - () - , - . ,

35

, , - . ( ) - - , - .

, -, , - , - : - ; - , , .

- , -, , - , :

,

() ,

,

,

.

36

- . , - , - [, 2003] , [, 1997; , 2004; ., 2007 ; ., 2008 ; , 2001; , 1985].

1.5.1.

- , . , , .

-, , , , - . - , - , .

, t1 - z1, (t2, t3) z2, t4 z4 z5. [, 1985].

- , , , - ,

37

, , - . , - [, 2008; ., 1991], - -, [, 2008].

, , , . , - , - .

, - - .

1.5.2.

- -. - , . - , , , - , . , - , - , . - :

38

, , - - , . -, [ ., 1989].

, - . , -, , , - . - [, 2008; -, 1981].

, , , . , - , , -, , , , , . - - . - , , - , . [, 2008; ., 2008; , 2007].

, ,

39

, , , - . - [, 2004] .

- . -, , . -. -, . -, -, . -, - , -, .

- - . - , , , .

1. -

(), ?

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40

3. , ?

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( )

-.

- [, 2004]: , , , . - - . , - , - , - , . - . - - ,

41

, .

, .

1. .

. - - , - (). , , . () - - .

. , , },{ ii tx . x t0 ti tn, ( ) Tr. Tr , , , - [, 2004]. , },{ ii tx , Tr , - .

2. . , , ,

.

42

, , . , , , - , . - , - , .

. - , . , - , . , , . , , , . .

3. . , ,

. . -

, - . - Tr . Tr , - , , . .

4. . -

, -

43

. -, , , -, . , . , , , .

. Tr , - . . - , , - . , - , , .

1. -

? 2.

. 3.

. 4. -

. 5.

.

44

- , - , (-) , - . - , , , , , , , .

1. [, 2008 ] , . . -

/ . // (-2008): (. , 27-29 , 2008 .). 2. : , 2008. . 3-9.

2. [, 2008 ] , . . / . - // (-2008) : - (. , 27-29 , 2008 .). . 2. - : , 2008. . 9-23.

3. [ ., 1986] - / . . , . . , . . . ; . . . . . : . . . .-. ., 1986. 312 .

45

4. [ ., 2008] , . . - / . . , . . , . . // - -2008 (28 - 3 , 2008 ., . , ) : -. .1. . : , 2008. . 269-280.

5. [ ., 2008] , . . CAD/CAM/CAT- / . . , . . // - - (AIS08) (CAD-2008). 4- . . : , 2008. . 3. . 312-314.

6. [ ., 1990] , . . - / . . , . . , . . // . . . . . 29. . : , 1990. . 127-201.

7. [ ., 2008] , . . - / . . , . . - // - - (AIS08) (CAD-2008). 4- . . : , 2008. . 1. . 95-100.

8. [ ., 2003] , . . - : . / . . , . . , . . ; . . . . . : , 2003. 368 .

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46

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15. [ ., 2007 ] , . . - / . . , . . // . . 2. 2007. 1.

47

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18. [ ., 2002] , . . - / . . , . . , . . . . : , 2002.

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50

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54

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56

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57

2.

- , -. - , - - . - , , - , -. , - , , - () . - [Zadeh, 1965; , 1974; , 2007; , 1986; , 1989; , 1999; , 2004; , 2006; , 2006; ., 2007; ., 2007].

, , - (), , :

1. , - , - , . - , , - . , - .

58

2. , - : , , -, . .

3. . , , - . .

2.1.

, . [Zadeh, 1965] - , - , , - . , - , , .

- , . - , , . , - . , - .

59

, - .

, .

. - xX :

Y= (x,B), Y , -

() xX; , , :[0,1].

; X . -

, , - ( ). (x,B) - wX, (x,B) , - . - ;

B , .

, , X. - , - , . , - , - 1. -

60

, - 2.

-, : 1. . -

. , , Y= (x,B) - w, . - = {x1/y1, 2/2, .., n/yn}. - , Y= (x,B), , .

2. . , , , - . Y=(x,B) - (. 2.1).

2.1. - ={, c}:

)exp(),(2

cxBx ,

; .

61

. 2.1. ) , ) , )

2.2. -, B={a, b , c}, :

, , ,0

,

,

),(

cxax

cxbbcxc

bxaabax

Bx

b ; , . 2.3. -

, B={a, b, c, d}:

(x) 1

x

(x) 1

x

(x) 1

x)

) ) a b c a b c d

c

62

. , ,0

,

,1

,

),(

dxax

dxccdxd

cxb

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Bx

, - Y=() Y=(x,B). .

