CN103413038A - Vector quantization based long-term intuitionistic fuzzy time series prediction method - Google Patents

Abstract

The invention discloses a vector quantization based long-term intuitionistic fuzzy time series prediction method. The method includes the steps of A, intuitionistic fuzzification preprocessing of serial data and B, vector quantization based long-term intuitionistic fuzzy time series prediction. A long-term intuitionistic fuzzy time series prediction model built by the method expands single output of the serial data into multiple outputs, a predicated value is converted from a scalar into a vector, and accordingly long-term predication performance of a time series system is improved to a great extent. A sliding window mechanism is introduced into the method, fuzzy change characteristics of the serial data are acquired accurately and rapidly; a discourse domain internal is divided dynamically by the aid of an IFCM (intuitionistic fuzzy C-means) algorithm to be more close to the actual uncertain data distribution; by the aid of vector quantization based long-term time range prediction, the problems of zero matching of intuitionistic fuzzy rules and system error accumulation can be well solved; through example verification and result analysis, the model has good predication performance.

Description

Long-term intuitionistic fuzzy Time Series Forecasting Methods based on vector quantization

Technical field

What the present invention relates to is a kind of long-term intuitionistic fuzzy Time Series Forecasting Methods based on vector quantization.

Background technology

Time series refers to time dependent randomness and the front and back dynamic data sequence that is mutually related that has, time series analysis is important application branch of random mathematics, it is to use the method for Probability Theory and Math Statistics from the sequence historical data, extracting for information about, disclose the architectural feature of time series itself, thereby the related law between the grasp sequence data, predict and control future value with the past value of sequence ^[1].Fuzzy time series analysis is to be fuzzy number by the sequence specification of variables, utilizes fuzzy reasoning to carry out the scientific theory of time series forecasting.Owing to processing preferably ambiguous and incomplete fuzzy message, model has stronger robustness and compatibility, the Fuzzy Time sequence prediction has obtained the extensive concern of academia and field of engineering technology, and merge mutually with other optimum theories the multiple improvement algorithm that has been born, effectively improved the precision of time series forecasting ^[2-8].Yet along with reaching its maturity of Fuzzy Time sequence prediction theory, its limitation also shows especially gradually: the single real-time smear out effect trend that can not effectively describe and characterize sequence data of common fuzzy set degree of being subordinate to; Equidistantly the domain interval division can't reflect continuous data characteristic pockety; While processing the logical relation between fuzzy time series, usually follow a plurality of uncertain fringes, the system prediction precision can decrease; The Fuzzy Time sequence prediction is confined to the prediction of short-term time range mostly, even the minority model attempts carrying out long-term forecasting, but all be based on the mapping of the single output of many inputs, for the different time scope is set up different models, so not only increased system complexity, ignored the random dependence between predicted value and easily caused the accumulation of error.In fact, can obtain simultaneously a plurality of predicted values in a long-term time series forecasting step, form a predictive vector, if utilize vector quantization method will help to solve the concrete application problem of long-term time series forecasting.

List of references

[1]K.P.Harikrishnan，R.Misra，G.Ambika.Revisiting the box counting algorithm for the correlation dimension analysis of hyperchaotic time series[J].Communications in Nonlinear Science and Numerical Simulation，2012，17(1)：263-276.

[2]Q.Song，B.S.Chissom.Forecasting enrollments with fuzzy time series：Part I[J].Fuzzy Sets and Systems，1993，54(1)：1-9.

[3]Shiva Raj Singh.A computational method offorecasτing based on high-orderfuzzy time series[J].Expert Systems withApplications，2009，36(7)：10551-10559.

[4]Enjian Bai.A heuristic time-invariant model for fuzzy time series forecasτing[J].Expen Systems with Applications，2011，38：2701-2707

[5]Own C M，Yu P T.Forecasting Fuzzy Time Series on a Heu-ristic High-Order Model[J].Cybemetics and Systems，2005，36(7)：705-717.

[6]Sheng Tun Li.Deterministic vector long-term forecastingfor fuzzy time series[J].Fuzzy Sets and Systems，2010，161：1852-1870

[7]Li S.T.，Cheng Y.C.Deterministicfuzzy time series model for forecasting enrollments[J].Computers&Mathematics with Applications，2007，V53(12)：1904-1920.

[8]Li S.T.，Cheng Y.C.，Lin S.Y.A FCM-based deterministic forecasting model for fuzzy time series[J].Computers&Mathematics with Applications，2008，V56(12)：3052-3063.

[9]Lendasse A，Francois D，Wertz V.Vector quantization：a weighted version for time-series forecasting[J].Future Generation Computer Systems，2005，V21(7)：1056-1067.

[10]E.Mwebaze，P.Schneider，F.M.Schleif.Divergence-based classification in learning vector quantization[J].Neurocomputing，201l，74(9)：1429-1435.

