CN102096672A - Method for extracting classification rule based on fuzzy-rough model - Google Patents

Abstract

The invention relates to a method for extracting a classification rule based on a fuzzy-rough model. Since fuzzy boundaries of continuous attribute values are not considered in the conventional continuous attribute discretization method, a data mining rule is not refined or accurate enough and important data information is easy to lose during discretization. The method for extracting the classification rule comprises the following steps of: performing attribute fuzzification on continuous attributes in an information sheet by using a membership function in a fuzzy set; and extracting parameters such as approaching precision approximate measure, rough approaching precision approximate measure, approaching precision classification quality measure, approaching precision relative classification measure and the like by using a rough set in a fuzzy similarity relation so as to establish an approaching approximate-based fuzzy-rough set reduction algorithm to solve the classification rule. In the method, each continuous attribute is added into an attribute reduction set in a descending order according to importance until the reduction condition is met, and particularly, the attribute reduction can be quickly solved when multiple condition attributes are available.

Description

A kind of based on Fuzzy and Rough model classification Rules extraction method

Technical field:

The invention belongs to the data mining technology in the intelligent decision support system, relate to a kind of model classification Rules extraction method, specifically be meant a kind of based on Fuzzy and Rough model classification Rules extraction method.

Background technology:

Rough set theory is a kind of mathematical tool of analyzing data, not needing to be characterized in the quantity of some feature given in advance or attribute to describe, but directly from the description set of given problem, finds out the inherent law in this problem.It has Knowledge Extraction is not needed artificial hypothesis fully, simplifies advantage such as the simple and easy operating of expression of space, the algorithm of input information by data-driven.But the Fundamentals of Mathematics of rough set are set theory, and are very limited to the processing power of connection attribute in the information table.Present data mining problem at information table with connection attribute, the most general method is that continuous data is carried out discretize, divide and to have method not of the same race because the value of connection attribute is carried out discretize, verified all the optimum discretization methods that may divide state of existing experiment are a kind of NP-hard problems.

At present the method to the connection attribute discretize has three kinds of classification at present: one has the discretize and the unsupervised discretize of supervision; Its two, overall discretize and local discretize; Its three, static discretize and dynamic discreteization.

Only consider the distribution character of this attribute data when unsupervised discretize process (Unsupervised discretization procedures) is divided a continuous variable, and have the discretize process (Superviseddiscretization procedures) of supervision in addition also need consider the classified information of each object.Unsupervised discretize process commonly used comprises: 1, wide interval method (equal-width-intervals); 2, the interval method (equal-freguency-intervals) of equifrequency; 3, string parsing method.The discretize that supervision is arranged is to estimate maximization in order to make by certain relation between discretize attribute and the categorical attribute, for example can utilize entropy to estimate or information gain is estimated (for example:Quinlan 1993; Catlett 1991; Fayyad ﹠amp; Irani 1993).Unsupervised discretize algorithm travelling speed is fast, and the discretize algorithm of supervision is arranged owing to considered class indication thereby can produce the higher discrete tree of precision.

Overall situation discretize (Global Discretization Method) be meant synchronization to decision table in the whole property value of condition of continuity attributes methods of dividing, local discretize (Local DiscretizationMethod) then is meant the method for only property value of a connection attribute being divided at synchronization.Then overall discretize can only produce one group of discrete divide value in the discretize process of whole connection attributes, and local discretize all can produce division not of the same race at same connection attribute.Mainly contain following several strategy for overall discrete method: merging method and division methods, partitioning are divided into dynamic type and static type again; Dynamically division is main relevant with decision tree, Yi Bian it is to generate decision tree, Yi Bian carry out the division in successive value interval; The static division method is called the pre-service type again, promptly before the training example set just connection attribute discretize all in advance, thereby when machine learning, can improve learning efficiency greatly.Use has the overall discretize of the most of use of the system of supervision discretization method.

Static discretization method such as binding method (Binning) all are at different attribute a with method based on entropy _iCan produce the discretize space-number k of different numbers _i, the dynamic discrete method then is only can produce same discrete interval to count k on all properties.The discretization method of document record at present all belongs to static discretization method, and dynamic discreteization is the target that the scholar is studying.