() - ( ) . - Z ( ) Z=Z(). - , . - x, Z, , x Z Z(x). , Z Z(), - , , - . - Z Z() .

}{xX ( ), - . X : A=, B=, C=, . , xX A

)}(,{ xxA A , B )}(,{ xxB B , )}(,{ xxC C . , ,

63

: )(xA A , )(xB B , )(xC C .

m - : 1) , ; 2) }{xX , -

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4) .

1. -

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64

8. , ?

9. ? 10. , -

. 11. .

2.2. , -

. , , -

, , - -. , , , , . - , - , -, , , , , - , [, 1976].

, . - , -

65

? . , , () [, 1974].

PGXXName ,,,~, ,

Name ; x; X~ -, -

, , X~ ={, , , .};

G () X~ , -, - ;

P , - X~ X~ . , [, 2007], . 2.2.

. 2.2.

66

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1. . 2. , -

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, X~ -, G - () , P .

2.3.

() ,

- , . . - :

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(fuzzified) , , - . - .

67

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81

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2.1 IFSA05

. Toward a Computational Theory of Precisiation of Meaning Based on Fuzzy Logic The Concept of Cointensive Precisiation ,

. , .

Order Structure, Topology and Fuzzy Sets ,

. From Natural Language to Formalized Language and Back

. On the Links between Probability and Possibility Theories

. Knowledge-based Clustering for Human-Centric Systems, ,

2.2

IFSA07

.

Fuzzy Logic as the Logic of Natural Languages

. Computing with Words and Granules

. Control/Robotics Applications based on Soft Computing Technology ,

. Computing with words, usuality qualification and linguistic quantifiers: tools for human-centric computing , :

. Dynamic and Distributed (D2) Fuzzy Modeling

82

. 2.2 . Novel Weighted Averages as a Computing With Words Engine

. Uncertainty and Fuzziness in Knowledge Discovery from Large Databases

. ( )

OWA Operators for Gene Product Similarity, Clustering, and Knowledge Discovery OWA ,

2.3

IFSA09

. A Unified View of Uncertainty Theories

. Fuzzy Modeling: Fundamentals, Design and Challenges : ,

. Visual Clustering Methods

. Fuzzy and Probabilistic Clustering

. Artificial Neural Networks

. , .

Introduction to Fuzzy Networks

83

. 2.3

. -

Fuzzy Data in Statistics: Formalization and Main Problems :

. Soft Computing for Sensor and Algorithm Fusion

. Robust Statistics

. An Axiomatic Approach to the Notion of Rational Preference Structures

. Feature Selection

2.4

IFSA- EUSFLAT09

. , .

Casual Communication with Robots using Speech Recognition Module , -

. Fuzzy Logic in Machine Learning

. Capacities and the Choquet integral in decision making: a survey of funda-mental concepts and recent advances : -

. Fuzzy Systems, Choice Paradoxes and Optimal Committees ,

84

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- , IFSA07 . . , - , , - , . . -, , - . - , , .

. - , - . . -, . , . -, . . IFSA05 . - , . , . Theory of Precisiation of Meaning (TPM), . , [Zadeh, 2006].

85

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86

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SA07 IFSA09 . IFSA07 14 128 , IFSA09 - 32 (240 ). , ( , , Data Mining, - Web), (. 2.6).

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94

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6. . IFSA05, . IFSA07. . IFSA07.

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95

2.6 IFSA09

Recent advances in Evolving Fuzzy Systems -

E. Lughofer, D. Filev, P. Angelov

Advances in Soft Computing Applied to Databases and Information Systems ,

P. Bosc, A. Hadjali, O. Pivert

Transforms, Time Series and Other Applications ,

I. Perfilieva, V. Novak, N. Yarushkina

Fuzzy and Possibilistic Optimization

M. Inuiguchi, W. A. Lodwick, M. Luhandjula

Fuzzy Differential Equations

Y. Chalco-Cano, W. A. Lodwick

Soft-computing for Web 2.0 and Semantic Web Web 2.0 Web

R. Yager, M. Reformat

Solvability of Fuzzy Relation Equations and Fuzzy Inter-polation

I. Perfilieva, M. Stepnicka

Aggregation Operators

H. Bustince, T. Calvo, R. Mesiar

Fuzzy Sets in Computational Biology

U. Bodenhofer, E. Huellermeier, F. Klawonn

Mathematical Fuzzy Logic

P. Cintula, C. Noguera

Machine Learning and Data Mining

P. Angelov, E. Huellermeier, F. Klawonn, D. Sanchez

Type-2 Fuzzy Logic, Advances and Applications 2,

A. Celikyilmaz, I. B. Turksen

Inter-relation Between Interval and Fuzzy Techniques

V. Kreinovich

Advances in Soft Computing for Spatiotemporal Informa-tion Systems -

G. De Tr, R. Ribeiro, J. Dujmovic

Interpretability of Fuzzy systems: Theory and Applications :

