CN106845142A

CN106845142A - Quality evaluation method based on improved rough set Set Pair Analysis

Info

Publication number: CN106845142A
Application number: CN201710136671.4A
Authority: CN
Inventors: 王栋; 卢媛; 王远坤; 吴吉春
Original assignee: Nanjing University
Current assignee: Nanjing University
Priority date: 2017-03-09
Filing date: 2017-03-09
Publication date: 2017-06-13

Abstract

The present invention discloses a kind of quality evaluation method based on improved rough set Set Pair Analysis, the three-unit connection number of Set Pair Analysis Theory is generalized to hexa-atomic contact number first, respective level is corresponded to respectively, and primary Calculation goes out the Pair Analysis of each sample, then Pair Analysis of each evaluation index actual measurement index value relative to index grade grade scale are calculated, the importance degree and weight of each evaluation index are calculated according to improved rough set conditional information entropy simultaneously, weight is combined with the Pair Analysis of each evaluation index, obtain each Pair Analysis for evaluating sample, each component is finally normalized the average Pair Analysis for obtaining various kinds sheetUsing the grade of greatest measure representative as the nutrient laden grade of the sample.With Set Pair Analysis be combined improved rough set conditional information entropy by the present invention, can both solve the influence of human factor during weight determines, the misgivings that weight is 0 can be eliminated again, while comprehensive multiple index is evaluated, with reasonability and validity.

Description

Quality evaluation method based on improved rough set-Set Pair Analysis

Technical field

The invention belongs to water quality assessment technical field, and in particular to a kind of water quality based on improved rough set-cloud model Evaluation method.

Background technology

Industrial wastewater, sanitary sewage and other discarded objects enter the water bodys such as rivers,lakes and seas, have exceeded the self-purification capacity of water body, Cause the change of the aspect feature such as its physics, chemistry, biology, so as to influence the value of water body, restriction social economy can Sustainable development；Meanwhile, natural process including corrode change, Crust Weathering etc. can also weaken water body drinking, industry, agricultural, give pleasure to Happy and otherwise purposes.Therefore, one that quality evaluation is rational exploitation and utilization and water conservation is carried out to water body Groundwork, is the important leverage of social sustainable development steady production.With the development of theory and technology, quality evaluation method day Become various, include that analytic hierarchy process (AHP), Grey System Appraisal method, fuzzy mathematics are commented using more method in water quality assessment at present Valency method and artificial neural network method.

The policy-making thought of complication system, can be carried out stratification by the 1st, analytic hierarchy process (AHP) (AHP), qualitative fixed in decision process The factor of amount organically combines, and makes the question simplification of complexity, but qualitative composition is more, and quantitative data is less, is difficult order People convinces.Schemes ranking and science decision are carried out with AHP methods to be obtained using the mode that compares two-by-two, for some because Element, when each expert opinion is inconsistent, cannot just set up judge completely and put to the proof, and judgment matrix does not have absolute consistency.

2nd, Grey System Appraisal method, can be used in analysis imprecise data, short sample and incomplete hydrographic data, but Variate-value must be standardized before cluster process is carried out, that is, eliminate the influence of dimension, distinct methods are standardized Different cluster results can be caused.

3rd, assessment of fuzzy math, can effectively solve the problem that smeared out boundary problem and control monitoring error to assessment result Influence, but it is determined that each index factor weight when, typically by with people basic experience and knowledge, with subjectivity Property.

4th, artificial neural network method, with stronger adaptability, evaluation result is objective, but requirement to training sample is high, Implementation process is complicated, with limitation.BP neural network and RBF neural are the relatively broad two kinds of network models for using, Easily there is local minimization in BP neural network, and convergence rate is slow, and network structure selects the problems such as differing；RBF neural is worked as When data are insufficient, cannot just work, and sample data is excessively relied on.

The content of the invention

Goal of the invention：It is an object of the invention to solve the deficiencies in the prior art, there is provided one kind is based on improved Rough set-Set Pair Analysis quality evaluation method.

