CN109118009A - Time Series Forecasting Methods, system and medium based on polar coordinates fuzzy information granule - Google Patents
Time Series Forecasting Methods, system and medium based on polar coordinates fuzzy information granule Download PDFInfo
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Abstract
The invention discloses Time Series Forecasting Methods, system and media based on polar coordinates fuzzy information granule, comprising: according to the length of sliding window predetermined, numerical value time series is divided into the time window of several constant durations；The data of each time window are fitted and establish regression equation, and then find out the regression coefficient of regression equation；Deflection angle is calculated using regression coefficient, and the deflection angle found out between two neighboring angle is poor；Determine the most value of deflection angle and deflection angle difference；The domain that deflection angle and deflection angle difference are constructed on polar coordinates, marks off several sections, each section is defined as an information, and different section definitions goes out the information of different names on domain；Fuzzy logical relationship between mined information grain establishes fuzzy logical relationship group, to establish the transmission network model between information；Transmission network model is trained, time series to be predicted is predicted using trained transmission network model.
Description
Technical field
The present invention relates to Time Series Forecasting Methods, system and media based on polar coordinates fuzzy information granule.
Background technique
Time series refers to sequence made of the chronological order arrangement by the numerical value of same statistical variable according to its generation
Column.The modeling and prediction of time series are always the classical problem that researcher studies extensively.Researcher's early utilization is linearly
System is theoretical, theory of random processes and black-box approach develop the classical numerical models of many time serieses, such as ARMA, ARIMA,
ARARMA, ANN (artificial neural network) model etc..Time series forecasting have been widely applied to meteorology, farm output,
The numerous areas such as tourist arrivals and the energy especially have extremely important meaning, but these in control field and financial market
Model is since its interpretation is low and indigestion.Fuzzy set theory (Zadeh, 1965) can be used to remission time series model
Explanatory low disadvantage, the concept of Fuzzy time sequence are proposed by Song and Chissom, it is related to fuzzy set theory
Form, the forecasting problem under the imperfect or fuzzy uncertain environment of historical data can be coped with, be widely used at present
Predict that school attendance rate, the multiple fields such as temperature have preferable estimated performance.Fuzzy reasoning provides a kind of feasible substitution simultaneously
Scheme ensures that this also relates to the modeling of time series to intrinsic probabilistic robustness.
Although classical time series models are widely used, there is also some shortcomings, such as AR, MA,
VECM etc. establish time series data have linear structure hypothesis under, and data in the real world usually have compared with
Strong nonlinear organization；Predict to obtain is quantitative as a result, being not easy to be realized；For fuzzy or incomplete time sequence
It arranges, prediction deviation is larger, etc..In view of the problem of above method prediction result Semantic deficiency, there is human perception and place
The time series Fuzzy Time Series Model for managing the ability of abstract entity (rather than digital entities) is more suitable for certain decisions and asks
Topic, has preferable effect for the time series forecasting of fuzzy semantics variable.
Information is the concept that Zadeh was proposed in 1979, and general type is
Wherein, X is the value variable on domain U, and G is the Convex Fuzzy Subset in domain U, is portrayed by subordinating degree function, λ
A possibility that expression value X belongs to fuzzy subset G probability.Information Granularity and Granular Computing play a part of essence, and researcher builds
The time series models of fuzzy information granule of being based on mainly include five committed steps: (1) being divided into domain if time series
A series of sections；(2) according to demarcation interval ambiguity in definition collection；(3) digit time sequence is converted into Fuzzy time sequence, i.e. mould
The historical data of gelatinization time sequence；(4) from fuzzy time series data mining fuzzy logical relationship；(5) prediction and deblurring output.
Summary of the invention
In order to solve the deficiencies in the prior art, the present invention provides the time series forecastings based on polar coordinates fuzzy information granule
Method, system and medium；
As the first aspect of the present invention, the Time Series Forecasting Methods based on polar coordinates fuzzy information granule are provided；
Time Series Forecasting Methods based on polar coordinates fuzzy information granule, comprising:
Step (1): according to the length of sliding window predetermined, numerical value time series is divided into the times such as several
Interval time window；
Step (2): being fitted the data of each time window and establish regression equation, and then finds out returning for regression equation
Return coefficient；The regression coefficient includes: slope and intercept；Deflection angle is calculated using regression coefficient, and is found out two neighboring
Deflection angle between angle is poor；Determine the most value of deflection angle and deflection angle difference；On polar coordinates construct deflection angle and partially
The domain of gyration difference, marks off several sections on domain, and each section is defined as an information, different sections
Define the information of different names；
Step (3): the fuzzy logical relationship between mined information grain establishes fuzzy logical relationship group, to establish information
Between transmission network model；
Step (4): being trained transmission network model, using trained transmission network model to the time to be predicted
Sequence is predicted.
Further, are fitted to the data of each time window the step of establishing regression equation are as follows:
Pt i=ait+bi,
Wherein, Pt iIndicate the regression equation of i-th of time window, aiAnd biIt is the regression equation of i-th of time window
Regression coefficient；aiIt is the slope of regression equation, biIt is the intercept of regression equation.
Measure the regression coefficient a of each time window regression equationiAnd bi, to acquire regression coefficient aiAnd biSet
{[a1, b1], [a2, b2] ... [αi, bi] ... [am, bm]}；amAnd bmIt is the recurrence system of the regression equation of m-th of time window
Number；
Further, the step of calculating deflection angle using regression coefficient are as follows:
According to the regression coefficient a of the regression equation of i-th of time windowiAcquire corresponding deflection angle αi:
αi=arctan (ai)；
Further, the step of the deflection angle difference between two neighboring angle is found out are as follows:
Δαi=αi+1-αi；
Then each time window corresponds to one group of parameter alphaiWith Δ αi；To obtain
Set A={ [α1, Δ α1], [α2, Δ α2] ... [αi, Δ αi] ... [αm, Δ αm]}。
αiRefer to deflection angle of the curve relative to horizontal axis, behind be translated into the polar angle in polar coordinate system；ΔαiIt is phase
Difference between adjacent deflection angle, behind be translated into the polar radius ° in polar coordinate system
Further, the domain that deflection angle and deflection angle difference are constructed in polar coordinate system, if being marked off on domain
The step of dry section are as follows:
Obtain set A={ [α1, Δ α1], [α2, Δ α2] ... [αi, Δ αi] ... [αm, Δ αm]}；It is number by set A points
According to fitting deflection angle set Ai={ α1, α2..., αnAnd deflection angle situation of change set Δ Ai={ Δ α1, Δ α2... Δ
αnTwo set, deflection angle set A is fitted based on dataiWith the situation of change set Δ A of deflection angleiConstruct domain, building opinion
Deflection angle is considered as the polar angle in polar coordinate system during domain, the variation of deflection angle is considered as the polar radius in polar coordinate system, from
And domain is constructed in polar coordinate system；
Define the most value of deflection angle and deflection angle difference
Aimin=min { α1, α2..., αn}；
Aimax=max { α1, α2..., αn}；
ΔAimin=min { Δ α1, Δ α2... Δ αn}；
ΔAimax=max { Δ α1, Δ α2... Δ αn}；
Wherein, AiminIndicate the minimum value of the deflection angle amplitude of time series fitting, AimaxIndicate time series fitting
The maximum value of deflection angle amplitude；ΔAiminIndicate the minimum value of deflection angle difference, Δ AimaxIndicate deflection angle difference most
Big value；
U=[U1, U2] indicate deflection angle codomain,
U=[U1, U2]=[Aimin-l1, Aimax+l2]；
Wherein, l1And l2It is trimming factor t rim factor,
R=[R1, R2] indicate deflection angle difference codomain,
R=[R1, R2]=[Rimim-m1, Rimax+m2]；
Wherein m1And m2It is trimming factor t rim factor,
The data information after fitting is indicated on polar coordinates, wherein the value of polar angle θ is corresponding by the slope of regression equation
Deflection angle determine, polar radius ρ be adjacent polar angle difference, according to the value range of polar angle and polar radius, on polar coordinates
Establish fan-shaped domain；
Lateral division is carried out to domain according to the division number h being set in advance, according to the division number i of setting to domain into
Row is longitudinally divided；Wherein, domain is finally divided into the section of h × i by h >=2, i >=2, and each section is defined as an information
Grain.