J. M. Alonso, L. Magdalena

Computing With Words, Actions and Perceptions ,

S. Guadarrama

New trends in Fuzzy Reasoning of Robotic Systems

P. J. Sequeira Gonalves, L. F. Mendona

96

. 2.6 Fuzzy Numbers and Fuzzy Arithmetic

P. Grzegorzewski, L. Stefanini

Intuitionistic Fuzzy Sets

E. Szmidt, J. Kacprzyk

New Advances on Genetic Fuzzy Systems

Y. Nojima, R. Alcal

Measures and Integrals

M. Grabisch

Fuzzy Geographical Information

C. C. Fonte, J. Santos, M. Caetano, L. Gonalves

Soft Computing in Image Processing and Computer Vision

Soft Computing in Image Processing and Computer Vision

Models and Fuzzy Arithmetic in Economics and Business

M. L. Guerra and L. Stefanini

Soft Computing in Finance

R. J. Almeida, M. Lovric, V. Milea

Topics in Decision-Making Using Fuzzy Sets ,

D.Ralescu

Decision Making in Fuzzy Environments

M. T. Lamata, D. Pelta

Soft Computing in Medical Imaging

I. K. Vlachos, G. Schaefer

Medical Concepts in Soft Computing

C. Schuh, R. Seising

Philosophical, Sociological and Economical Thinking ,

E. Trilla, R. Seising, H. Nurmi

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Control. 1965.

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5. [ ., 2007] , . . / . . , . . , . . . . : -, 2007. 284 .

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ARIMA(p,d,q), p, d, q, , : 1. AR(p) ARIMA(p,0,0). - AR(p) :

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],[ 1kk xx ;

125

5) ],[ bax 1)(1

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126

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127

; (b) ; (c) F- - Npp ,...,1 . , kp (, , N), nFf , . F-, , [Perfilieva, 2006].

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128

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130

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131

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137

. grx = ( gmrgjrgrgr xxxx ,...,,...,, 21 ) = (zg, ur, zr) r, . xj (tjk), mj ,1 , tjk yi (k) tk,

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138

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139

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)( iJr J .

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(

N)

(N)

(N

)

1 1

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3.2 , -

- 1, 3, 6 1, 2, 5, 7.

140

1. . 2. . 3. ? 4. . 5.

. 6. ?

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20. [, 2008] , . . , - / . . [ : http://www.exponenta.ru/educat/news/degtyarev/paper2.pdf; 30.12.2009].

21. [ ., 2007] , . . - / . . , . . -, . . // , , , 2007. 12. . 12-15.

22. [ ., 2009] , . . F- - / . . , . . , . . // 2009 : -. : , 2009. . 459-461.

23. [, 2008] , . - / . , . , . . // . 2008. 4 . . 65-68.

3.4.

, , , , - , , . , - , - . -

143

, , - -

3.4.1. -

,

, - - . , (Least-square), , - . - -, . ( -, ). - .

, 1982 . , - . , , .

-

144

. (vagueness) () ( ).

- .

, -, , - , ( -) .

(. 3.3).

PossibilisticFuzzyRegressionModel

Fuzzyleast-squareregressionanalysis

. 3.3.

, (Possibilistic Fuzzy Regression Model) [Tanaka, 1982]. , FLSRA (Fuzzy least-square regression analysis) [Diamond, 1988; Celmi, 1987].

, , , , .

, - -

145

, , - , -.

, .

: mjxxy jnjj ,...,1,,..., 1 , :

nn xAxAAY~

1~

1~0

~... ,

nissaA RiLicii ,...,1),,,( ; cia ~iA ;

Ri

Li ss , . : 1. jy

~jY mjhyY jj ,...,1,)(~ , h -, , .

2. . - . , - mjxxy jnjj ,...,1,,..., 1 :

),,...( 0 cnc aa ),,...( 0 LnLL sss ),,...( 0 RnRR sss

n

I

m

jij

Ri

Li

LRL xsssssmZ1 1

000 )( .

, - . - (MSE) :

146

n

jjj Ydefym

MSE1

2)]([1 ,

)( jYdef . , -

: CICO (Crisp-Input and CrispOutput), - FIFO (Fuzzy-Inputs and Fuzzy-Outputs) CIFO (Crisp-Inputs and Fuzzy-Outputs) [D'Urso, 2003; Hojati, 2005; Bisserier, 2009].