[11] Shen Xiaoyong, the thunder hero, lijin, Cai Ru. the clustering method [J] of the intuitionistic fuzzy set data of based target function. systems engineering and electronic technology, 2009,31 (11): 2732-2735. (SHEN XY, LEI YJ, LI J, CAI R.Clustering technique to intuitionistic fuzzy sets data based on objective function[J] .Systems Engineering and E1ectronics, 2009,31 (11): 2732-2735)

[12] Zheng Kouquan, the thunder hero, Wang Rui, Wang Yi. based on the IFTS Study on Forecasting Method [J] of determinacy conversion. applied science journal, 2013,31 (2): 204-211. (ZHENG KQ, LEI YJ, WANG R WANG Y.The Research for Forecasting Method of IFTS Based on Deterministic Transition[J] .Journal of Applied Sciences, 2013,31 (2): 204-211.)

Summary of the invention

Given this, the present invention incorporates the time series analysis theory by Intuitionistic Fuzzy Reasoning, use sliding window mechanism easy to identify to obtain the distribution characteristics of sequence data, based on intuitionistic fuzzy C mean cluster (IFCM) algorithm optimization domain interval division standard and set up on the basis of determinacy conversion intuitionistic fuzzy rule base, long-term intuitionistic fuzzy Time Series Forecasting Methods based on vector quantization has been proposed, solved preferably the bottleneck problem of Fuzzy Time sequence prediction theoretical developments, and method is simple, predict the outcome more accurate.

Technical scheme of the present invention is as follows:

A kind of long-term intuitionistic fuzzy Time Series Forecasting Methods based on vector quantization comprises the following steps:

The intuitionistic fuzzy pre-service of A sequence data

If given length is the time series historical data X=(x of l ₁, x ₂..., x _τ..., x _l), definition moving window width w, sequence former piece length p and predicted vector dimension d, wherein w=p+d; Sequence data intuitionistic fuzzy Preprocessing Algorithm is specially:

A1: carry out sliding window mechanism at moment τ along the X sequence, build the subsequence S of X _τ, can be expressed as:

Comprising n sub-sequence data collection S may be defined as:

$S=S_1^w,S_{1+d}^{w+d},S_{1+2d}^{\mathrm{\τ}++2d},\·\·\·,S_{1+(n-1)d}^{w+(n-1)d}---\left(4\right)$

Wherein, n=(l-p)/d;

A2: utilize IFCM clustering algorithm antithetical phrase sequence data collection S to carry out cluster, obtain c cluster centre, i.e. interval center M _k={ M ₁, M ₂..., M _c, k=1,2 ..., c; Therefore, the interval capable of dynamic of domain is divided into c optimization sub-range, its corresponding linguistic variable intuitionistic Fuzzy Sets A _jBe defined as:

$A_j=\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}<{\mathrm{\&mu;}}_{\mathrm{jk}},{\mathrm{\&gamma;}}_{\mathrm{jk}}>/M_k---\left(5\right)$

Wherein,<μ _Jk, γ _Jk>expression M _kBelong to intuitionistic Fuzzy Sets A _jDegree of membership and non-membership function pair, be calculated as follows:

$<{\mathrm{\&mu;}}_{\mathrm{jk}},{\mathrm{\&gamma;}}_{\mathrm{jk}}>=\left\{\begin{array}{cc}<\mathrm{1,0}>& k=j\\ <\mathrm{0.5,0.5}>& k=j-1\mathrm{orj}+1\\ <\mathrm{0,1}>& \mathrm{others}\end{array}\right.---\left(6\right)$

A3: intuitionistic fuzzy original series; According to all subsequence S in (7) formula computational data collection S _τBelong to A _jDegree of membership and non-membership function pair:

$<{\mathrm{\&mu;}}_{\mathrm{j\&tau;}},{\mathrm{\&gamma;}}_{\mathrm{j\&tau;}}>=<\frac{{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}}{\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}},1-\frac{{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}}{\mathrm{\&lambda;}\left[\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_k\left|\right|}^2)}^{1/(e-1)}\right]}>---\left(7\right)$

Wherein, e is smoothing parameter (usually getting e=2); λ≤1 is hesitation degree regulatory factor; The corresponding IFTS of sequence X can be expressed as: F (n)=F ₁, F ₂..., F _t..., F _n, F wherein _t∈ { A ₁, A ₂..., A _c;

A4: dynamic construction determinacy conversion intuitionistic fuzzy rule base DCRIF_base;

B, based on the long-term intuitionistic fuzzy time series forecasting of vector quantization

If after the intuitionistic fuzzy pre-service IFTS to be predicted is F certain time period _r=(f ₁, f ₂..., f _t...,, f _r), corresponding query time sequence is X=(x ₁, x ₂..., x _w); According to (2) formula, sequence data f _tThrough reasoning, can obtain corresponding to X at moment w+ (t-1) d, w+ (t-1) d-(d-1), w+ (t-1) d-(d-2) ... d dimension predicted value, its as a result time series be expressed as:

$X=(x_1,x_2,\&CenterDot;\&CenterDot;\&CenterDot;,x_w,\stackrel{\&RightArrow;}{V}(f_2,d),\&CenterDot;\&CenterDot;\&CenterDot;,\stackrel{\&RightArrow;}{V}(f_t,d),\&CenterDot;\&CenterDot;\&CenterDot;)---\left(8\right)$

Wherein, Therefore, the long-term IFTS prediction algorithm based on vector quantization can be described as:

Input: predicted vector dimension d, interval clustering center M _k, the maximum length q that determinacy conversion intuitionistic fuzzy rule is itched DCRIF_base and regular former piece thereof, inquire about intuitionistic fuzzy seasonal effect in time series length r;

Output: F _rNext state F _R+1Corresponding predicted value;

Concrete steps are:

B1: determine intuitionistic fuzzy observation subsequence Temp F;

If r>q, only needing to observe length is the intuitionistic fuzzy subsequence TempF=F of q _R+q+s..., F _R-1, F _rOtherwise, make s ∈ [1, r], Temp F=F _S-1, F _s..., F _r

B2: subsequence carries out checking of intuitionistic fuzzy rule base and mates according to the observation;

The heuristic rule that the present invention adopts list of references [7] theorem to set forth, if Temp F and determinacy conversion intuitionistic fuzzy rule i ^*Former piece rd_cause (i ^*) be complementary, i.e. Temp F → rb_cause (i ^*); F _R+1Rule of correspondence i ^*Consequent, i.e. TempF _R+1→ rb_effect (i ^*), skip to B4; Otherwise, forward B3 to;

B3: vector quantization method is estimated to predict the outcome;

Make F _r=A _j, A _j∈ { A ₁, A ₂..., A _c, in the intuitionistic fuzzy time series, p dimension historical data can be expressed as: past (A _j, p)=(m _Jw-p+1..., m _Jw-l, m _Jw), d dimension intuitionistic fuzzy vector value to be predicted is defined as: Add historical data, the intuitionistic fuzzy expansion

Dimensional vector, namely $D_{r+1}=\left(\mathrm{past}(A_j,p)\right|\stackrel{\&RightArrow;}{V}(F_{r+1},d))=(m_{j_{w-p+1}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_{w-1}},m_{j_w},x_{{(r+1)}_1},x_{{(r+1)}_2},\&CenterDot;\&CenterDot;\&CenterDot;,x_{{(r+1)}_d});$ According to (3) formula, calculate distance B _R+1The Intuitionistic Fuzzy Clustering center that barycenter is nearest Namely $M_{j^{*}}\left(D_{r+1}\right)=\left|\right|D_{r+1}-M_{j^{*}}\left|\right|=\underset{j}{\min }\left|\right|D_{r+1}-M_j\left|\right|.$ Output

B4: go intuitionistic fuzzyization accurately to export;

If predict the outcome into $\mathrm{Defuzz}\left(A_{j^{*}}\right)=M_{j^{*}}=(m_{j_1^{*}},m_{j_1^{*}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_w^{*}});$ Therefore, d dimension predicted vector can be expressed as: $\stackrel{\&RightArrow;}{V}(F_{r+1},d)=(m_{j_{w-d+1}^{*}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_{w-1}^{*}},m_{j_w^{*}}).$

The long-term intuitionistic fuzzy time series predicting model that the present invention sets up expands to many output by the output of sequence data list, and predicted value is converted to vector by scalar, has improved largely the performance of sequential system long-term forecasting.In the present invention, introduce sliding window mechanism, obtain quickly and accurately the smear out effect feature of sequence data; Utilize the IFCM algorithm dynamically to divide the domain interval, more close to the reality that uncertain data distributes; Based on the long-term time range prediction of vector quantization, intuitionistic fuzzy rule zero coupling and systematic error accumulation problem have been solved preferably.By case verification and interpretation of result, model possesses estimated performance preferably.

The accompanying drawing explanation

Fig. 1 is long-term intuitionistic fuzzy time series predicting model;

Fig. 2 is Taipei daily mean temperature in June value in 1996;

Fig. 3 is the comparison diagram that predicts the outcome;

Embodiment

Below in conjunction with specific embodiment, the present invention is described in detail.