Further, the step of new domain being divided are as follows:
According to the amplitude of deflection angle, horizontal partition point s=[p is used1, p2..., ph-1] divided, then l1=[U1,
p1], l2=[p1, p2] ..., lj=[pj-1, pj] ..., lh=[ph-1, U2], similarly, use longitudinally split point t=[h1,
h2..., hi-1] divided, then t1=[R1, h1], t2=[h1, h2] ..., tj=[hj-1, hj] ... th=[hi-1, R2]。
Further, the specific steps of step (3) are as follows:
Assuming that particle time series is by N number of information A1, A2..., ANComposition predicts the N+1 information AN+1；
Single order fuzzy logical relationship: Ai, Ai+1For the particle that two continuous observations arrive in time series, then between them
Relationship is indicated with a fuzzy logical relationship, is denoted as Ai→Ai+1Wherein, AiThe referred to as left member of fuzzy logical relationship, Ai+1Referred to as mould
The right member of fuzzy logic relationship；
Second order fuzzy logical relationship: Ai-1, Ai, Ai+1For the particle that three continuous observations arrive in time series, then they it
Between relationship indicated with a fuzzy logical relationship, be denoted as Ai-1, Ai→Ai+1；
Three rank fuzzy logical relationships: Ai-2, Ai-1, Ai, Ai+1For the particle that four continuous observations arrive in time series, then he
Between relationship indicated with a fuzzy logical relationship, be denoted as Ai-2, Ai-1, Ai→Ai+1；
Step 31: according to single order fuzzy logical relationship, first determining whether observation sequence AN' corresponding information ANIt is patrolled fuzzy
Whether the consequent in volume relationship is unique value, if it is unique, then can directly predict AN+1；
Otherwise, observation sequence A is judged according to second order fuzzy logical relationshipN-1', AN' corresponding information AN-1, ANIn second order
Whether corresponding consequent is unique value in fuzzy logical relationship, if it is unique value, then directly predicts AN+1；
Otherwise, information A is judged according to three rank fuzzy logical relationshipsN-2, AN-1, ANIt is corresponding in three rank fuzzy logical relationships
Consequent whether be unique value, if it is unique, then directly predict AN+1, otherwise enter step 32；
Step 32: judging observation sequence AN-2' corresponding information AN-2Position in fan-shaped domain,
If AN-2Positioned at the leftmost side edge or rightmost side edge of domain, then information is found comprising including oneself
4 informations；
If AN-2Positioned at the top side edge or lower side edge of domain, then information is found comprising including oneself
6 informations；
If AN-2Positioned at the middle section of domain, then to find information includes 9 informations including oneself；
Same operation determines observation sequence A respectivelyN-1' and AN' corresponding information AN-1And ANPosition in fan-shaped domain
It sets；
Step 33: finding out observation sequence AN-2' degree of membership f (the x with peripheral information grain；μ, y, ν, σ), and take out degree of membership
Maximum two informations, are denoted as { a1, a2}；Similarly, observation sequence A is successively found outN-1' the degree of membership with peripheral information grain, and
Maximum two informations of degree of membership are taken out, { b is denoted as1, b2}；Observation sequence AN' the degree of membership with peripheral information grain, and take out
Maximum two informations of degree of membership, are denoted as { c1, c2}；
Step 34: successively respectively from { a1, a2, { b1, b2, { c1, c2One information of middle taking-up, permutation and combination is carried out,
One shares eight kinds of combinations, is { a respectively1, b1, c1}、{a1, b2, c1}、{a1, b1, c2}、{a1, b2, c2}、{a2, b1, c1}、
{a2, b2, c1}、{a2, b1, c2}、{a2, b1, c1}；In three rank fuzzy logical relationships, calculates the probability that eight kinds of combinations occur and look for
To the corresponding consequent of every kind of combination, just give up if a certain combination is not present in three rank fuzzy logical relationships, to remaining
Combination is normalized；
Step 35: taking out the maximum combination of probability of occurrence, and find out the transmitting in combination and consequent between each information
Frequency is denoted as weights omega
AN+1It is the A that prediction obtainsN+1' middle maximum the information of weight；
Wherein, weight vector (ω1, ω2..., ωN-3) and matching degree [ω '1, ω '2..., ω 'N-3] in proportional
Relationship is defined as following form:
Wherein, ω ' i is observation sequence (A 'N-2, A 'N-1, A 'N) and the i-th rule antecedents (Ai, Ai+1, Ai+2)
Matching degree, i=1,2 ..., N-3.
Define α (Ai, Aj) it is AiAnd AjThe measurement of matching degree；α(Ai, Aj) be expressed as
Wherein weighted index m > 1 is referred to as Fuzzy Exponential；Blurring Coefficient m is set as 2.
Observation sequence (A 'N-2, A 'N-1, A 'N) and Rulei antecedents (Ai, Ai+1, Ai+2) matching degree be represented as
Two o'clock A on complex planei=(α1, Δ α1) and Aj=(α2, Δ α2) between Euclidean distance:
Different types of information is defined as to the node of transmission network model, size of node reflects same name information
The number that grain occurs, and the transmission of information is defined as edge, the weight at edge is the biography between the information of two kinds of titles
Frequency is passed, to establish the transmission network model between information.
Further, observation sequence A is found out according to formula (2)N-2' degree of membership f (the x with peripheral information grain；μ, y, v, σ):
Y (t)=kt+b, k ≠ 0 (3)
Wherein, k indicates that the slope of the tropic, b indicate the intercept of the tropic, and μ indicates slope corresponding angle in the planes,
Y indicates the difference of the angle between adjacent angular, and σ indicates standard deviation；
It is the closed interval determined by k value, indicates the value range of μ, is i.e. m is to make y (t)=kt+b, and k ≠ 0 is at one section
The minimum value fluctuated in time,It is to make y (t)=kt+b, the maximum value that k ≠ 0 is fluctuated whithin a period of time；It has been reflected and has been worked as
Data float section in preceding time zone；
Being the closed interval determined by μ value, indicates the value range of v, i.e. n is fluctuating change speed minimum value,It is
Fluctuating change speed maximum value；All data of fitting data collection i.e. in time series are fallen inm、 nWithThe sector of composition
In region.