[, 1997; Bardossy, 1990; Sabic, 1991], , - . [, 2000] , - 40% - .

ARIMA -

, . - (FARIMA) [Tsen-ga, 2001]. , - - ARIMA - . FARIMA - ARIMA -.

[Khashei, 2008] , - ARIMA

147

- . , ARIMA + + - .

3.4.2. - , -

, - [, 2007; , 2008].

, [Huarng, 2006; Yu, 2008] .

[Alizadeh, 2009] - - . - . - : , , . - .

[Kuo, 2001] . [, 2006] - - , , [ ., 2007; , 2008]

148

- .

() , -

- -, - [, 2004].

- , .

- , - . - , - . , , : -, , - .

ANFIS TSK. , - . - -. [, 2004; ., 2007; , 2007; ., 2007].

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18. [, 2000] , . . / . . // . . . 308. . : , 2000. 220 .

151

19. [, 2008] , . . / . . // - . 2008. 3.

20. [, 1997] , . . / . . // . 1997. 11. . 27-32.

21. [, 2004] , . . - : . / . . . . : -, 2004. 320 .

22. [, 2007] , . . - / . . , . . , . . // - . 2007. 4. . 15-19.

3.5.

3.5.1. -

. ,

, - - , .

, . () - . .

[, 2009]. -

152

() - k X.

1,...,2,1),( kniwkxW i k- X. ,

iw . -, s : ),...,2,1( siCi .

siai ,...2,1 . -

mjjjaaaxD ,...,,)(

21 .

, , . - , , - - .

- , . - . , , - [, 2009].

, (computing with words and perceptions CWP) [Zadeh, 2001; Batyrshin, 2004].

() - , . . . (attribute-based) - .

153

- (generalized constraint) [Zadeh, 2006]. -

X isr R,

X ; r ; R () . : X n- , X= (X1, , Xn); X ; X : X=f(Y); X X/Y; X , , X= Location (Residence(Carol)); X X: Y isr R; X G[A]: (Name1, , Namen), -

Namei, i =1, , n, Ai. X isr R: r: = : X=R, X is=R; r: : X R; r: : X R; r: blank : X is R, R

X; r: v : X isv R, R X; r: p : X isp R, R -

X; r: bm : X R is bm;

154

r: rs : X isrs R, R - X;

r: fg : X isfg R, X R ; r: u ( usually): X isu R

(X is R); r: g : X isg R , R

.

: Generalized Constraint Language (GCL). -

. : 1) ; 2) ; 3) ; 4) . -

-: . (computing with words and perceptions CWP) - : ( perception) - . - (generalized constraints). , .

3.5.2. (Time Series Data Mining)

, Data Mining,

155

Time Series Data Mining (TSDM).

, - .

Data Mining , . . (CWP) - , . Data Mining , - , , . , - .

Data Mining - , [Batyrshin, 2007]:

1) [Graves, 2009]; 2) [Giove, 2009]; 3)

[Herbst, 2009]; 4)

; 5) (summarization) ,

[Kacprzyk, 2009];

6) , ; 7) ; 8) ;

156

9) , - .

- : -, . . : , , , . . - -- , : .

TSDM , [, 2007]:

1) ;

2) - , - .

- ( - ).

- [, 2007]: 1) -

; 2)

; 3) -

( ); 4) -

.

157

[, 2007] - , . - : - - . - . - .

- , :

)),((&)),((),( qttttytt bababa .

[ta, tb] q . - , -. , , . - , .

CWP - [, 2009]:

(precisiation) , ; (gene-

ralized constraints);

; -

(generalized constraints);

.

158

Time Series Data Mining :

1) [, 2004];

2) : If trend is F then next point is Y [, 2004];

3) - ;

4) [Yu, 2005];

5) [Batyrshin, 2004].

1. . 2. . 3. Data

Mining?

4. Data Mining? 5. - . 6. Time Series Data Mining.

- , 3, , :

1. . -

, . , ,

159

, - .

2. . , -

, - . , . .

3. . :

, - , , - () , , , -.

4. ().

, - . : - . - , , , - , . . - .

160

3.3 / .

, - , , .

, - , - , , .

2004 . . [, 2004] , . , - , .

3.3

/ ( )

/

1. - 2. 3.

( )

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1. 2. 3.

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1. 2. 3.

161

. 3.3 - ( )

/

1. - 2. 3.

- ( )

/