For existing Fuzzy Time sequence prediction theory, be confined to short-term time range prediction more and, to the problem of uncertain data collection smear out effect trend study deficiency, set up the long-term intuitionistic fuzzy time series predicting model based on vector quantization.As shown in Figure 1, model of the present invention is by excavating the real-time smear out effect characteristic of historical data, set up determinacy conversion intuitionistic fuzzy rule base, grasp the distribution character of sequence data, introducing sliding window mechanism and vector quantization technology processes predicted data, solved preferably the problem of intuitionistic fuzzy rule zero coupling, describe exactly and reflected the smear out effect trend of uncertain sequential system data, reduced the accumulation of error of the long-term time range prediction of sequence, improved the precision of system secular trend predictions, expanded the range of application of intuitionistic fuzzy time series theory.

Below several key contents of model of the present invention are described respectively.

1, basic definition

Definition 1 make Y (f), t=l, 2 ..., be n) time series on domain U, to graded, cut apart set

Its linguistic variable is { L _i, i=1,2 ..., r}.If at { L _i) upper intuitionistic Fuzzy Sets F (t) with respect to Y (t) have degree of membership and non-membership function right<μ _i(Y (t)), γ _i(Y (t))>, μ wherein _i(Y (t)), γ _i(Y (t)) ∈ [0,1] and μ _i(Y (t))+γ _i(Y (t))≤1, claim F (t) for being defined in the intuitionistic fuzzy time series on Y (t), and note:

F(t)＝<μ ₁(Y(t))，γ ₁(Y(t))>/L ₁+<μ ₂(Y(t))，γ ₂(Y(t))>/L ₂+…+<μ _n(Y(t))，γ _n(Y(t))>/L _n (1)

Wherein, "+" is junction symbol.If by f _t(t)=<μ _i(Y (t)), γ _i(Y (t))>/L _iBe interpreted as the linguistic variable value, F (t) just can be understood as the function of time t as the set of intuitionistic Fuzzy Sets.As can be seen here, different from the Fuzzy Time sequence is that intuitionistic fuzzy seasonal effect in time series data set is intuitionistic Fuzzy Sets.

Definition 2 is established F (t) and is the intuitionistic fuzzy time series on given domain, and its intuitionistic fuzzy relational expression can be expressed as:

F(t)＝(F(t-1)*F(t-2)*…*F(t-m))οR _w(t，t-m) (2)

Wherein, R (t, t-m)=<μ _R(t, t-m), γ _R(t, t-m)>be the intuitionistic fuzzy relational matrix; " w " is the moving window parameter: if F (t) is only determined by F (t-1), perhaps only by F (t-2) ... or only by F (t-m) (m>0), determined, " * " cut-off is felt fuzzy union, otherwise, if F (t) is by F (t-1), F (t-2) ... F (t-m) determines simultaneously, and " * " cut-off is felt the fuzzy calculation of shipping; Intuitionistic fuzzy compose operation symbol " ο " is got " ∧-∨ " computing.

Define the data set D of the 3 given w of comprising dimensional vectors _r,

Vector quantization method refers to attempts determining predefined " the best " quantized values M _j(j ∈ [1, c]), by the nearest barycenter of given data coordinate in the computational data vector, estimate that predicted value can be positioned the corresponding coordinate of its barycenter, reduces the error between measurement data with this.And in case scrambler generates, according to the code book theories of learning, each D _rJust by apart from its nearest barycenter

Quantize ^[9,10], calculation expression may be defined as:

$C_{j^{*}}\left(D_r\right)=\left|\right|D_r-M_{j^{*}}\left|\right|=\underset{j}{\min }\left|\right|D_r-C_j\left|\right|---\left(3\right)$

Wherein, " || || " be intuitionistic fuzzy norm operational symbol.

2, the intuitionistic fuzzy pre-service of sequence data

The present invention utilizes intuitionistic fuzzy C average (IFCM) clustering algorithm to carry out the domain partition zone optimizing, and introduces sliding window mechanism easy to identify before demarcation interval, realizes the intuitionistic fuzzy pre-service of sequence data.

If given length is the time series historical data X=(x of l ₁, x ₂..., x _τ..., x _l), definition moving window width w, sequence former piece length p and predicted vector dimension d, wherein w=p+d.Sequence data intuitionistic fuzzy Preprocessing Algorithm specifically can be described as:

Step1: carry out sliding window mechanism at moment τ along the X sequence, build the subsequence S of X _τ, can be expressed as:

Comprising n sub-sequence data collection S may be defined as:

$S=S_1^w,S_{1+d}^{w+d},S_{1+2d}^{\mathrm{\&tau;}++2d},\&CenterDot;\&CenterDot;\&CenterDot;,S_{1+(n-1)d}^{w+(n-1)d}---\left(4\right)$

Wherein, n=(l-p)/d.