Further, the specific steps of step (4) are as follows:
Aforecast(t+1)=Forecast (A (t), A (t-1), A (t-2))
The data of forecast set are expressed as A as test data for calculating precision of predictionforecasted(nt+ i), i=1,
2 ..., nf.It is obtained by above formula
Aforecast(nt+ 1)=Forecast (A (nt), A (nt- 1), A (nt- 2)),
Aforecast(nt+ 2)=Forecast (A (nt+ 1), A (nt), A (nt- 1)),
Aforecast(nt+nf)=Forecast (A (nt+nf- 1), A (nt+nf- 2), A (nt+nf- 3)),
The information predicted contains variation range, the variation tendency of predicted next stage data.
Wherein, Aforecast(t+1) information at the t+1 moment of prediction is indicated；The information of A (t) expression t moment；A(t-
1) information at t-1 moment is indicated；The information at A (t-2) expression t-2 moment；Aforecast(nt+ 1) n of prediction is indicatedtWhen+1
The information at quarter；A(nt) indicate ntThe information at moment；A(nt- 1) n is indicatedtThe information at -1 moment；A(nt- 2) n is indicatedt-2
The information at moment；Aforecast(nt+nf) indicate the n predictedt+nfThe information at moment；A(nt+nf- 1) n is indicatedt+nf- 1 moment
Information；A(nt+nf- 2) n is indicatedt+nfThe information at -2 moment；A(nt+nf- 3) n is indicatedt+nfThe information at -3 moment.
As a second aspect of the invention, the time series forecasting system based on polar coordinates fuzzy information granule is provided；
Time series forecasting system based on polar coordinates fuzzy information granule, comprising: memory, processor and be stored in
The computer instruction run on reservoir and on a processor when the computer instruction is run by processor, is completed any of the above-described
Step described in method.
As the third aspect of the present invention, a kind of computer readable storage medium is provided；
A kind of computer readable storage medium, is stored thereon with computer instruction, and the computer instruction is transported by processor
When row, step described in any of the above-described method is completed.
Compared with prior art, the beneficial effects of the present invention are:
The invention proposes one kind to be based on the isometric division data of sliding window thought, establishes regression equation and on polar coordinates
The method of division information grain.The advantage of this method is not only to consider the variation of value data but also considers the fast of variation tendency
Slowly, data obfuscation later interpretation and precision of prediction are improved, be can make up for it and be evenly dividing domain, be not overlapped the graduation such as non-
Divide domain and the problem that prediction accuracy is lower, semantic information is less caused by domain is divided with the experience of life of people, simultaneously
Compensate for using optimization algorithm (such as particle swarm algorithm, genetic algorithm, bat algorithm) divide domain can not it is explanatory not
Foot, has given full play to fuzzy theory and has solved the problems, such as the advantage in time series forecasting.
We establish a fan-shaped information in the present invention, and unlike Interval Fuzzy information, its domain is not
It is raw value but is converted on polar coordinates corresponding polar angle by linear fit and polar radius, its section are no longer sizes
Identical section, and in the band-like of angle change, i.e. section size is sequentially increased from inside to outside.Longitudinal 2 observation is can be found that
Data fluctuations amplitude in same time, laterally observation can intuitively reflect the speed of velocity of wave motion.
Detailed description of the invention
The accompanying drawings constituting a part of this application is used to provide further understanding of the present application, and the application's shows
Meaning property embodiment and its explanation are not constituted an undue limitation on the present application for explaining the application.
Fig. 1 is flow chart of the invention；
Fig. 2 is numeric type time series；
Fig. 3 is to divide time series using sliding window；
Fig. 4 is fan-shaped fuzzy information granule schematic diagram on polar coordinates；
Fig. 5 is the inference pattern based on fan-shaped fuzzy information granule；
Fig. 6 is the process for defining Regression Model；
Fig. 7 is based on average weighted sliding window Fuzzy inferential engine；
Fig. 8 is the transmission network figure of fuzzy message intergranular.
Specific embodiment
It is noted that following detailed description is all illustrative, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms that the present invention uses have logical with the application person of an ordinary skill in the technical field
The identical meanings understood.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
As shown in Figure 1, we define the length of sliding window first and numerical value time series were divided between some time
Every just as time window find out the slope of regression equation, and find out song by being fitted to the data in each time window
Line is poor relative to the deflection angle between the deflection angle and adjacent curve of horizontal axis.Time series is indicated on polar coordinates, polar angle is
The deflection angle acquired on plane right-angle coordinate, polar radius are that deflection angle is poor, therefore can construct on polar coordinates newly
Domain, demarcation interval establish information.By the fuzzy relation of mined information intergranular, fuzzy relation group and transmission network are established,
Transmission network is trained, time series is predicted with trained model.
As shown in Fig. 2, conventional time series are based on numerical value fluctuations.
As shown in figure 3, dividing object time sequence using sliding window, retain the inherent law between data and transmission spy
Property.
As shown in figure 4, we indicate the data information after fitting on polar coordinates, wherein the value of polar angle θ is by returning
The corresponding deflection angle of the slope of equation determines that polar radius ρ is the difference of adjacent polar angle, according to the value model of polar angle and polar radius
It encloses, fan-shaped domain is established on polar coordinates.New domain, demarcation interval, according to the data of time series are constructed on polar coordinates
And its corresponding variation (trend) constructs fan-shaped fuzzy information granule.
As shown in figure 5, the prediction model that the fuzzy relation based on fuzzy information granule is established, three inputs, an output.
As shown in fig. 6, data volume that the number of pre-defined sliding window and each window include and to sliding window
Data, which are fitted, establishes regression equation, finds out slope and intercept, and finds out deflection angle and adjacent song of the curve relative to horizontal axis
Deflection angle between line is poor.
As shown in fig. 7, in an experiment it is considered that information AN+1With history particle data A1, A2... ANIt is related, therefore
In predictive information grain AN+1Shi Yunyong is based on average weighted Fuzzy inferential engine and explains.On the basis of this hypothesis, benefit
It is predicted with the fuzzy logical relationship of foundation.Fuzzy prediction machine is considered to be constructed by a series of conditions judgment rule
's.In real life, some data theoretically will be inexhaustible, therefore will will use a large amount of rule, to increase
Computation system complexity and precision of prediction, and adjacent time data can bring certain influence to the prediction of next data.
Therefore, sliding time window is introduced in our Fuzzy inferential engine.Fuzzy inferential engine use information grain time series and
It is not directly to be predicted using initial data, so what is finally exported will be the messenger particle for considering multistep time domain
As shown in figure 8, mutually transmitting forms fuzzy relation between information there are much information grain in time series, because
Different types of information, is defined as the node of transmission network model by this, and size of node reflection same name information goes out
Existing number, and the transmission of information is defined as edge, the weight at edge is the transmitting pin between the information of two kinds of titles
Rate.