Technical scheme：It is of the invention a kind of based on improved rough set-Set Pair Analysis quality evaluation method, successively including as follows Step：

(1) first by the three-unit connection number u of Set Pair Analysis Theory_t=a+bi+cj is generalized to hexa-atomic contact number u_t=a+bi₁+ ci₂+di₃+ej₁+fj₂, I, II, III, IV, V, VI grade is corresponded to respectively；

(2) the Pair Analysis u of each sample of primary Calculation_t；

(3) Pair Analysis u of each evaluation index actual measurement index value relative to index grade grade scale is determined_tk, for More big more excellent type index, Pair Analysis u_tkExpression formula is：

For smaller more excellent type index, Pair Analysis u_tkExpression formula is：

Wherein, S_i(i=1,2 ..., 6) represents level value.

(4) weight is determined：The importance degree sig and weight of each evaluation index are determined using improved rough set conditional information entropy w；

Wherein, rough set define decision table S=(U, A, V, f) in, U is domain, U={ x₁, x₂..., x_k, A=C ∪ D, C It is Criterion Attribute, D is decision attribute, U/C={ C₁, C₂..., C_m, U/D={ D₁, D₂..., D_n, I (D | C) represent decision attribute Conditional information entropies of the D relative to Criterion Attribute C, a ∈ C, a (x)=U/ { a }, c ∈ C.

(5) by w (c) and Pair Analysis u_tkCombine, calculate each Pair Analysis for evaluating sample

(6) willIn same, difference, each component of opposing be normalized the average Pair Analysis for obtaining various kinds sheetUsing the grade of greatest measure representative as the nutrient laden grade of the sample.

Beneficial effect：The present invention calculates the Pair Analysis of each sample, improved rough set conditional information entropy by Set Pair Analysis Used as the determination method of weight, the present invention has advantages below compared with existing method：

(1) certainty present in water analysis is solved with uncertainty.During water analysis, exist deterministic Evaluation criterion, and randomness and ambiguity, Set Pair Analysis are processing system certainty and the uncertain mathematics for interacting Theory, therefore water quality can be evaluated with Set Pair Analysis.

(2) objectivity that weight determines.Improved rough set conditional information entropy Weight Determination, with objective reality data It is foundation, it is not necessary to which any priori outside processing data set needed for problem is provided, eliminates the influence of artificial subjectivity, together When, it is to avoid the situation that weight is 0, the evaluation index that determines is removed, it is ensured that each index meaning present in decision-making.

In sum, the present invention combines Set Pair Analysis and improved rough set conditional information entropy, can solve water Matter evaluate present in certainty with it is uncertain, artificial subjective influence during weight determines can be eliminated again, with reasonability and Validity.

Brief description of the drawings

Fig. 1 is flow chart of the invention；

Specific embodiment

Technical solution of the present invention is described in detail below, but protection scope of the present invention is not limited to the implementation Example.

For ease of understanding the present invention, following explanation is done：

Set Pair Analysis：

Define 1:：There is the be made antithetical phrase referred to as set pair of 2 set of certain contact.

Set Pair Analysis be from, portray two different things comprehensively in terms of different, anti-three between contact, its core concept It is that the certainty contact of studied objective things is contacted as a determination uncertain system to analyze place with uncertainty Reason.

Define 2：Two set A and B are given, and sets this 2 collection and be combined into set pair H=(A, B), in certain particular problem W Under, set pair H has N number of characteristic, wherein：There is S individual for two set A and B have jointly in set pair H；In P characteristic upper set A and B opposes, neither mutually contradictory in remaining F=N-S-P characteristic, and does not claim then for this 2 set have jointly Ratio：

S/N is this 2 identical degrees being integrated under problem W, is designated as a；

P/N is this 2 opposition degree being integrated under problem W, is designated as c；

F/N is this 2 diversity factoies being integrated under problem W, is designated as b；

And use formulaTwo Pair Analysis of set of A, B are represented, it is also writeable to be u=a+bi+cj.I and J regards different situations value, j=-1 respectively as diversity factor and the coefficient of opposition degree, usual i between interval [- 1,1]；I and j Mark can also only be played.

In hexa-atomic contact number u=a+bi₁+ci₂+di₃+ej₁+fj₂In, i₁、i₂、i₃Represent diversity factor coefficient, j₁、j₂ It is opposition degree coefficient, i, j only play mark.