Step2: utilize IFCM clustering algorithm antithetical phrase sequence data collection S to carry out cluster, obtain c cluster centre, i.e. interval center M _k={ M ₁, M ₂..., M _c, k=1,2 ..., c.Therefore, the interval capable of dynamic of domain is divided into c optimization sub-range, its corresponding linguistic variable intuitionistic Fuzzy Sets A _jMay be defined as:

$A_j=\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}<{\mathrm{\&mu;}}_{\mathrm{jk}},{\mathrm{\&gamma;}}_{\mathrm{jk}}>/M_k---\left(5\right)$

Wherein,<μ _Jk, γ _Jk>mean that Mk belongs to intuitionistic Fuzzy Sets A _jDegree of membership and non-membership function pair, can be calculated as follows:

$<{\mathrm{\&mu;}}_{\mathrm{jk}},{\mathrm{\&gamma;}}_{\mathrm{jk}}>=\left\{\begin{array}{cc}<\mathrm{1,0}>& k=j\\ <\mathrm{0.5,0.5}>& k=j-1\mathrm{orj}+1\\ <\mathrm{0,1}>& \mathrm{others}\end{array}\right.---\left(6\right)$

Step3: intuitionistic fuzzy original series.According to all subsequence S in (7) formula computational data collection S _τBelong to A _jDegree of membership and non-membership function pair:

$<{\mathrm{\&mu;}}_{\mathrm{j\&tau;}},{\mathrm{\&gamma;}}_{\mathrm{j\&tau;}}>=<\frac{{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}}{\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}},1-\frac{{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}}{\mathrm{\&lambda;}\left[\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_k\left|\right|}^2)}^{1/(e-1)}\right]}>---\left(7\right)$

Wherein, e is smoothing parameter (usually getting e=2); λ≤1 is hesitation degree regulatory factor.The corresponding IFTS of sequence X can be expressed as: F (n)=F ₁, F ₂..., F _t..., F _n, F wherein _t∈ { A ₁, A ₂..., A _c.

Step4: dynamic construction determinacy conversion intuitionistic fuzzy rule base DCRIF_base (list of references [12] algorithm).

3, based on the long-term intuitionistic fuzzy time series forecasting of vector quantization

Long-term IFTS prediction based on vector quantization is to take into full account on the fuzzy fluctuation tendency of uncertain sequence data collection and the basis based on the prediction of determinacy conversion intuitionistic fuzzy rule base, the uncertain state that utilizes the vector quantization method processing rule to mate, advance-walk the model structure and the precision of prediction that improve and improve IFTS.

If after the intuitionistic fuzzy pre-service IFTS to be predicted is F certain time period _r=(f ₁, f ₂..., f _t...,, f _r), corresponding query time sequence is X=(x ₁, x ₂..., x _w).According to (2) formula, sequence data f _tThrough reasoning, can obtain corresponding to X at moment w+ (t-1) d, w+ (t-1) d-(d-1), w+ (t-1) d-(d-2) ... d dimension predicted value, its as a result time series can be expressed as:

$X=(x_1,x_2,\&CenterDot;\&CenterDot;\&CenterDot;,x_w,\stackrel{\&RightArrow;}{V}(f_2,d),\&CenterDot;\&CenterDot;\&CenterDot;,\stackrel{\&RightArrow;}{V}(f_t,d),\&CenterDot;\&CenterDot;\&CenterDot;)---\left(8\right)$

Wherein,

Therefore, the long-term IFTS prediction algorithm based on vector quantization can be described as:

Input: predicted vector dimension d, interval clustering center M _k, the maximum length q of determinacy conversion intuitionistic fuzzy rule base DCRIF_base and regular former piece thereof, inquiry intuitionistic fuzzy seasonal effect in time series length r;

Output: F _rNext state F _R+1Corresponding predicted value.

Step1: determine intuitionistic fuzzy observation subsequence Temp F.

If r>q, only needing to observe length is the intuitionistic fuzzy subsequence Temp F=F of q _R-q+s..., F _R-1, F _rOtherwise, make s ∈ [1, r], Temp F=F _S-1, F _s..., F _r.

Step2: subsequence carries out checking of intuitionistic fuzzy rule base and mates according to the observation.

The heuristic rule that the present invention adopts list of references [7] theorem to set forth, if Temp F and determinacy conversion intuitionistic fuzzy rule i ^*Former piece rd_cause (i ^*) be complementary, i.e. Temp F → rd_cause (i ^*).F _R+1Rule of correspondence i ^*Consequent, i.e. TempF _R+1→ rd_effect (i ^*), skip to Step4; Otherwise, forward Step3 to.

Step3: vector quantization method is estimated to predict the outcome.