1.1 Fuzzy time sequence
The definition of Fuzzy time sequence is proposed by Song and Chissom (1993,1993,1994), if U=
{u1, u2..., unIt is domain, with the element u in domainiWith its degree of membership fA(ui) fuzzy set A is indicated:
Wherein fAIt is the membership function of fuzzy set A, fA: U → [0,1], fA(ui) (1≤i≤n) be uiIn fuzzy set A
Degree of membership,Indicate the element u in domainiWith its degree of membership fA(ui) between corresponding relationship.
Define 1: Fuzzy time sequence .R1Subset Y (t) (t=..., 0,1,2 ...) be to be defined on fuzzy set fi(t)(i
=1,2 ...) on domain, if F (t) is f1(t), f2(t) set, then F (t) can be referred to as one be defined on Y (t)
A Fuzzy time sequence
Find that traditional time series is maximum with Fuzzy time sequence not to be both, Fuzzy time sequence according to definition 1
Value is fuzzy set, i.e., linguistics describes, and the value of traditional time series is true number.F (t) is considered as a language
Variable and fi(t) regard possible linguistic variable value (the regard as/view as possible linguistic of F (t) as
Value of) use fuzzy set representations fi(t) (i=1,2 ...).
It is worth noting that, the value of F (t) is different in different times, i.e. F (t) is related with time t.If F (t) is only by F
(t-1) it determines, then there are a kind of fuzzy logical relationships between them, and wherein F (t-1) indicates the former piece of fuzzy logical relationship, F
It (t) is the consequent of fuzzy logical relationship.
2. prediction model
Modeled and predicted to be the classical problem being widely studied to time series, by exploring for a long time,
Researcher establishes many numeric type time series models, is widely used in every field and achieves preferably in numerical value level
Prediction effect, but due to these models semantically explanatory low so model is difficult to be understood, and fuzzy set theory can be with
This disadvantage is made up, fuzzy set theory is based on, Song and Chissom are the pre- of the time series that solution historical data is semantic values
Survey problem proposes the concept of Fuzzy time sequence earliest.They establish two kinds of time series models --- time-varying model and when
It varying model and does not predict the admission number of A Dabama university, and proposes the method mould of a set of predictive fuzzy time series
Type mainly includes five steps: (1) domain for dividing time series is the set in section, and (2) are according to demarcation interval ambiguity in definition
Collection, (3) are Sequence Transformed for Fuzzy time sequence by digit time, that is, are blurred the historical data of time series, realize that numerical value arrives
Fuzzy logical relationship (mining fuzzy relationships from fuzzy time is established in semantic conversion (4)
Series), (5) prediction and de-fuzzy output.
Although Song proposes Fuzzy Time Series Model earliest, since the model computation complexity of proposition is higher, institute
It is all based on the model of Chen by most Fuzzy Time Series Model, modeling process is divided by the model that Chen is proposed
Four committed steps: (1) data is observed according to time series and determines domain, and it is divided, (2) define the mould on domain
Paste collection, then will observe data obfuscation, and (3) establish fuzzy logical relationship and fuzzy logical relationship group, and (4) utilize fuzzy relation
It is predicted.
The general step of model is established according to Fuzzy time sequence and combines actual conditions, foundation proposed by the invention
The step of time series models, is as follows:
Setp1: object time sequence is divided using sliding window；
Setp2: blurring observation data, tectonic information grain；
Step3: building Fuzzy estimation system (establishing fuzzy logical relationship)；
Step4: predictive information grain；
2.1. object time sequence is divided
In fact, information is that main feature based on the perception of people, based on things is established, it is a kind of abstract
Process, and abstract rank is related with Information Granularity, in other words, Information Granularity can help us to pay close attention to crucial spy
Sign ignores those features for increasing computation complexity, in short, information can make according to the potential applications of data as far as possible
Data are indicated with some Precise Representation methods such as Interval Set, fuzzy set, shade collection, but using only includes data amplitudes
Fuzzy set such as " heat " " very cold " indicates that these data are inappropriate, if an information had both included sometime interior counts
It can reflect that the pace of change speed of data is just more reasonable again according to value range.
The division of domain has important influence to the result of time series forecasting, and sequence is using different at the same time
Domain division methods will generate different prediction results, thus before this researcher carry out many experiments just divide domain this
Problem is studied, and prediction model is continued to optimize, it has been found that the distribution that the data of time series itself are able to reflect data is close
Degree and variation tendency can reflect the fluctuations of data.We will not only examine in the time series models for establishing fuzzy information granule
The problem of considering the algorithm complexity, precision of prediction and interpretation for the model established also needs to consider that can the information that established both
Reflection numerical value can embody the rate of change of numerical value again, and these problems are difficult to accomplish that equilibrium, such as the division of domain need to meet two
The requirement of a potential (underlying): it is capable of the characteristic distributions of objective reasonable reflection data in 1. sections divided；2. dividing
Semanteme preferably.Therefore it is proposed that a kind of new division methods, pre-define the length of sliding window, to each time window
Data be fitted and ask regression equation and its coefficient.Wherein, slope, also known as " ascent " indicate straight line relative to cross
The inclined degree coefficient of axis is amount of the curve about (cross) reference axis inclined degree.New domain is constructed on polar coordinates, is divided
Section constructs information according to the data of time series and its corresponding variation (trend), it is ensured that fuzzy based on numerical value
The Memorability and transmission characteristic of data between information.
Even so, classifying rationally observation data (choosing suitable Information Granularity) is also essential, time window
Length can not only influence the number of information and also will affect the determination of main Regression Model (information).Information Granularity it is general
Thought is to be put forward for the first time by Zadeh in 1979.The information of one data set, simple to summarize be reasonable Information Granularity and just
When semantic interpretation.Information Granularity falls into information data by calculating and is judged, for first requirement, falls into information
Data it is The more the better.And require the more hypologia justice of data for falling into information more clear for second.In conclusion above-mentioned two
A requirement is contradictory.In the present invention by selecting suitable siding-to-siding block length, optimize Information Granularity, so that information includes number
According to number it is appropriate rationally on this basis with regard to the length of information to information number, main information grain type and transmission network
Influence discuss.
Processing numeric data establishes information process and is divided into three steps:
Step1: consider the length of given time sequence, determine the length of time window ω.The length ω of sliding window can
To be set according to demand, very flexibly.For the time series of different time length, we can set the value of ω also not
Together, when the amount of data is large, can be larger by the setting of time window length, it, can be by time window if data volume is smaller
Length setting is smaller, to further quantify to each time window.