Yet the connection attribute discretization method of any type no matter all should satisfy following 3 points for discrete normalized result:

1, the space dimensionality after the connection attribute discretize is as far as possible little, and just the kind of the property value after each discrete normalization is few as far as possible;

2, the information dropout after the discrete normalization of property value quilt is few as far as possible;

3,, should keep the compatibility of decision system after the discretize for small sample; For large sample, can provide the decision system incompatibility level after the discretize.

Therefore, in sum, at present the weak point of connection attribute discretization method is because the smeared out boundary of connection attribute value is not considered, thereby in the discretize process, if between discrete regions too many then follow-up data mining process too complexity cause not refining of mining rule accurate; If then can lose significant data information very little between discrete regions.

Summary of the invention:

The technical problem to be solved in the present invention provides a kind of based on Fuzzy and Rough model classification Rules extraction method, this method is in the connection attribute fuzzification process of fuzzy set theory, to accurately link together from new angle with fuzzy, provide a kind of new method for handling uncertain information, delineate fuzzy concept by subordinate function, can solve smeared out boundary problem in the rough set effectively, thereby make that the refining of data mining rule is accurate, avoid losing significant data information.

For solving the problems of the technologies described above, the technical solution used in the present invention is: a kind of based on Fuzzy and Rough model classification Rules extraction method, may further comprise the steps: at first utilize the subordinate function in the fuzzy set that the connection attribute in the information table is carried out the attribute obfuscation, so both can prevent the loss of data, can express the difference of each property value again, thereby structure has the decision system of fuzzy property value; Use rough set in the fuzzy resembling relation again and propose parameters such as approximation accuracy approximate measure, coarse approximation accuracy approximate measure, approximation accuracy classification quality are estimated, the relative categorical measure of approximation accuracy, ask for classifying rules thereby set up based on the reduction algorithm of fuzzy-rough set of approximation accuracy.

Above-mentionedly comprise based on fuzzy-coarse reduction algorithm:

1, parameter declaration and definition

If m attribute: C arranged among the condition community set C in the decision system ₁, C ₂, Λ, C _m, decision kind set is combined into D, by being divided into of D decision: { Y ₁, Y ₂, Λ, Y _k, to each conditional attribute C _iCalculate a following k+4 parameter:

I=1 Λ m wherein, j=1 Λ k.Order With

Be respectively the count average and the geometric mean of this k+4 parameter; At each conditional attribute C _iK+4 parameter in considered absolute classification and the relative classification of conditional attribute simultaneously with decision attribute, make conditional attribute to the decision-making classification importance the comprehensive and rationality of tool is more arranged;

2, attribute C _iImportance be defined as:

$Z_{c_i}={\mathrm{\α}}_1{\mathrm{\τ}}_{c_1}+{\mathrm{\α}}_2{\mathrm{\κ}}_{c_i}$

α ₁And α ₂Be respectively the importance parameter of the count average and the geometric mean of user's appointment, all non-0 the time when all k+4 parameter, show that this attribute is all influential to each subclass of dividing, thereby increase geometric mean

Be to occur for this importance influence is embodied.

Above-mentioned algorithm may further comprise the steps:

(1) γ of design conditions community set _C(L);

(2) calculate for any conditional attribute $Z=\left\{Z_{C_i}\right\};$

(3) initialization C ⁰=φ;

(4) $C^0=C^0+\left\{C_i\right|\∀i,$ Get C _iMake

Maximum };

(5) judge ${\mathrm{\&gamma;}}_{C_0}L<{\mathrm{\&gamma;}}_C\left(L\right),$ Then continue next step if satisfy, otherwise return previous step;

(6) C ⁰Being a minimum subtracts approximately.

The present invention is with respect to prior art, by utilizing algorithm approximately to subtract concentrated by the descending attribute that joins successively of importance each connection attribute based on the approximation accuracy parameter, up to satisfy subtract condition approximately till, algorithm has the advantages that to be simple and easy to realize, especially at conditional attribute more for a long time, can obtain attribute quickly and subtract approximately.