Make Fr=A _j, A _j∈ { A ₁, A ₂..., A _c, in the intuitionistic fuzzy time series, p dimension historical data can be expressed as: past (A _j, p)=(m _Jw-p+1..., m _Jw-1, m _Jw), d dimension intuitionistic fuzzy vector value to be predicted (missing values) may be defined as:

Add historical data, the intuitionistic fuzzy expansion Dimensional vector, namely $D_{r+1}=\left(\mathrm{past}(A_j,p)\right|\stackrel{\&RightArrow;}{V}(F_{r+1},d))=(m_{j_{w-p+1}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_{w-1}},m_{j_w},x_{{(r+1)}_1},x_{{(r+1)}_2},\&CenterDot;\&CenterDot;\&CenterDot;,x_{{(r+1)}_d}).$ According to (3) formula, calculate distance B _R+1The Intuitionistic Fuzzy Clustering center that barycenter is nearest

Namely $M_{j*}\left(D_{r+1}\right)=\left|\right|D_{r+1}-M_{j*}\left|\right|=\underset{j}{\min }\left|\right|D_{r+1}-M_j\left|\right|.$ Output

.

Step4: go intuitionistic fuzzyization accurately to export.

If predict the outcome into

$\mathrm{Defuzz}\left(A_{j*}\right)=M_{j*}=(m_{j_1^{*}},m_{j_1^{*}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_w^{*}}).$ Therefore, d dimension predicted vector can be expressed as: $\stackrel{\&RightArrow;}{V}(F_{r+1},d)=(m_{j_{w-d+1}^{*}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_{w-1}^{*}},m_{j_w^{*}}).$

4, model application

In order to verify the validity of forecast model, as shown in Figure 2, the observation data that the present invention chooses in the serial document of document [8] fuzzy time series forecast model research is tested, its list entries can be expressed as X (t)=(26.1,27.8 ..., 30.2), getting first 20 days average temperature records is training sample, utilizes and predicts based on the long-term intuitionistic fuzzy time series models of vector quantization.

Step 1: sequence data intuitionistic fuzzy pre-service

Step1: carry out the moving window operation and obtain data set S, and utilize the IFCM clustering algorithm to optimize interval division;

Make p=2, d=2, w=4.As can be known according to (4) formula:

Each subsequence data value is as shown in table 1.Get c=3, namely domain can be divided into 3 sub-ranges, utilizes the IFCM algorithm to obtain corresponding cluster centre to be: M ₁=(26.15,27.84,29.10,30.47); M ₂=(29.42,29.81,29.23,30.04); M ₃=(29.04,28.61,28.15,27.32).

Table 1 subsequence data set value table

Step2: build intuitionistic fuzzy time series and the dynamic intuitionistic fuzzy rule base of determinacy conversion thereof.

Setting linguistic variable IFS is: A ₁={ low }, A ₂={ moderate }, A ₃={ height }, wherein

According to (5), (6) formula definable intuitionistic Fuzzy Sets A _jFor:

$\left\{\begin{array}{c}{A}_1=<\mathrm{1,0}>/M_1+<\mathrm{0.5,0.5}>/M_2+<\mathrm{0,1}>M_3\\ A_2=<\mathrm{0.5,0.5}>/M_1+<\mathrm{1,0}>/M_2+<\mathrm{0.5,0.5}>/M_3\\ A_3=<\mathrm{0,1}>/M_1+<\mathrm{0.5,0.5}>/M_2+<\mathrm{1,0}>/M_3\end{array}\right.---\left(9\right)$

Make hesitation degree regulatory factor λ=0.97.According to all subsequences in (7) formula computational data collection S, belong to A _jDegree of membership and non-membership function pair, value is as shown in table 2.

Table 2 intuitionistic Fuzzy Sets degree of membership and non-membership function value table

According to the intuitionistic fuzzy expectation value theory of computation, observe F (t) to A _jPreference order, obtain the intuitionistic fuzzy time series and be: F ₉=(A ₁, A ₂, A ₂, A ₂, A ₃, A ₃, A ₃, A ₂, A ₂).Therefore, as shown in table 3 by determinacy conversion intuitionistic fuzzy rule base algorithm its rule of correspondence storehouse as can be known.

Table 3 determinacy conversion intuitionistic fuzzy rule base

Step 2: based on the long-term IFTS prediction of vector quantization

Step1: determine and observe subsequence Temp F.Given test data set t=1 data information constantly, time series (x ₁, x ₂, x ₃, x ₄) intuitionistic Fuzzy Sets can be expressed as F ₁→ F (1) → A ₃.Search sequence A ₃Length r=1, the maximum length q=3 of former piece in rule base, i.e. r<q, therefore, IFTS observes subsequence Temp F=F ₀, F ₁.

Step2: the intuitionistic fuzzy rule base is checked and is mated.The determinacy conversion intuitionistic fuzzy rule base of traversal queries table 3 is as can be known, the rule be not complementary.Therefore, call vector quantization method and carry out the prediction of IFTS secular trend.

Step3: vector quantization method obtains and predicts the outcome.At first, investigate the IFTS historical data of p=2 dimension.Such as past (A ₃, 2)=(28.15,27.32), increase predicted vector and expand,

Wherein,

For missing data, when spread vector and IFCM cluster centre are compared, do not consider this missing data.Finally, according to (3) formula, calculate distance B ₂The Intuitionistic Fuzzy Clustering center M that barycenter is nearest _jAs can be known: Therefore, prediction of output F as a result ₂→ A ₃.