Improved rough set conditional information entropy：

Define 1：Decision table S=(U, A, V, f) in, U is domain, U={ x₁, x₂..., x_k, A=C ∪ D, C are condition Property set, D is decision kind set,V_aIt is the conditional attribute collection of a, V=∪ V_a, f：U × C → V is an information function.

Define 2：Decision table S=(U, A, V, f) in, A=C ∪ D, Criterion Attribute C, U/C={ C₁, C₂..., C_m, decision-making Attribute D, U/D={ D₁, D₂..., D_n, then decision attribute is relative to the conditional information entropy of Criterion Attribute

Define 3：Decision table S=(U, A, V, f) in, A=C ∪ D,A ∈ C, x ∈ U, the then weight of conditional attribute c Spend and be

Wherein a (x)=U/ { a }.

Define 4：Decision table S=(U, A, V, f) in, A=C ∪ D,Then the weight of conditional attribute c is

Embodiment 1：The present embodiment is using 12 water quality of representativeness Hu Ku of China as practical application

By taking 12 measured datas of representativeness Hu Ku of China as an example, using Chla, TP, TN, COD, SD as evaluation points, use Improved rough set-cloud model carries out water quality assessment.

(1) lake storehouse measured data

(2) China lake storehouse Evaluation of Eutrophication standard

(3) the importance degree sig and weight w of each evaluation index

				COD(mg/L)	SD(m)
						Sig	0.2	0.2	0.2	0.2	0.2
w	0.189	0.222	0.157	0.254	0.178

(4) final appraisal results

Claims

It is 1. a kind of to be based on improved rough set-Set Pair Analysis quality evaluation method, it is characterised in that：In turn include the following steps：

(1) first by the three-unit connection number u of Set Pair Analysis Theory_t=a+bi+cj, a+b+c=1, u_tPair Analysis are represented, a is same Degree, b is diversity factor, and c is opposition degree, and i and j is respectively the coefficient of diversity factor and opposition degree, and i is in interval [- 1,1] value, j=- 1；I and j only play mark；

It is generalized to hexa-atomic contact number u_t=a+bi₁+ci₂+di₃+ej₁+fj₂, a+b+c+d+e+f=1, a, b, c, d, e, f are right respectively I, II, III, IV, V, VI number of levels of water quality assessment is answered to account for the ratio of general comment valence mumber, i and j only play mark；

(2) according to formula u_t=a+bi₁+ci₂+di₃+ej₁+fj₂, the Pair Analysis u of each water quality sample of primary Calculation_t；

(3) Pair Analysis u of each evaluation index actual measurement index value relative to index grade grade scale is determined_tk, for bigger More excellent type index, evaluation index is relative to grade grade scale Pair Analysis u_tkExpression formula is：

$u_{t k} = \{\begin{matrix} 1 + 0 i_{1} + 0 i_{2} + 0 i_{3} + 0 j_{1} + 0 j_{2} & x &Element; [S_{1}, + \infty] \\ \frac{x - S_{2}}{S_{1} - S_{2}} + \frac{S_{1} - x}{S_{1} - S_{2}} i_{1} + 0 i_{2} + 0 i_{3} + 0 j_{1} + 0 j_{2} & x &Element; [S_{2}, S_{1}] \\ 0 + \frac{x - S_{3}}{S_{2} - S_{3}} i_{1} + \frac{S_{2} - x}{S_{2} - S_{3}} i_{2} + 0 i_{3} + 0 j_{1} + 0 j_{2} & x &Element; [S_{3}, S_{2}] \\ 0 + 0 i_{1} + \frac{x - S_{4}}{S_{3} - S_{4}} i_{2} + \frac{S_{3} - x}{S_{3} - S_{4}} i_{3} + 0 j_{1} + 0 j_{2} & x &Element; [S_{4}, S_{3}] \\ 0 + 0 i_{1} + 0 i_{2} + \frac{x - S_{5}}{S_{4} - S_{5}} i_{3} + \frac{S_{4} - x}{S_{4} - S_{5}} j_{1} + 0 j_{2} & x &Element; [S_{5}, S_{4}] \\ 0 + 0 i_{1} + 0 i_{2} + 0 i_{3} + \frac{x - S_{6}}{S_{5} - S_{6}} j_{1} + \frac{S_{5} - x}{S_{5} - S_{6}} j_{2} & x &Element; [S_{6}, S_{5}] \\ 0 + 0 i_{1} + 0 i_{2} + 0 i_{3} + 0 j_{1} + 1 j_{2} & x &Element; [0, S_{6}] \end{matrix}$

