CN109345066A - A kind of river isotope enrichment degree evaluation method based on Variable Fuzzy theory - Google Patents
A kind of river isotope enrichment degree evaluation method based on Variable Fuzzy theory Download PDFInfo
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 78
- 230000007547 defect Effects 0.000 claims abstract description 35
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Abstract
The present invention relates to a kind of river isotope enrichment degree evaluation methods based on Variable Fuzzy theory, it is the following steps are included: step 1, data acquisition, watershed carry out the acquisition of river water sample, be fitted into vial at once；Step 2, the introduction of variable fuzzy sets theory；Step 3, it determines variable fuzzy assessment model, and level evaluation is carried out to sample according to corresponding fuzzy evaluation model；The present invention is directed to the unicity and limitation of existing river water Oxygen and Hydrogen isotope enrichment degree method of discrimination, by introducing variable fuzzy assessment method, Conjoint Analysis is carried out to two kinds of hydrogen, oxygen isotopes, water body isotope sample index is determined to the relative defects and Relative Subordinate Function in criterion sections at different levels, to improve the confidence level evaluated river isotope enrichment intensity grade.
Description
Technical field
The invention patent belongs to river ecosystem protection technique field, and in particular to a kind of theoretical based on Variable Fuzzy
River isotope enrichment degree evaluation method.
Background technique
Because of the physics and chemical behavior difference of isotope caused by quality difference, referred to as " isotope effect ", and in the hydrology
Field, it will usually be related to hydrogen (1H、2H、3H, wherein2H also can be described as D) and oxygen (16O、17O、18O isotope) is referred to as
For water isotope, it is different from other isotopes soluble in water, the composition part of their inherently hydrones, thus in the hydrology
Have great importance in circulation and all kinds of hydrologic processes；Meanwhile the stable hydrogen and oxygen isotopes relationship of precipitation, it is isotope water
The core of literature has GLOBAL CHARACTERISTICS, and it is to study its correlation and causality that also generation area, the evolution point in place are different
Foundation；In practical applications, stable hydrogen and oxygen isotopes play more and more important role, institute in water circulating research field
With, the reasonable enrichment degree for determining Oxygen and Hydrogen isotope in river water, for seeking rainfall, runoff mutually convert process tool
It is significant.
Currently, stable hydrogen and oxygen isotopes relationship develops in water circulation and a point different process mainly relies on isotope in water body
The enrichment degree of enrichment degree and stable isotope in precipitation compares and association analysis, to carry out sentencing for water source evolution
Not, the method for use predominantly exists2H and18In O relational graph to water body sample point location, according to acquisition water body point according to2H and18O
The position of relation line qualitatively differentiates the enrichment degree of the Oxygen and Hydrogen isotope of water source and water body, lacks to two kinds of hydrogen, oxygen isotopes
Conjoint Analysis, and lack quantitative assessing index.
Summary of the invention
The purpose of the invention is to overcome the prior art, and provide a kind of for existing river water hydrogen, oxygen
The unicity and limitation of isotope enrichment degree method of discrimination, by introducing variable fuzzy assessment method, together to hydrogen, two kinds of oxygen
Position element carries out Conjoint Analysis, determines water body isotope sample index to the relative defects in criterion sections at different levels and opposite person in servitude
Membership fuction, so that the river based on Variable Fuzzy theory for improving the confidence level evaluated river isotope enrichment intensity grade is same
The plain enrichment degree evaluation method in position.