Description of drawings:

Fig. 1 is input data mode F _jMembership function π function distribution plan.

Embodiment:

A kind of based on Fuzzy and Rough model classification Rules extraction method, may further comprise the steps: at first utilize the subordinate function in the fuzzy set that the connection attribute in the information table is carried out the attribute obfuscation, so both can prevent the loss of data, can express the difference of each property value again, thereby structure has the decision system of fuzzy property value; Use rough set in the fuzzy resembling relation again and propose parameters such as approximation accuracy approximate measure, coarse approximation accuracy approximate measure, approximation accuracy classification quality are estimated, the relative categorical measure of approximation accuracy, ask for classifying rules thereby set up based on fuzzy-coarse reduction algorithm of approximation accuracy.

Above-mentionedly comprise based on fuzzy-coarse reduction algorithm:

1, parameter declaration and definition

If m attribute: C arranged among the condition community set C in the decision system ₁, C ₂, Λ, C _m, decision kind set is combined into D, by being divided into of D decision: { Y ₁, Y ₂, Λ, Y _k, to each conditional attribute C _iCalculate a following k+4 parameter:

I=1 Λ m wherein, j=1 Λ k; Order

With

Be respectively the count average and the geometric mean of this k+4 parameter; At each conditional attribute C _iK+4 parameter in considered absolute classification and the relative classification of conditional attribute simultaneously with decision attribute, make conditional attribute to the decision-making classification importance the comprehensive and rationality of tool is more arranged.

2, attribute C _iImportance be defined as:

$Z_{c_i}={\mathrm{\&alpha;}}_1{\mathrm{\&tau;}}_{c_1}+{\mathrm{\&alpha;}}_2{\mathrm{\&kappa;}}_{c_i}$

α ₁And α ₂Be respectively the importance parameter of the count average and the geometric mean of user's appointment, all non-0 the time when all k+4 parameter, show that this attribute is all influential to each subclass of dividing, thereby increase geometric mean

Be to occur for this importance influence is embodied.

Above-mentioned algorithm comprises the steps:

(1) γ of design conditions community set _C(L);

(2) calculate for any conditional attribute $Z=\left\{Z_{C_i}\right\};$

(3) initialization C ⁰=φ;

(4) $C^0=C^0+\left\{C_i\right|\&ForAll;i,$ Get C _iMake

Maximum };

(5) judge ${\mathrm{\&gamma;}}_{C_0}L<{\mathrm{\&gamma;}}_C\left(L\right),$ Then continue next step if satisfy, otherwise return previous step;

(6) C ⁰Being a minimum subtracts approximately.

Embodiment:

A kind of based on Fuzzy and Rough model classification Rules extraction method, comprising:

1, connection attribute obfuscation

(1) decision system of connection attribute value

Be provided with a decision system (U, Q, V, f), U={x wherein ₁, x ₂, Λ, x _nBe the limited domain of non-NULL, indicated object; Q is the property set of non-NULL, Q=CY{d}, C={q ₁, q ₂, Λ, q _mBe a non-NULL, limited conditional attribute collection, and d} is a decision kind set, d:U → 1,2, Λ, g}; V is a property value, V=V _cYV _d, V _C={ V _q: q ∈ C} is a conditional attribute value collection, V _dBe decision attribute value collection, and i the property value v of object under j conditional attribute _Ij(1=1 Λ n, j=1 Λ m) is the connection attribute value; F:U * Q → V is an information mapping function, and obviously this is a decision system that property value is continuous.