Step2: regression equation is established.One regression equation is established to each time window.The recurrence of i-th of time window
Equation can be expressed as Pt i=ait+bi, wherein Pt iIndicate the price of i-th of time window, aiAnd biIt is the parameter of regression equation,
Firstly, measuring the parameter a of each time window regression equationiAnd bi, it is possible thereby to acquire parameter aiAnd biSet
{[a1, b1], [a2, b2] ... [ai, b] ... [am, bm], then according to the parameter a of each time windowiIt acquires corresponding inclined
Gyration αi, and two neighboring time window does difference can acquire deflection angle difference Δ αi=αi+1-αi, then each time window
Mouth all corresponds to one group of parameter alphaiWith Δ αi, set A={ [α may further be obtained1, Δ α1], [α2, Δ α2] ... [αi, Δ
αi] ... [αm, Δ αm]}。
αiIt indicates for the data in a period of time to be fitted the deflection angle for finding out slope and further finding out, and Δ αiInstead
Data value angle changing on adjacent equal length time window is reflected, divide domain on polar coordinates on this basis and establishes sector
Fuzzy information granule
Step3: domain and tectonic information grain are divided
Step3.1: in view of in rapid 2, we obtain set A={ [α1, Δ α1], [α2, Δ α2] ... [αi, Δ
αi] ... [αm, Δ αm], now set A is divided for Ai={ α1, α2..., αnAnd Δ Ai={ Δ α1, Δ α2... Δ αnTwo
Set, we define A respectivelyimin=min { α1, α2..., αnAnd Aimax=max { α1, α2..., αn, Δ Aimin=min { Δ
α1, Δ α2... Δ αnAnd Δ Aimax=max { Δ α1, Δ α2... Δ αn, AiminAnd AimaxRespectively indicate time series fitting
Deflection angle amplitude minimum value and maximum value.U=[U1, U2] indicate deflection angle codomain, U=[U1, U2]=[Aimin-
l1, Aimax+l2], wherein l1, l2It is the trimming factor (trim factors), similarly Δ AiminWith Δ AimaxRespectively indicate deflection angle
Spend the minimum value and maximum value of difference.R=[R1, R2] indicate deflection angle difference codomain, R=[Ri, R2]=[Rimin-m1, Rimax
+m2], wherein m1, m2It is the trimming factor (trim factors), according to division the number h and i (h >=2, i >=2) being set in advance points
Domain is not divided laterally and longitudinally, according to following step, as shown in figure 4, domain is divided into h × i sizes such as or not us
Section.
Step3.2: we indicate the data information after fitting on polar coordinates, wherein the value of polar angle θ is by recurrence side
The corresponding deflection angle of the slope of journey determines that polar radius ρ is the difference of adjacent polar angle, according to the value model of polar angle and polar radius
It encloses, fan-shaped domain is established on polar coordinates.
Step3.3: dividing domain, determines siding-to-siding block length.According to the amplitude of deflection angle, laterally we find cut-point s=
[p1, p2..., ph-1], then l1=[U1, p1], l2=[p1, p2] ..., lj=[pj-1, pj] ..., lh=[ph-1, U2], similarly,
It is longitudinal that we find cut-point t=[h1, h2..., hi-1], then t1=[R1, h1], t2=[h1, h2] ..., tj=[hj-1,
hj] ... th=[hi-1, R2].
It is worth noting that, the method for above-mentioned division domain is realized on polar coordinates.
2.2 blurring observation data, tectonic information grain
The invention proposes a kind of novel fuzzy information granule, referred to as fan-shaped fuzzy information granule (english abbreviation FSFIG).It is setting
When counting such messenger particle, we using using arcuation section as the fuzzy information granule of core in the form of express tendency information,
Degree of membership is calculated with Gaussian Profile simultaneously.
Definition.A sector fuzzy information granule
Y (t)=kt+b (k ≠ 0) (3)
Wherein k, b respectively represent the slope and intercept of the tropic, and μ indicates slope corresponding angle in the planes, and v indicates phase
The difference of angle between the degree of adjacent angle, standard deviation sigma determine the density of distribution, and core-wire y (t)=kt+b (k ≠ 0) is reflected currently
Linear trends of change in time interval.By converting in plane corresponding angle for slope and further obtaining adjacent angular
Difference, be able to reflect in data undulation variation, standard deviation sigma reflects the dispersion degree of data Yu tropic μ (t), σ
Bigger, representing the information has bigger dispersion degree.It is the closed interval determined by k value, indicates the value range of μ, i.e.,mIt is the minimum value for fluctuating y (t)=kt+b (k ≠ 0) whithin a period of time,It is to make y (t)=kt+b (k ≠ 0) at one section
The maximum value of interior fluctuation.The data float section in present-time field is reflected, similarly,It is to be determined by μ value
Closed interval, indicate the value range of V, i.e.,nIt is fluctuating change speed minimum value,It is fluctuating change speed maximum value, i.e., should
All data of data set are fallen inm、 nWithIn the fan-shaped region made pottery.
We establish a fan-shaped information in the present invention, and unlike Interval Fuzzy information, its domain is not
It is raw value but is converted on polar coordinates corresponding polar angle by linear fit and polar radius, its section are no longer sizes
Identical section, and in the band-like of angle change, i.e. section size is sequentially increased from inside to outside.Longitudinal 2 observation is can be found that
Data fluctuations amplitude in same time, laterally observation can intuitively reflect the speed of velocity of wave motion.
Determine that sector fuzzy information granule needs 7 parameters altogether, i.e. k, b, σ,m、、nWith, wherein k, b and σ can pass through line
Property return determine.Why we select least-squares linear regression, and (quadratic sum by minimizing error finds the best of data
Function matching), it mainly considers its computation complexity and is acceptable.Give a sequence
Time range t={ t1, t2..., tN, linear regression is carried out to it and is obtained
Xt=kt+b+ ∈ (4)
Wherein, (0, σ ∈~N2).We obtain parameter k, b and σ as a result,.AndmWithDetermination, be using μ0(t)=kt
What the obtained slope of fitting data collection was calculated,nWithIt is to further calculatemWithIt obtains, includes by all data values
Wherein, so far, we construct a complex plane sector fuzzy information granule CPSFIG.
Generally speaking, fan-shaped fuzzy information granule has done further improvement, energy on the basis of common block information grain
Enough while indicating data fluctuations variation range and fluctuating change speed, the variation tendency (via k) and data fluctuations of data set
(discrete) situation (via σ), preferably resolve it is proposed that urgently to be resolved two problem, be ideal information
Form.
2.3. Fuzzy estimation system Long-term prediction with fuzzy inference system is constructed
(FIS)based on weighted average
Assuming that our particle time series is by N number of information A1, A2..., ANComposition is pushed away by fuzzy based on weight
Manage N+1 information A of predictive system pointN+1, under this research background, such mapping, which is able to reflect, outputs and inputs letter
Cease the relationship between grain.Our use information grain time serieses rather than directly predicted using initial data, do so
It is advantageous in that, output will be messenger particle (a granule concerning multi- for considering multistep time domain
Step time horizon) if predicts the numerical value of identical quantity using the digital model as ARIMA, SVR, it needs to single step
Predict that (one-step prediction) result carries out a series of iteration.Due to inevitable error, it is inclined to will lead to prediction
Poor continuous accumulation, if prediction scope is larger, prediction result will be no longer accurate.
In an experiment it is considered that information AN+1With history particle data A1, A2..., ANIt is related, therefore in predictive information
Grain AN+1Shi Yunyong is based on average weighted Fuzzy inferential engine and explains.On the basis of this hypothesis, the mould of foundation is utilized
Fuzzy logic relationship is predicted.In the present invention, more acurrate more convincing in order to make to predict, we establish different orders
Fuzzy logical relationship, and such as given a definition to the fuzzy logical relationship of single order, second order and three ranks respectively,
Define A:Ai, Ai+1For the particle that two continuous observations arrive in time series, then the relationship between them can use one
A fuzzy logical relationship indicates, is denoted as Ai→Ai+1Wherein, AiThe referred to as left member (abbreviation left member) of fuzzy logical relationship, Ai+1Referred to as
The right member (abbreviation right member) of fuzzy logical relationship
Define B:Ai-1Ai, Ai+1For the particle that three continuous observations arrive in time series, then the relationship between them can be with
It is indicated with a fuzzy logical relationship, is denoted as Ai-1, Ai→Ai-1.