The object of the present invention is achieved like this: a kind of river isotope enrichment degree evaluation based on Variable Fuzzy theory
Method, this method reasonably determine out hydrogen in sampled water, oxygen heavy isotope enrichment degree by variation model and its parameter
Differentiate grade, improves the confidence level evaluated water body isotope enrichment intensity grade, specifically includes the following steps:
Step 1, data acquire
Watershed carry out the acquisition of river water sample, is fitted into vial at once, the bottle cap of vial be seal threaded cap, and with seal
Membrana oralis is sealed, to prevent isotope fractionation caused by evaporation；
Step 2, variable fuzzy sets theory
Variable Fuzzy theory and method are the further development of engineering fuzzy set theory and method, and opposite as its core is subordinate to
The concept of function, relative different function and Variable Fuzzy Set and definition be mathematical linguistics when describing things quantitative change, qualitative change and
Quantification tool provides new thinking for the necessity of engineering field variation model and model parameter and possibility, to increase evaluation
The confidence level and reliability of identification and decision；
Definition: domain is setOn a fuzzy concept, rightIn arbitrary element, in the continuum of Relative Subordinate Function
On number axis any point,Property is attracted to expressionRelative defects be, property is repelled to expressionOpposite person in servitude
Category degree isIf:
(1)
Referred to asIt is rightRelative difference；
Mapping
(2)
Referred to asIt is rightRelative different function；
According to
(3)
Then
(4)
Or
(5)
Definition: it enables
(6)
(7)
(8)
(9)
In formula:Referred to as Variable Fuzzy Set,、、It is referred to as Variable Fuzzy SetDomain of attraction, region of rejection and
Gradual change type qualitative change circle；
Definition: it setsIt isVariable factor collection, it may be assumed that
(10)
In formula:For variable model collection,For variable model parameter set,For in addition to model and its parameter can be changed other because
Subset；
It enables
(11)
(12)
It is collectively referred to as Variable Fuzzy SetAbout variable factor collectionVariable domain；
It enables
(13)
(14)
It is collectively referred to as Variable Fuzzy SetAbout variable factor collectionQuantitative change domain；
Relative different function model: it setsFor Variable Fuzzy Set on real axisDomain of attraction, i.e.,Section,For comprisingA certain Lower and upper bounds range domain section；
It is defined according to Variable Fuzzy SetWithThe region of rejection for being, i.e.,Section,
IfFor domain of attraction sectionInMidrange,ForThe magnitude of arbitrary point in section, thenIt falls intoRelative different function model when point left side can are as follows:
(15)
It falls intoWhen point right side, relative different function model can are as follows:
(16)
(17)
In formula (15) and formula (16)It is usually desirable for non-negative exponent, i.e. relative different function model is linear function,
Formula (15) and formula (16) meet: (1) whenWhen,；(2) whenWhen,；
WhenWhen,；Meet relative different function definition,After determination, according to formula (5)
Relative defects can be solved；
Step 3, variable fuzzy assessment model
Water body stable isotope enrichment degree work is identifiedA sample set:
(18)
TheThe characteristic of a sample is usedA index feature value indicates:
(19)
Then sample set is availableRank index feature value matrix indicates:
(20)
In formula:For sampleIndexCharacteristic value；Sample
Collect foundationA index is pressedThe criterion characteristic value of a rank is identified then haveRank criterion characteristic value square
Battle array:
(21)
In formula:For sampleIndexCharacteristic value,；
Water body isotope enrichment variable degrees set is determined referring to the actual conditions of criterion value matrix and area to be evaluated
Attract domain matrix and range domain matrix:
(22)
23)
It is divided into according to water body isotope enrichment degreeThe actual conditions of a rank determine domain of attractionInPoint valueMatrix:
(24)
According to formula (22) ~ formula (24) judgement sample characteristic value?Point left side or right side, accordingly select formula (15) ~
Formula (17) calculates diversity factor, then by formula (5) parameter pairThe relative defects of gradeMatrix:
(25)
According to fuzzy evaluation model
(26)
In formula:For non-normalized synthesis relative defects；For model optimization criteria parameter；For index weights；
For distinguishing indexes number；For distance parameter,For Hamming distances,For Euclidean distance；
Non-normalized synthesis relative defects matrix can be obtained by formula (26):
(27)
Formula (27) normalized is obtained into comprehensive relative defects matrix:
(28)
In formula:
(29)
Application level characteristic value
(30)
Level evaluation is carried out to sample.
In the step 1,WithValue is measured in ambient stable isotopic laboratory, and measurement result is with respective dimension
Also receive Copenhagen water standard thousand points of deviations indicate:
In formula:、Indicate the ratio of heavy isotope and light isotope,Refer to sample
Thousand point deviations of the Stable isotope ratio of certain element relative to the corresponding ratio of standard in product；It is worth smaller, shows light isotope
More it is enriched with.