For smaller more excellent type index, evaluation index is relative to grade grade scale Pair Analysis u_tkExpression formula is：

$u_{t k} = \{\begin{matrix} 1 + 0 i_{1} + 0 i_{2} + 0 i_{3} + 0 j_{1} + 0 j_{2} & x &Element; [0, S_{1}] \\ \frac{S_{2} - x}{S_{2} - S_{1}} + \frac{x - S_{1}}{S_{2} - S_{1}} i_{1} + 0 i_{2} + 0 i_{3} + 0 j_{1} + 0 j_{2} & x &Element; [S_{1}, S_{2}] \\ 0 + \frac{S_{3} - x}{S_{3} - S_{2}} i_{1} + \frac{x - S_{2}}{S_{3} - S_{2}} i_{2} + 0 i_{3} + 0 j_{1} + 0 j_{2} & x &Element; [S_{2}, S_{3}] \\ 0 + 0 i_{1} + \frac{S_{4} - x}{S_{4} - S_{3}} i_{2} + \frac{x - S_{3}}{S_{4} - S_{3}} i_{3} + 0 j_{1} + 0 j_{2} & x &Element; [S_{3}, S_{4}] \\ 0 + 0 i_{1} + 0 i_{2} + \frac{S_{5} - x}{S_{5} - S_{4}} i_{3} + \frac{x - S_{4}}{S_{5} - S_{4}} j_{1} + 0 j_{2} & x &Element; [S_{4}, S_{5}] \\ 0 + 0 i_{1} + 0 i_{2} + 0 i_{3} + \frac{S_{6} - x}{S_{6} - S_{5}} j_{1} + \frac{x - S_{5}}{S_{6} - S_{5}} j_{2} & x &Element; [S_{5}, S_{6}] \\ 0 + 0 i_{1} + 0 i_{2} + 0 i_{3} + 0 j_{1} + 1 j_{2} & x &Element; [S_{6} + \infty] \end{matrix}$

Wherein, S_i(i=1,2 ..., 6) represents the bound numerical value of each grade of water quality assessment standard；

(4) weight is determined：The importance degree sig and weight w of each evaluation index are determined using improved rough set conditional information entropy；

$s i g (c) = I (D | C - {c}) - I (D | C) + \frac{Σ_{a &Element; C} | a (x) | - Σ_{a &Element; C - {c}} | a (x) |}{Σ_{a &Element; C} | a (x) |}$

$w (c) = \frac{s i g (c) + I (D | C)}{Σ_{a &Element; C} {s i g (a) + I (D | {a})}}$

$I (D | C) = Σ_{i = 1}^{m} \frac{| C |^{2}}{| U |^{2}} Σ_{j = 1}^{n} \frac{| D_{j} \cap C_{i} |}{| C_{i} |} (1 - \frac{| D_{j} \cap C_{i} |}{| C_{i} |})$

Wherein, rough set define decision table S=(U, A, V, f) in, U is domain, U={ x₁, x₂..., x_k, A=C ∪ D, C are finger Mark attribute, D is decision attribute, U/C={ C₁, C₂..., C_m, U/D={ D₁, D₂..., D_n, I (D | C) represent decision attribute D phases For the conditional information entropy of Criterion Attribute C, a ∈ C, a (x)=U/ { a }, c ∈ C；

(5) by w (c) and Pair Analysis u_tkCombine, calculate each Pair Analysis for evaluating sample

$\overset{&OverBar;}{{u_{t}}^{'}} = u_{t} \times Σ_{k = 1}^{n} (w_{c} \times u_{t k})$

(6) willIn same, difference, each component of opposing be normalized the average Pair Analysis for obtaining various kinds sheetWith Greatest measure represent grade as the water quality sample nutrient laden grade.

Normalized process：

According to formula

Tried to achievea′+b′+c′+d′+ E '+f ' ≠ 1, need to be converted into according to arithmetic mean method Meet a+b+c+d+e+f =1.