Table 4 is based on the long-term intuitionistic fuzzy time series forecasting of vector quantization result

Step4: go intuitionistic fuzzy output.By F ₂→ A ₃As can be known, Defuzz (A ₃)=(29.04,28.61,28.15,27.32), 2 dimension vector to be predicted can be expressed as:

The same whole data set of algorithm traversal, if intuitionistic fuzzy time series F=F ₁, F ₂, F ₃→ A ₃A ₃A ₃, predicted IFTS length r=3, r>=q, change intuitionistic fuzzy rule base rb:8 according to determinacy and know: F ₄→ A ₂, vector to be predicted can be expressed as:

Therefore, table 4 has shown that test data predicts the outcome based on the long-term IFTS of vector quantization.

Step 3: algorithm performance is assessed and is compared

As shown in Figure 3, the long-term intuitionistic fuzzy time series predicting model based on vector quantization and several Fuzzy Time Series Forecasting Model commonly used that the present invention is set up compare on document [12] data set, and utilize the time complexity (T (n)) of mean square deviation (MSE), average forecasting error rate (AFER) and algorithm in module to test the system prediction performance, result is as shown in table 5.As can be seen here, the short-term Fuzzy Time Series Forecasting Model easily is absorbed in local convergence to the sequence data with obvious nonlinear characteristic in the secular trend prediction; Though can be from holding in essence the fluctuation characteristic of nonlinear data based on the time series forecasting of determinacy conversion intuitionistic fuzzy, the smear out effect trend that reflects preferably sequence data, but for the long-term time range prediction that does not have rule to be complementary, ignored the fuzzy dependency between data, precision of prediction is not high; Long-term intuitionistic fuzzy time series predicting model based on vector quantization is vector prediction by the secular trend predictive conversion, not only simplified the complexity of algorithm, accurate description the uncertainty essence of sequence data, and taken into full account the impact of historical knowledge on predicted vector, though the accuracy of short-term scope prediction is fluctuateed to some extent, but along with the extension of time, the precision of prediction of system is greatly improved.

Table 5 prediction algorithm Performance Ratio

Should be understood that, for those of ordinary skills, can be improved according to the above description or conversion, and all these improve and conversion all should belong to the protection domain of claims of the present invention.

Claims (1)

1. the long-term intuitionistic fuzzy Time Series Forecasting Methods based on vector quantization, is characterized in that, comprises the following steps:

The intuitionistic fuzzy pre-service of A sequence data

If given length is the time series historical data X=(x of l ₁, x ₂..., x _τ..., x _l), definition moving window width w, sequence former piece length p and predicted vector dimension d, wherein w=p+d; Sequence data intuitionistic fuzzy Preprocessing Algorithm is specially:

A1: carry out sliding window mechanism at moment τ along the X sequence, build the subsequence S of X _τ, can be expressed as:

Comprising n sub-sequence data collection S may be defined as:

$S=S_1^w,S_{1+d}^{w+d},S_{1+2d}^{\mathrm{\&tau;}++2d},\&CenterDot;\&CenterDot;\&CenterDot;,S_{1+(n-1)d}^{w+(n-1)d}---\left(4\right)$

Wherein, n=(l-p)/d;

A2: utilize IFCM clustering algorithm antithetical phrase sequence data collection S to carry out cluster, obtain c cluster centre, i.e. interval center M _k={ M ₁, M ₂..., M _c, k=1,2 ..., c; Therefore, the interval capable of dynamic of domain is divided into c optimization sub-range, its corresponding linguistic variable intuitionistic Fuzzy Sets A _jBe defined as:

$A_j=\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}{<\mathrm{\&mu;}}_{\mathrm{jk}},{\mathrm{\&gamma;}}_{\mathrm{jk}}>/M_k---\left(5\right)$

Wherein,<μ _Jk, γ _Jk>expression M _kBelong to intuitionistic Fuzzy Sets A _jDegree of membership and non-membership function pair, be calculated as follows:

$<{\mathrm{\&mu;}}_{\mathrm{jk}},{\mathrm{\&gamma;}}_{\mathrm{jk}}>=\left\{\begin{array}{cc}<\mathrm{1,0}>& k=j\\ <\mathrm{0.5,0.5}>& k=j-1\mathrm{orj}+1\\ <\mathrm{0,1}>& \mathrm{others}\end{array}\right.---\left(6\right)$

A3: intuitionistic fuzzy original series; According to all subsequence S in (7) formula computational data collection S _τBelong to A _jDegree of membership and non-membership function pair:

$<{\mathrm{\&mu;}}_{\mathrm{j\&tau;}},{\mathrm{\&gamma;}}_{\mathrm{j\&tau;}}>=<\frac{{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}}{\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}},1-\frac{{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_j\left|\right|}^2)}^{1/(e-1)}}{\mathrm{\&lambda;}\left[\underset{k=1}{\overset{c}{\mathrm{\&Sigma;}}}{(1/{\left|\right|S_{\mathrm{\&tau;}}-M_k\left|\right|}^2)}^{1/(e-1)}\right]}>---\left(7\right)$

Wherein, e is smoothing parameter (usually getting e=2); λ≤1 is hesitation degree regulatory factor; The corresponding IFTS of sequence X can be expressed as: F (n)=F ₁, F ₂..., F _t..., F _n, F wherein _t∈ { A ₁, A ₂..., A _c;

A4: dynamic construction determinacy conversion intuitionistic fuzzy rule base DCRIF_base;

B, based on the long-term intuitionistic fuzzy time series forecasting of vector quantization

If after the intuitionistic fuzzy pre-service IFTS to be predicted is F certain time period _r=(f ₁, f ₂..., f _t...,, f _r), corresponding query time sequence is X=(x ₁, x ₂..., x _w); According to (2) formula, sequence data f _tThrough reasoning, can obtain corresponding to X at moment w+ (t-1) d, w+ (t-1) d-(d-1), w+ (t-1) d-(d-2) ... d dimension predicted value, its as a result time series be expressed as:

$X=(x_1,x_2,\&CenterDot;\&CenterDot;\&CenterDot;,x_w,\stackrel{\&RightArrow;}{V}(f_2,d),\&CenterDot;\&CenterDot;\&CenterDot;,\stackrel{\&RightArrow;}{V}(f_t,d),\&CenterDot;\&CenterDot;\&CenterDot;)---\left(8\right)$

Wherein, Therefore, the long-term IFTS prediction algorithm based on vector quantization can be described as:

Input: predicted vector dimension d, interval clustering center M _k, the maximum length q of determinacy conversion intuitionistic fuzzy rule base DCRIF_base and regular former piece thereof, inquiry intuitionistic fuzzy seasonal effect in time series length r;

Output: F _rNext state F _R+1Corresponding predicted value;

Concrete steps are:

B1: determine intuitionistic fuzzy observation subsequence Temp F;

If r>q, only needing to observe length is the intuitionistic fuzzy subsequence Temp|F=F of q _R-q+s..., F _R-1, F _rOtherwise, make s ∈ [1, r], Temp|F=F _S-1, F _s..., F _r

B2: subsequence carries out checking of intuitionistic fuzzy rule base and mates according to the observation;

The heuristic rule that the present invention adopts list of references [7] theorem to set forth, if Temp F and determinacy conversion intuitionistic fuzzy rule i ^*Former piece rb_cause (i ^*) be complementary, i.e. Temp F → rb_cause (i ^*); F _R+1Rule of correspondence i ^*Consequent, i.e. TempF _R+1→ rb_effect (i ^*), skip to B4; Otherwise, forward B3 to;

B3: vector quantization method is estimated to predict the outcome;

Make F _r=A _j, A _j∈ { A ₁, A ₂..., A _c, in the intuitionistic fuzzy time series, p dimension historical data can be expressed as: past (A _j, p)=(m _Jw-p+1..., m _Jw-1, m _Jw), d dimension intuitionistic fuzzy vector value to be predicted is defined as:

Add historical data, the intuitionistic fuzzy expansion

Dimensional vector, namely $D_{r+1}=\left(\mathrm{past}(A_j,p)\right|\stackrel{\&RightArrow;}{V}(F_{r+1},d))=(m_{j_{w-p+1}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_{w-1}},m_{j_w},x_{{(r+1)}_1},x_{{(r+1)}_2},\&CenterDot;\&CenterDot;\&CenterDot;,x_{{(r+1)}_d});$ According to (3) formula, calculate distance B _R+1The Intuitionistic Fuzzy Clustering center that barycenter is nearest

Namely $M_{j^{*}}\left(D_{r+1}\right)=\left|\right|D_{r+1}-M_{j^{*}}\left|\right|=\underset{j}{\min }\left|\right|D_{r+1}-M_j\left|\right|.$ Output

B4: go intuitionistic fuzzyization accurately to export;

If predict the outcome into

$\mathrm{Defuzz}\left(A_{j^{*}}\right)=M_{j^{*}}=(m_{j_1^{*}},m_{j_2^{*}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_w^{*}});$ Therefore, d dimension predicted vector can be expressed as: $\stackrel{\&RightArrow;}{V}(F_{r+1},d)=(m_{j_{w-d+1}^{*}},\&CenterDot;\&CenterDot;\&CenterDot;,m_{j_{w-1}^{*}},m_{j_w^{*}}).$

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