Define C:Ai-2, Ai-1, Ai, Ai+1For the particle that four continuous observations arrive in time series, then the relationship between them
It can be indicated with a fuzzy logical relationship, be denoted as Ai-2, Ai-1, Ai→Ai+1.
Fuzzy prediction machine, which is considered, to be constructed by a series of conditions judgment rule.If the condition of rule is expired
Foot, it may be considered that corresponding result is correct to a certain extent.For single order fuzzy logical relationship, certain predictive information
Grain AN+1' can uniquely determine, it is determined if being unable to satisfy the condition uniquely determined and may determine that according to second order fuzzy logical relationship
AN+1', otherwise use three rank fuzzy logical relationships, target prediction information AN+1' can be by three continuous historical information grains
AN-2', AN-1', AN' determined by algorithm.
Fuzzy logic ordination are as follows:
According to C is defined, the thought of this (ensuing) logical relation can be indicated by simple (schematically)
At
At-2, At-1, At→At+1
This indicates to carry out the prediction of the information at t+1 moment in t moment.
It was noticed that regular item number increases with the increase of input information number.If there is N number of information to input, need
Construct N-2 rule.In real life, some data theoretically will be it is inexhaustible, at any time endlessly
It generates, therefore a large amount of rule will be will use, to increase algorithm complexity and precision of prediction, and certain data are often presented
Periodically interim feature, adjacent time data can bring certain influence to the prediction of next data.Therefore, at me
Fuzzy inferential engine in introduce sliding time window.It is unique for not being due to the fuzzy logical relationship consequent that we establish
Value, for example, F8, F7.E7→F7, F8, G8, D6, E6, E7, G9, J10, D7, C6, H9, but previous time window is to the latter time window
For the information of mouth output by different weights, this relates to the calculating of degree of membership.Three inputs, single to export, (N-3) rules and regulations
Basic structure then is shown in Fig. 7.
The input form of fuzzy prediction machine is last three particles of the training set of particle sequence, i.e. A 'N-2=AN-2, A 'N-1
=AN-1, A 'N=ANFor fuzzy rule Rule i (i=1,2 ..., N-3), if making premise
A‘N-2 is AN-2,
A‘N-1is AN-1,
A‘Nis AN
Guarantee a degree of confidence level (reliability) (i.e. emissive porwer, the firing strength) (is true
To a certain degree), i.e. observation sequence (A 'N-2, A 'N-1, A 'N) and antecedents (antecedents) (Ai, Ai+1,
Ai+2) there are certain matching degree, it is denoted as
ω‘i=ω 'i(Ai, Ai+1, Ai+2；AN-2, AN-1, AN)
So corresponding conclusion of this premise " AN+1isAi+3" also there is identical confidence level.According to three rank fuzzy logics of foundation
Relationship calculates separately antecedents (antecedents) (Ai, Ai+1, Ai+2) corresponding observation sequence (A 'N-2, A 'N-1, A 'N) and
Degree of membership between peripheral information grain improves the accuracy rate of predictive information grain to be predicted.It says below and is specifically described use
The step of fuzzy rule inference that fuzzy logical relationship is established:
Step 1: according to single order fuzzy logical relationship group, first determining whether observation sequence AN' corresponding information ANIt is patrolled fuzzy
Whether the consequent in volume relationship group is unique value, if it is unique, then can directly predict AN+1, otherwise, patrolled according to second order is fuzzy
It collects relationship group and judges observation sequence AN-1', AN' corresponding information AN-1, ANIn second order fuzzy logical relationship group it is corresponding after
Whether part is unique value, if it is unique value, then can directly predict AN+1, otherwise, judged according to three rank fuzzy logical relationship groups
Information AN-2, AN-1, ANWhether corresponding consequent is unique value in fuzzy logical relationship group, then can be straight if it is unique
Meet prediction AN+1, otherwise carry out step 2；
Step 2: judging observation sequence AN-2' corresponding information AN-2Position in fan-shaped domain, if AN-2Positioned at opinion
The leftmost side or rightmost side marginal portion in domain, the such as { A in Fig. 40, A11, L0, L11, then needing to find information includes certainly
4 informations including oneself；If AN-2Positioned at the top side or lower side marginal portion of domain, the such as { B in Fig. 40, C0,
D0, E0, F0, G0, H0, I0, J0, K0}；{L1, L2, L3, L4, L5, L6, L7, L8, L9, L10}；{B11, C11, D11, E11, F11, G11, H11,
I11, J11, K11, then needing to find information includes 6 informations including oneself；If if AN-2Positioned at the centre of domain
{ B in part, such as Fig. 41, C1, D1, E1, F1, G1, H1, I1, J1, K1, then needing to find information includes 9 including oneself
A information is similarly operated determines observation sequence A respectivelyN-1' and AN' corresponding information AN-1And ANIn fan-shaped domain
Position；
Step 3: observation sequence A is found out according to formula (2)N-2' the degree of membership with peripheral information grain, and take out degree of membership most
Two big informations, are denoted as { a1, a2, similarly, successively find out observation sequence AN-1' the degree of membership with peripheral information grain, observation
Sequence AN' the degree of membership with peripheral information grain, and maximum two informations of degree of membership are taken out, it is denoted as { b respectively1, b2}、{c1,
c2}.
Step 4: by step 3 it is found that 6 informations are taken out altogether, successively respectively from { a1, a2, { b1, b2, { c1, c2In take
An information out carries out permutation and combination, and it is { a respectively that one, which shares eight kinds of combinations,1, b1, c1}、{a1, b2, c1}、{a1, b1,
c2}、{a1, b2, c2}、{a2, b1, c1}、{a2, b2, c1}、{a2, b1, c2}、{a2, b1, c1In three rank fuzzy logical relationship groups,
It calculates the probability that eight kinds of combinations occur and finds the corresponding consequent of every kind of combination, if a certain combination is closed in three rank fuzzy logics
It is that remaining combination is normalized there is no just giving up in group.
Step 5: by the processing of step 4, taking out maximum group of merging of probability of occurrence and find out each letter in combination and consequent
The transfer probability between grain is ceased, weights omega is denoted asij
AN+1It is the A that prediction obtainsN+1' middle maximum the information of weight
Wherein, weight vector (ω1, ω2..., ωN-3) and matching degree [ω '1, ω '2..., ω 'N-3] in proportional
Relationship (is set to be proportional to the matching degree), is defined as following form:
Wherein, ω 'iIt is observation sequence (A 'N-2, A 'N-1, A 'N) and Rule i antecedents (Ai, Ai+1, Ai+2) matching
Degree, i=1,2 ..., N-3.