(2) attribute obfuscation

In actual applications, the key of connection attribute being carried out obfuscation is to determine membership function, utilizes the π function that attribute is blured division.In fuzzy set fuzzy member to be worth with three parametric representations be low (L), medium (M), high (H), then the data pattern F that ties up of any one n _j=[F _J1, F _J2, Λ, F _Jn] can be with the vector representation of 3n dimension:

$F_j=[{\mathrm{\&mu;}}_{\mathrm{low}\left(F_{j1}\right)}\left(F_j\right),\mathrm{\&Lambda;},{\mathrm{\&mu;}}_{\mathrm{high}\left(F_{\mathrm{jn}}\right)}\left(F_j\right)]$

Wherein the μ value representation is corresponding to fuzzy three parameter l ow of π collection (L), medium (M), the membership function value of high (H).As input data mode F _jWhen being successive value, its degree of membership μ is expressed as in the one-dimensional space:

Wherein r (＞0) is to be the radius of the π function of round spot coordinate with c, and x is the membership function variable.Input data mode F _jMembership function be illustrated in fig. 1 shown below:

As input data mode F _jThe time, three parameter l ow (L) of fuzzy π collection, medium (M), high (H) is defined as follows:

$\mathrm{low}\&equiv;\{\frac{\mathrm{Th}}{L},\frac{\mathrm{\&mu;}(F_j(\frac{\mathrm{Th}}{L};c_{\mathrm{jm}},r_{\mathrm{jm}})}{M},\frac{\mathrm{\&mu;}(F_j(\frac{\mathrm{Th}}{L};c_{\mathrm{jh}},r_{\mathrm{jh}})}{H}\}$

$\mathrm{medium}\&equiv;\{\frac{\mathrm{\&mu;}(F_j(\frac{\mathrm{Th}}{M};c_{\mathrm{jl}},r_{\mathrm{jl}})}{L},\frac{\mathrm{Th}}{M},\frac{\mathrm{\&mu;}(F_j(\frac{\mathrm{Th}}{M};c_{\mathrm{jh}},r_{\mathrm{jh}})}{H}\}$

$\mathrm{high}\&equiv;\{\frac{\mathrm{\&mu;}(F_j(\frac{\mathrm{Th}}{H};c_{\mathrm{jl}},r_{\mathrm{jl}})}{L},\frac{\mathrm{\&mu;}(F_j(\frac{\mathrm{Th}}{H};c_{\mathrm{jm}},r_{\mathrm{jm}})}{M},\frac{\mathrm{Th}}{H}\}$

C wherein _Jl, r _Jl, c _Jm, r _Jm, c _Jh, r _JhBe illustrated respectively in input data mode F _jDown, the round spot coordinate and the radius of three fuzzy characteristics parameters of fuzzy π collection,

Represent input pattern F respectively _jFollowing three parameters are resulting eigenwert under the Th in threshold value.

Input specific data pattern F _jAfter, the breakpoint that the fuzzy interval of its continuous eigenwert is divided is c _L, c _M, c _H, its radius is r _L, r _M, r _Hc _L(F _j), c _M(F _j), c _H(F _j) and r _L(F _j), r _M(F _j), r _H(F _j) value obtain by following formula:

$m_j=\frac{1}{3}\mathrm{\&Sigma;}(\mathrm{low}+\mathrm{medium}+\mathrm{high})$

$m_{\mathrm{jl}}=\frac{1}{2}\mathrm{\&Sigma;}(F_{j\min }+m_j)$

$m_{\mathrm{jh}}=\frac{1}{2}\mathrm{\&Sigma;}(F_{j\max }+m_j)$

c _L(F _j)＝m _jl

c _M(F _j)＝m _j

c _H(F _j)＝m _jh

r _L(F _j)＝c _M(F _j)-c _L(F _j)

r _H(F _j)＝c _H(F _j)-c _M(F _j)

r _M(F _j)＝0.5(c _H(F _j)-c _L(F _j))

M wherein _jFuzzy three the parameter l ow of π collection of expression, medium, the arithmetic mean value of high, m _JlBe F _JminWith m _jThe arithmetic mean value, m _JhBe F _JmaxWith m _jThe arithmetic mean value, F _Jmin, F _JmaxBe respectively data pattern F _jMinimum value and maximal value.

In decision system, each conditional attribute can be regarded as any input data mode F _j, can be to each condition of continuity attribute q with the above parameter of π function _j∈ C, j=1 Λ m determines its subordinate function and fuzzy interval number, establishes Q _j ^kBe conditional attribute q _jK fuzzy region, μ _Ij ^kIndicated object x _i∈ U (i=1 Λ n) is at fuzzy region Q _j ^kIn membership function value.