Beneficial effects of the present invention: the present invention is by being applied to river water isotope enrichment for variable fuzzy assessment method
In degree evaluation, and the judgement rank of water body Oxygen and Hydrogen isotope enrichment degree in sample is reasonably determined out, solved existing
It needs individually to evaluate this limitation of Oxygen and Hydrogen isotope enrichment degree in river water isotope enrichment degree evaluation, by true
Determine river water sample index to the variation of the relative defects and Relative Subordinate Function and model in criterion sections at different levels and
Its parameter, it is final to determine river water isotope enrichment intensity grade.
Specific embodiment
Embodiment 1
A kind of river isotope enrichment degree evaluation method based on Variable Fuzzy theory, this method pass through variation model and its ginseng
Number reasonably determines out the differentiation grade of hydrogen in sampled water, oxygen heavy isotope enrichment degree, improves to water body isotope enrichment
The confidence level of intensity grade evaluation, specifically includes the following steps:
Step 1, data acquire
Watershed carry out the acquisition of river water sample, is fitted into vial at once, the bottle cap of vial be seal threaded cap, and with seal
Membrana oralis is sealed, to prevent isotope fractionation caused by evaporation；
Step 2, variable fuzzy sets theory
Variable Fuzzy theory and method are the further development of engineering fuzzy set theory and method, and opposite as its core is subordinate to
The concept of function, relative different function and Variable Fuzzy Set and definition be mathematical linguistics when describing things quantitative change, qualitative change and
Quantification tool provides new thinking for the necessity of engineering field variation model and model parameter and possibility, to increase evaluation
The confidence level and reliability of identification and decision；
Definition: domain is setOn a fuzzy concept, rightIn arbitrary element, in the continuum of Relative Subordinate Function
On number axis any point,Property is attracted to expressionRelative defects be, property is repelled to expressionOpposite person in servitude
Category degree isIf:
(1)
Referred to asIt is rightRelative difference；
Mapping
(2)
Referred to asIt is rightRelative different function；
According to
(3)
Then
(4)
Or
(5)
Definition: it enables
(6)
(7)
(8)
(9)
In formula:Referred to as Variable Fuzzy Set,、、It is referred to as Variable Fuzzy SetDomain of attraction, region of rejection and
Gradual change type qualitative change circle；
Definition: it setsIt isVariable factor collection, it may be assumed that
(10)
In formula:For variable model collection,For variable model parameter set,For in addition to model and its parameter can be changed other because
Subset；
It enables
(11)
(12)
It is collectively referred to as Variable Fuzzy SetAbout variable factor collectionVariable domain；
It enables
(13)
(14)
It is collectively referred to as Variable Fuzzy SetAbout variable factor collectionQuantitative change domain；
Relative different function model: it setsFor Variable Fuzzy Set on real axisDomain of attraction, i.e.,Section,For comprisingA certain Lower and upper bounds range domain section；
It is defined according to Variable Fuzzy SetWithThe region of rejection for being, i.e.,Section,
IfFor domain of attraction sectionInMidrange,ForThe magnitude of arbitrary point in section, thenIt falls intoRelative different function model when point left side can are as follows:
(15)
It falls intoWhen point right side, relative different function model can are as follows:
(16)
(17)
In formula (15) and formula (16)It is usually desirable for non-negative exponent, i.e. relative different function model is linear function,
Formula (15) and formula (16) meet: (1) whenWhen,；(2) whenWhen,；WhenWhen,；Meet relative different function definition,Determine with
Afterwards, relative defects can be solved according to formula (5)；
Step 3, variable fuzzy assessment model
Water body stable isotope enrichment degree work is identifiedA sample set:
(18)
TheThe characteristic of a sample is usedA index feature value indicates:
(19)
Then sample set is availableRank index feature value matrix indicates:
(20)
In formula:For sampleIndexCharacteristic value；Sample
Collect foundationA index is pressedThe criterion characteristic value of a rank is identified then haveRank criterion characteristic value square
Battle array:
(21)
In formula:For sampleIndexCharacteristic value,；
Water body isotope enrichment variable degrees set is determined referring to the actual conditions of criterion value matrix and area to be evaluated
Attract domain matrix and range domain matrix:
(22)
23)
It is divided into according to water body isotope enrichment degreeThe actual conditions of a rank determine domain of attractionInPoint valueMatrix:
(24)
According to formula (22) ~ formula (24) judgement sample characteristic value?Point left side or right side, accordingly select formula (15) ~
Formula (17) calculates diversity factor, then by formula (5) parameter pairThe relative defects of gradeMatrix:
(25)
According to fuzzy evaluation model
(26)
In formula:For non-normalized synthesis relative defects；For model optimization criteria parameter；For index weights；
For distinguishing indexes number；For distance parameter,For Hamming distances,For Euclidean distance；
Non-normalized synthesis relative defects matrix can be obtained by formula (26):
(27)
Formula (27) normalized is obtained into comprehensive relative defects matrix:
(28)
In formula:
(29)
Application level characteristic value
(30)
Level evaluation is carried out to sample.