We define α (Ai, Aj) it is AiAnd AjThe measurement of similarity degree (matching degree).Obviously, the distance between two particles
Smaller, similarity degree is bigger.Therefore, α (Ai, Aj) can be represented as
Similar to Fuzzy c-mean Algorithm, wherein weighted index m > 1 is referred to as Fuzzy Exponential.In the present invention, it is blurred
Coefficient m is set as 2.Therefore, observation sequence (A 'N-2, A 'N-1, A 'N) and Rule i antecedents (antecedents) (Ai, Ai+1,
Ai+2) matching degree be represented as
Two o'clock A on complex planei=(α1, Δ α1) and Aj=(α2, Δ α2) between Euclidean distance:
3. predictive information grain
Length is the particle time series A={ A (i) } of n, and i=1,2 ..., n are divided into and are initialized as preceding ntA
Grain is constituted, length ntTraining set and by following nfThe forecast set that a particle is constituted.The length of training set increases at any time
Add, maximum is equal to sliding window length+2.In next experiment, the length minimum of training set is equal to total collection Y (particle time
Sequence A or digit time sequence X) 8/9ths, i.e. nt>=8n/9=8 (nt+nf)/9
Model is constructed according to training set data, to predict the data of forecast set, is expressed as
Aforecast(t+1)=Forecast (A (t), A (t-1), A (t-2))
The data of forecast set are expressed as A as test data for calculating precision of predictionforecasted(nt+ i), i=1,
2 ..., nf.It can be obtained by above formula
Aforecast(nt+ 1)=Forecast (A (nt), A (nt- 1), A (nt- 2)),
Aforecast(nt+ 2)=Forecast (A (nt+ 1), A (nt), A (nt- 1)),
Aforecast(nt+nf)=Forecast (A (nt+nf- 1), A (nt+nf- 2), A (nt+nf- 3)),
The information predicted contains variation range, the variation tendency of predicted next stage data.
The foregoing is merely preferred embodiment of the present application, are not intended to limit this application, for the skill of this field
For art personnel, various changes and changes are possible in this application.Within the spirit and principles of this application, made any to repair
Change, equivalent replacement, improvement etc., should be included within the scope of protection of this application.
Claims (10)
1. the Time Series Forecasting Methods based on polar coordinates fuzzy information granule, characterized in that include:
Step (1): according to the length of sliding window predetermined, numerical value time series is divided into several constant durations
Time window；
Step (2): being fitted the data of each time window and establish regression equation, and then finds out the recurrence system of regression equation
Number；The regression coefficient includes: slope and intercept；Deflection angle is calculated using regression coefficient, and finds out two neighboring angle
Between deflection angle it is poor；Determine the most value of deflection angle and deflection angle difference；Deflection angle and deflection angle are constructed on polar coordinates
The domain for spending difference, marks off several sections, each section is defined as an information, different section definitions on domain
The information of different names out；
Step (3): the fuzzy logical relationship between mined information grain establishes fuzzy logical relationship group, to establish between information
Transmission network model；
Step (4): being trained transmission network model, using trained transmission network model to time series to be predicted
It is predicted.
2. the Time Series Forecasting Methods as described in claim 1 based on polar coordinates fuzzy information granule, characterized in that each
The data of time window are fitted the step of establishing regression equation are as follows:
Pt i=ait+bi,
Wherein, Pt iIndicate the regression equation of i-th of time window, aiAnd biIt is the recurrence system of the regression equation of i-th of time window
Number；aiIt is the slope of regression equation, biIt is the intercept of regression equation；
Measure the regression coefficient a of each time window regression equationiAnd bi, to acquire regression coefficient aiAnd biSet { [a1,
b1], [a2, b2], [ai, bi] ... [am, bm]}；amAnd bmIt is the regression coefficient of the regression equation of m-th of time window.
3. the Time Series Forecasting Methods as described in claim 1 based on polar coordinates fuzzy information granule, characterized in that utilize back
The step of returning coefficient to calculate deflection angle are as follows:
According to the regression coefficient a of the regression equation of i-th of time windowiAcquire corresponding deflection angle αi:
αi=arctan (ai)。
4. the Time Series Forecasting Methods as described in claim 1 based on polar coordinates fuzzy information granule, characterized in that find out phase
The step of deflection angle difference between adjacent two angles are as follows:
Δαi=αi+1-αi；
Then each time window corresponds to one group of parameter alphaiWith Δ αi；To obtain
Set A={ [α1, Δ α1], [α2, Δ α2], [αi, Δ αi] ... [αm, Δ αm]}；
αiRefer to deflection angle of the curve relative to horizontal axis, behind be translated into the polar angle in polar coordinate system；ΔαiIt is adjacent inclined
Difference between corner, behind be translated into the polar radius in polar coordinate system.
5. the Time Series Forecasting Methods as described in claim 1 based on polar coordinates fuzzy information granule, characterized in that sat in pole
Mark fastens the domain of construction deflection angle and deflection angle difference, in the step of marking off several sections on domain are as follows:
Obtain set A={ [α1, Δ α1], [α2, Δ α2], [αi, Δ αi] ... [αm, Δ αm]}；Set A is divided for data fitting
Deflection angle set Ai={ α1, α2..., αnAnd deflection angle situation of change set Δ Ai={ Δ α1, Δ α2... Δ αnTwo
Set is fitted deflection angle set A based on dataiWith the situation of change set Δ A of deflection angleiConstruct domain, construct domain during
Deflection angle is considered as the polar angle in polar coordinate system, the variation of deflection angle is considered as the polar radius in polar coordinate system, to be sat in pole
Mark fastens building domain；
Define the most value of deflection angle and deflection angle difference
Aimin=min { α1, α2..., αn}；
Aimax=max { α1, α2..., αn}；
ΔAimin=min { Δ α1, Δ α2... Δ αn}；
ΔAimax=max { Δ α1, Δ α2... Δ αn}；
Wherein, AiminIndicate the minimum value of the deflection angle amplitude of time series fitting, AimaxIndicate the deflection of time series fitting
The maximum value of angle amplitude；ΔAiminIndicate the minimum value of deflection angle difference, Δ AimaxIndicate the maximum of deflection angle difference
Value；
U=[U1, U2] indicate deflection angle codomain,
U=[U1, U2]=[Aimin-l1, Aimax+l2]；
Wherein, l1And l2It is trimming factor t rim factor,
R=[R1, R2] indicate deflection angle difference codomain,
R=[R1, R2]=[Rimin-m1, Rimax+m2]；
Wherein m1And m2It is trimming factor t rim factor,
The data information after fitting is indicated on polar coordinates, wherein the value of polar angle θ is corresponding partially by the slope of regression equation
What gyration determined, polar radius ρ is that the difference of adjacent polar angle is established on polar coordinates according to the value range of polar angle and polar radius
Fan-shaped domain；
Lateral division is carried out to domain according to the division number h being set in advance, domain is indulged according to the division number i of setting
To division；Wherein, domain is finally divided into the section of h × i by h >=2, i >=2, and each section is defined as an information.