2, fuzzy-rough set model

(1) fuzzy resembling relation

Common rough set is based on a kind of relation of equivalence of the relation of can not differentiating, and in actual applications, as if the constraint condition of loosening in the set relations, removal can not be differentiated the transitivity of relation, and relation of equivalence is extended to fuzzy resembling relation.

Definition for $\&ForAll;x_s{x}_t\&Element;U,\&ForAll;q_j\&Element;C,j=1\mathrm{\&Lambda;m},$ The ambiguity in definition relation

As follows:

$x_s\tilde{R}{x}_t=\{(x_s,x_t)\&Element;U\&times;U|{\mathrm{\&mu;}}_{\mathrm{sj}}^k,{\mathrm{\&mu;}}_{\mathrm{tj}}^k>0\}$

And

Satisfy following condition:

Reflexivity: ${\mathrm{\&mu;}}_{\tilde{R}}(x_s,x_s)=1,\&ForAll;x_s\&Element;U$

Symmetry: ${\mathrm{\&mu;}}_{\tilde{R}}(x_s,x_t)={\mathrm{\&mu;}}_{\tilde{R}}(x_t,x_s),\&ForAll;x_s,x_t\&Element;U$

Definition U={x ₁, x ₂, Λ, x _nBe limited domain, the fuzzy resembling relation on the U $\tilde{R}\&Element;R_{n\&times;n}$ Be called fuzzy similarity matrix, promptly

Be fuzzy matrix, and satisfy following condition:

Reflexivity: μ _St=1 s, t=1 Λ n; Symmetry: μ _St=μ _TsS, t=1 Λ n

In order to set up fuzzy similarity matrix, need to calculate fuzzy similarity coefficient r _St, this paper utilizes the hamming distance to define.Definition for $\&ForAll;x_s{x}_t\&Element;U,\&ForAll;q_j\&Element;C,j=1\mathrm{\&Lambda;m},$ In fuzzy relation Down, x _sWith x _tBetween the fuzzy similarity coefficient be ${\mathrm{\&mu;}}_{\mathrm{st}}=1-\frac{1}{m}\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}|{\mathrm{\&mu;}}_{\mathrm{sl}}^k-{\mathrm{\&mu;}}_{\mathrm{tl}}^k|.$ Introduce confidence level λ, work as μ _StDuring 〉=λ, matrix element gets 1, and μ _StDuring＜λ, matrix element gets 0.At this moment, fuzzy similarity matrix is changed in quality and is common similar matrix.

(2) approximation accuracy measurement model under the fuzzy resembling relation

1. fuzzy equivalence class

In the application of fuzzy coarse central, the division of fuzzy equivalence class is the problem that must consider.In basic rough set, the equivalence class of attribute and combinations of attributes correspondence is an ordinary set, and the equivalence class of attribute and combinations of attributes correspondence is a fuzzy set in Rough Fuzzy Sets, and promptly each attribute can belong to a plurality of fuzzy equivalence classes, and the fuzzy equivalence class of combinations of attributes A ∈ Q is divided and is expressed as follows:

$U/\mathrm{IND}\left({\tilde{R}}_{\mathrm{\&lambda;}}^A\right)=\&CircleTimes;\{U/\mathrm{IND}\left({\tilde{R}}_{{\mathrm{\&lambda;}}_i}^{a_i}\right):a_i\&Element;A,{\mathrm{\&lambda;}}_i\&Element;\mathrm{\&lambda;}\}$

Wherein: U is a domain, and R is a fuzzy resembling relation, and A and λ be representation attribute combination and corresponding confidence level collection respectively; Operator definitions is as follows:

$C_1{\&CircleTimes;C}_2=\left\{x_{1}I{x}_2\right|{\&ForAll;x}_1\&Element;C_1,\&ForAll;x_2\&Element;C_2,x_{1}I{x}_2\&NotEqual;\mathrm{\&Phi;}\}$

If A={a ₁, a ₂, Λ, a _nThen (2-1) formula be expressed as:

$U/\mathrm{IND}\left({\tilde{R}}_{\mathrm{\&lambda;}}^A\right)=\left\{X_{1_{i1}}I{X}_{2_{i2}}\mathrm{I\&Lambda;I}{X}_{n_{\mathrm{in}}}\right|x_{1_{i1}}\&Element;U/\mathrm{IND}\left(a_1\right),\mathrm{\&Lambda;},x_{n_{\mathrm{in}}}\&Element;U/\mathrm{IND}\left(a_n\right),\}$

Use F _jExpression

Then object x ∈ U to the degree of membership of this fuzzy equivalence class is:

$\mathrm{\&mu;}<F_1{F}_1\mathrm{\&Lambda;}{F}_j\mathrm{\&Lambda;}>\left(X\right)=\min \{{\mathrm{\&mu;}}_{F_1}\left(x\right),{\mathrm{\&mu;}}_{F_2}\left(x\right),\mathrm{\&Lambda;},{\mathrm{\&mu;}}_{F_n}\left(x\right)\}$

2. the approximate up and down of Fuzzy and Rough collects

Concentrate in Fuzzy and Rough, to any one object set $X\&SubsetEqual;U,$ X is based on similarity relation

Approximate up and down collection definition as follows respectively:

${\tilde{R}}_{\mathrm{\&lambda;}}^{A^{-}}\left(X\right)=Y\left\{(Y,{\mathrm{\&mu;}}_{{\mathrm{px}}^{-}}\left(F_i\right):Y\&Element;U/\mathrm{IND}\left({\tilde{R}}_{\mathrm{\&lambda;}}^A\right),Y\&SubsetEqual;X\right\}$

${\tilde{R}}_{\mathrm{\&lambda;}}^{A_{-}}\left(X\right)=Y\left\{(Y,{\mathrm{\&mu;}}_{p{x}_{-}}\left(F_i\right):Y\&Element;U/\mathrm{IND}\left({\tilde{R}}_{\mathrm{\&lambda;}}^A\right),\mathrm{YIX}\&NotEqual;\mathrm{\&Phi;}\right\}$

Because each equivalence class all blurs, so fuzzy equivalence class F _iApproximate up and down can be defined as follows:

${\mathrm{\&mu;}}_{p{x}^{-}}\left(F_i\right)=\left\{\mathrm{in}{f}_x\max \right\{1-{\mathrm{\&mu;}}_{F_i}\left(x\right),{\mathrm{\&mu;}}_X\left(x\right)\},\&ForAll;i\}$

${\mathrm{\&mu;}}_{{\mathrm{px}}_{-}}\left(F_i\right)=\left\{{\sup }_x\min \right\{{\mathrm{\&mu;}}_{F_i}\left(x\right),{\mathrm{\&mu;}}_X\left(x\right)\},\&ForAll;i\}$

Fuzzy equivalence class F _iThe fuzzy positive territory of ∈ U/IND (A) can be defined by following formula:

${\mathrm{\&mu;}}_{\mathrm{PO}{S}_A}\left(F_i\right)=Y\{{\tilde{R}}_{{\mathrm{\&lambda;}}_{-}}^A\left(F_{\mathrm{ij}}\right):F_{\mathrm{ij}}\&Element;F_i\}$

3. the approximation accuracy metric parameter of Fuzzy and Rough

If S=(U CY{d}) is a decision system, $A\&SubsetEqual;C$ Be attribute set, L divides Y={Y1 by the fuzzy U that decision attribute determined, Y2 ... Yk}, $Y\&SubsetEqual;U,$ Then fuzzy set Y is about the approximation accuracy approximate measure α of attribute A _A(Y) be defined as:

${\mathrm{\&alpha;}}_A\left(Y\right)=\frac{\mathrm{card}\left({\tilde{R}}_{\mathrm{\&lambda;}}^{A_{-}}\left(Y\right)\right)}{\mathrm{card}\left({\tilde{R}}_{\mathrm{\&lambda;}}^{A^{-}}\left(Y\right)\right)}$

Wherein card is a potency function.