For the unicity and limitation of existing river water Oxygen and Hydrogen isotope enrichment degree method of discrimination, in order to more
Good evaluation river water isotope enrichment degree, can be allowed to quantification, so as to more intuitively differentiate survey region water body
The whole enrichment degree of isotope, the present invention is by introducing variable fuzzy assessment method, to join to two kinds of hydrogen, oxygen isotopes
Analysis is closed, so as to science, reasonably determines river water isotope sample index being subordinate to relatively to criterion sections at different levels
Degree and Relative Subordinate Function, and sampled water Oxygen and Hydrogen isotope can be reasonably determined out by variation model and its parameter
The differentiation grade of enrichment degree, to improve the confidence level evaluated river isotope enrichment intensity grade.
Embodiment 2
A kind of river isotope enrichment degree evaluation method based on Variable Fuzzy theory, this method pass through variation model and its ginseng
Number reasonably determines out the differentiation grade of hydrogen in sampled water, oxygen heavy isotope enrichment degree, improves to water body isotope enrichment
The confidence level of intensity grade evaluation, specifically includes the following steps:
Step 1, data acquire
Watershed carry out the acquisition of river water sample, is fitted into vial at once, the bottle cap of vial be seal threaded cap, and with seal
Membrana oralis is sealed, to prevent isotope fractionation caused by evaporation；
Step 2, variable fuzzy sets theory
Variable Fuzzy theory and method are the further development of engineering fuzzy set theory and method, and opposite as its core is subordinate to
The concept of function, relative different function and Variable Fuzzy Set and definition be mathematical linguistics when describing things quantitative change, qualitative change and
Quantification tool provides new thinking for the necessity of engineering field variation model and model parameter and possibility, to increase evaluation
The confidence level and reliability of identification and decision；
Definition: domain is setOn a fuzzy concept, rightIn arbitrary element, in the continuum of Relative Subordinate Function
On number axis any point,Property is attracted to expressionRelative defects be, property is repelled to expressionOpposite person in servitude
Category degree isIf:
(1)
Referred to asIt is rightRelative difference；
Mapping
(2)
Referred to asIt is rightRelative different function；
According to
(3)
Then
(4)
Or
(5)
Definition: it enables
(6)
(7)
(8)
(9)
In formula:Referred to as Variable Fuzzy Set,、、It is referred to as Variable Fuzzy SetDomain of attraction, region of rejection and
Gradual change type qualitative change circle；
Definition: it setsIt isVariable factor collection, it may be assumed that
(10)
In formula:For variable model collection,For variable model parameter set,For in addition to model and its parameter can be changed other because
Subset；
It enables
(11)
(12)
It is collectively referred to as Variable Fuzzy SetAbout variable factor collectionVariable domain；
It enables
(13)
14)
It is collectively referred to as Variable Fuzzy SetAbout variable factor collectionQuantitative change domain；
Relative different function model: it setsFor Variable Fuzzy Set on real axisDomain of attraction, i.e.,Section,For comprisingA certain Lower and upper bounds range domain section；
It is defined according to Variable Fuzzy SetWithThe region of rejection for being, i.e.,Section,
IfFor domain of attraction sectionInMidrange,ForThe magnitude of arbitrary point in section, thenIt falls intoRelative different function model when point left side can are as follows:
(15)
It falls intoWhen point right side, relative different function model can are as follows:
(16)
(17)
In formula (15) and formula (16)It is usually desirable for non-negative exponent, i.e. relative different function model is linear function,
Formula (15) and formula (16) meet: (1) whenWhen,；(2) whenWhen,；WhenWhen,；Meet relative different function definition,Determine with