6. the Time Series Forecasting Methods as described in claim 1 based on polar coordinates fuzzy information granule, characterized in that in domain
On the step of marking off several sections are as follows:
According to the amplitude of deflection angle, horizontal partition point s=[p is used1, p2..., ph-1] divided, then l1=[U1, p1], l2
=[p1, p2] ..., lj=[pj-1, pj] ..., lh=[ph-1, U2], similarly, use longitudinally split point t=[h1, h2...,
hi-1] divided, then t1=[R1, h1], t2=[h1, h2] ..., tj=[hj-1, hj] ... th=[hi-1, R2]。
7. the Time Series Forecasting Methods as described in claim 1 based on polar coordinates fuzzy information granule, characterized in that
The specific steps of step (3) are as follows:
Assuming that particle time series is by N number of information A1, A2..., ANComposition predicts the N+1 information AN+1；
Single order fuzzy logical relationship: Ai, Ai+1For the particle that two continuous observations arrive in time series, then the relationship between them is used
One fuzzy logical relationship indicates, is denoted as Ai→Ai+1Wherein, AiThe referred to as left member of fuzzy logical relationship, Ai+1Referred to as fuzzy logic
The right member of relationship；
Second order fuzzy logical relationship: Ai-1, Ai, Ai+1For the particle that three continuous observations arrive in time series, then the pass between them
System is indicated with a fuzzy logical relationship, is denoted as Ai-1, Ai→Ai+1；
Three rank fuzzy logical relationships: Ai-2, Ai-1, Ai, Ai+1For the particle that four continuous observations arrive in time series, then between them
Relationship indicated with a fuzzy logical relationship, be denoted as Ai-2, Ai-1, Ai→Ai+1；
Step 31: according to single order fuzzy logical relationship, first determining whether observation sequence AN' corresponding information ANIt is closed in fuzzy logic
Whether the consequent in system is unique value, if it is unique, then can directly predict AN+1；
Otherwise, observation sequence A is judged according to second order fuzzy logical relationshipN-1', AN' corresponding information AN-1, ANIt is fuzzy in second order
Whether corresponding consequent is unique value in logical relation, if it is unique value, then directly predicts AN+1；
Otherwise, information A is judged according to three rank fuzzy logical relationshipsN-2, AN-1, ANIn three rank fuzzy logical relationships it is corresponding after
Whether part is unique value, if it is unique, then directly predicts AN+1, otherwise enter step 32；
Step 32: judging observation sequence AN-2' corresponding information AN-2Position in fan-shaped domain,
If AN-2Positioned at the leftmost side edge or rightmost side edge of domain, then to find information includes 4 including oneself
Information；
If AN-2Positioned at the top side edge or lower side edge of domain, then to find information includes 6 including oneself
Information；
If AN-2Positioned at the middle section of domain, then to find information includes 9 informations including oneself；
Same operation determines observation sequence A respectivelyN-1' and AN' corresponding information AN-1And ANPosition in fan-shaped domain；
Step 33: finding out observation sequence AN-2' degree of membership f (the x with peripheral information grain；μ, y, v, σ), and take out degree of membership maximum
Two informations, be denoted as { a1, a2}；Similarly, observation sequence A is successively found outN-1' the degree of membership with peripheral information grain, and take out
Maximum two informations of degree of membership, are denoted as { b1, b2}；Observation sequence AN' the degree of membership with peripheral information grain, and take out and be subordinate to
Maximum two informations are spent, { c is denoted as1, c2}；
Step 34: successively respectively from { a1, a2, { b1, b2, { c1, c2One information of middle taking-up, permutation and combination is carried out, altogether
There are eight kinds of combinations, is { a respectively1, b1, c1}、{a1, b2, c1}、{a1, b1, c2}、{a1, b2, c2}、{a2, b1, c1}、{a2, b2,
c1}、{a2, b1, c2}、{a2, b1, c1}；In three rank fuzzy logical relationships, calculates the probability that eight kinds of combinations occur and find every kind
Combine corresponding consequent, if a certain combination in three rank fuzzy logical relationships there is no just giving up, to it is remaining combine into
Row normalized；
Step 35: the maximum combination of probability of occurrence is taken out, and finds out the transmitting frequency in combination and consequent between each information,
It is denoted as weights omega
AN+1It is the A that prediction obtainsN+1' middle maximum the information of weight；
Wherein, weight vector (ω1, ω2..., ωN-3) and matching degree [ω '1, ω '2..., ω 'N-3] it is in proportional relationship,
It is defined as following form:
Wherein, ω 'iIt is observation sequence (A 'N-2, A 'N-1, A 'N) and the i-th rule antecedents (Ai, Ai+1, Ai+2) matching
Degree, i=1,2 ..., N-3；
Define α (Ai, Aj) it is AiAnd AjThe measurement of matching degree；α(Ai, Aj) be expressed as
Wherein weighted index m > 1 is referred to as Fuzzy Exponential；Blurring Coefficient m is set as 2；
Observation sequence (A 'N-2, A 'N-1, A 'N) and Rulei antecedents (Ai, Ai+1, Ai+2) matching degree be represented as
Two o'clock A on complex planei=(α1, Δ α1) and Aj=(α2, Δ α2) between Euclidean distance:
Different types of information is defined as to the node of transmission network model, size of node reflection same name information goes out
Existing number, and the transmission of information is defined as edge, the weight at edge is the transmitting frequency between the information of two kinds of titles
Rate, to establish the transmission network model between information.
8. the Time Series Forecasting Methods as described in claim 1 based on polar coordinates fuzzy information granule, characterized in that
The specific steps of step (4) are as follows:
Aforecast(t+1)=Forecast (A (t), A (t-1), A (t-2))
The data of forecast set are expressed as A as test data for calculating precision of predictionforecasted(nt+ i), i=1,2 ...,
nf；It is obtained by above formula
Aforecast(nt+ 1)=Forecast (A (nt), A (nt- 1), A (nt- 2)),
Aforecast(nt+2)=Forecast (A (nt+1), A (nt), A (nt- 1)),
Aforecast(nt+nf)=Forecast (A (nt+nf- 1), A (nt+nf- 2), A (nt+nf- 3)),
The information predicted contains variation range, the variation tendency of predicted next stage data；
Wherein, Aforecast(t+1) information at the t+1 moment of prediction is indicated；The information of A (t) expression t moment；A (t-1) table
Show the information at t-1 moment；The information at A (t-2) expression t-2 moment；Aforecast(nt+ 1) n of prediction is indicatedt+ 1 moment
Information；A(nt) indicate ntThe information at moment；A(nt- 1) n is indicatedtThe information at -1 moment；A(nt- 2) n is indicatedt- 2 moment
Information；Aforecast(nt+nf) indicate the n predictedt+nfThe information at moment；A(nt+nf- 1) n is indicatedt+nfThe letter at -1 moment
Cease grain；A(nt+nf- 2) n is indicatedt+nfThe information at -2 moment；A(nt+nf- 3) n is indicatedt+nfThe information at -3 moment.
9. the time series forecasting system based on polar coordinates fuzzy information granule, characterized in that include: memory, processor and
The computer instruction run on a memory and on a processor is stored, when the computer instruction is run by processor, is completed
Step described in any one of the claims 1-8 method.
10. a kind of computer readable storage medium, characterized in that be stored thereon with computer instruction, the computer instruction quilt
When processor is run, step described in any one of the claims 1-8 method is completed.
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