The approximation accuracy approximate measure γ of L about property set A divided in the definition decision-making _A(L) be:

${\mathrm{\&gamma;}}_A\left(L\right)=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{card}\left({\tilde{R}}_{\mathrm{\&lambda;}}^{A_{-}}\left(Y_i\right)\right)/\mathrm{card}\left(U\right)$

The coarse approximation accuracy approximate measure α of L about property set A divided in the definition decision-making _A(L) be:

${\mathrm{\&alpha;}}_A\left(L\right)=1-(\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{card}\left({\tilde{R}}_{\mathrm{\&lambda;}}^{A^{-}}\left(Y_i\right)\right)-\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{card}\left({\tilde{R}}_{\mathrm{\&lambda;}}^{A_{-}}\left(Y_i\right)\right))/\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{card}\left({\tilde{R}}_{\mathrm{\&lambda;}}^{A^{-}}\left(Y_i\right)\right)$

The definition decision-making is divided L and is estimated about the approximation accuracy classification quality of property set A

For:

The definition decision-making is divided L and is estimated β about the relative classification quality of approximation accuracy of property set A _A(L) be:

${\mathrm{\&beta;}}_A\left(L\right)=\frac{\mathrm{card}\left({\mathrm{\&mu;}}_{{\mathrm{pos}}_A}\left(L\right)\right)}{\mathrm{card}\left(U\right)}=\frac{\mathrm{card}(\underset{Y_j\&Element;L}{Y}{\tilde{R}}_{{\mathrm{\&lambda;}}_{-}}^A\left(Y_{\mathrm{ij}}\right):Y_{\mathrm{ij}}\&Element;Y_j)}{\mathrm{card}\left(U\right)}$

The definition establish P, $R\&SubsetEqual;Q,$ And $R\&SubsetEqual;P,$ If γ _p(L)=γ _R(L) and R be the minimal set that satisfies this equation among the P, then R is that of P subtracts approximately, is designated as RED (P).Thus definition as can be known, divide before and after subtracting approximately L to the conditional attribute set to approach approximate measure constant.

Claims (3)

1. one kind based on Fuzzy and Rough model classification Rules extraction method, may further comprise the steps: at first utilize the subordinate function in the fuzzy set that the connection attribute in the information table is carried out the attribute obfuscation, structure has the decision system of fuzzy property value; Use rough set in the fuzzy resembling relation again and propose parameters such as approximation accuracy approximate measure, coarse approximation accuracy approximate measure, approximation accuracy classification quality are estimated, the relative categorical measure of approximation accuracy, ask for classifying rules thereby set up based on fuzzy-rough set reduction algorithm of approximation accuracy.

2. according to claim 1 a kind of based on Fuzzy and Rough model classification Rules extraction method, it is characterized in that: described bluring-coarse reduction algorithm comprises:

(1) parameter declaration and definition

If m attribute: C arranged among the condition community set C in the decision system ₁, C ₂, Λ, C _m, decision kind set is combined into D, by being divided into of D decision: { Y ₁, Y ₂, Λ, Y _k, to each conditional attribute C _iCalculate a following k+4 parameter:

I=1 Λ m wherein, j=1 Λ k; Order With

Be respectively the count average and the geometric mean of this k+4 parameter;

(2) attribute C _iImportance be defined as:

$Z_{c_i}={\mathrm{\&alpha;}}_1{\mathrm{\&tau;}}_{c_1}+{\mathrm{\&alpha;}}_2{\mathrm{\&kappa;}}_{c_i}$

Wherein, α ₁And α ₂Be respectively the average that counts of user's appointment

And geometric mean

The importance parameter.

3. according to claim 1 and 2 a kind of based on Fuzzy and Rough model classification Rules extraction method, it is characterized in that: described bluring-above-mentioned algorithm of coarse reduction algorithm may further comprise the steps:

(1) γ of design conditions community set _C(L);

(2) calculate for any conditional attribute $Z=\left\{Z_{C_i}\right\};$

(3) initialization C ⁰=φ;

(4)

(5) judge ${\mathrm{\&gamma;}}_{C_0}L<{\mathrm{\&gamma;}}_C\left(L\right),$ Then continue next step if satisfy, otherwise return previous step;

(6) C ⁰Being a minimum subtracts approximately.

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