Afterwards, relative defects can be solved according to formula (5)；
Step 3, variable fuzzy assessment model
Water body stable isotope enrichment degree work is identifiedA sample set:
(18)
TheThe characteristic of a sample is usedA index feature value indicates:
(19)
Then sample set is availableRank index feature value matrix indicates:
(20)
In formula:For sampleIndexCharacteristic value；Sample
Collect foundationA index is pressedThe criterion characteristic value of a rank is identified then haveRank criterion characteristic value square
Battle array:
(21)
In formula:For sampleIndexCharacteristic value,；
Water body isotope enrichment variable degrees set is determined referring to the actual conditions of criterion value matrix and area to be evaluated
Attract domain matrix and range domain matrix:
(22)
23)
It is divided into according to water body isotope enrichment degreeThe actual conditions of a rank determine domain of attractionInPoint valueMatrix:
(24)
According to formula (22) ~ formula (24) judgement sample characteristic value?Point left side or right side, accordingly select formula (15) ~
Formula (17) calculates diversity factor, then by formula (5) parameter pairThe relative defects of gradeMatrix:
(25)
According to fuzzy evaluation model
(26)
In formula:For non-normalized synthesis relative defects；For model optimization criteria parameter；For index weights；
For distinguishing indexes number；For distance parameter,For Hamming distances,For Euclidean distance；
Non-normalized synthesis relative defects matrix can be obtained by formula (26):
(27)
Formula (27) normalized is obtained into comprehensive relative defects matrix:
(28)
In formula:
(29)
Application level characteristic value
(30)
Level evaluation is carried out to sample.
In the step 1,WithValue is measured in ambient stable isotopic laboratory, and measurement result is with respective dimension
Also receive Copenhagen water standard thousand points of deviations indicate:
In formula:、Indicate the ratio of heavy isotope and light isotope,Refer to sample
Thousand point deviations of the Stable isotope ratio of certain element relative to the corresponding ratio of standard in product；It is worth smaller, shows light isotope
More it is enriched with.
For the unicity and limitation of existing river water Oxygen and Hydrogen isotope enrichment degree method of discrimination, in order to more
Good evaluation river water isotope enrichment degree, can be allowed to quantification, so as to more intuitively differentiate survey region water body
The whole enrichment degree of isotope, the present invention is by introducing variable fuzzy assessment method, to join to two kinds of hydrogen, oxygen isotopes
Analysis is closed, so as to science, reasonably determines river water isotope sample index being subordinate to relatively to criterion sections at different levels
Degree and Relative Subordinate Function, and sampled water Oxygen and Hydrogen isotope can be reasonably determined out by variation model and its parameter
The differentiation grade of enrichment degree, to improve the confidence level evaluated river isotope enrichment intensity grade.
River water Oxygen and Hydrogen isotope enrichment degree is determined according to above step by taking Qinghai-Tibet Nagqu basin as an example
Amount evaluation:
According to Nagqu basin river water 18O、The status index feature value and criterion value matrix of D
Wherein,i=1,2 be index number；j=1,2 ... .10 is fragment number；H=1,2,3,4 are rank number；
Referring to criterion matrixYWater body stable isotope enrichment degree variable set is determined with the actual conditions in Nagqu basin
Attract (based on) domain matrix and range domain matrix and point valueM ih Matrix be respectively as follows:
According to matrixI ab 、I cd WithMJudgement sample characteristic valuex ij ?M ih The left side or right side of point, select formula (15) or formula accordingly
(16) diversity factor is calculated, then by formula (5) parameter pairhThe relative defects of grade, now flowed with Nagqu
Domain mainstream M2(j=4) river water isotope enrichment level index to 2 grades (h=2) relative defectsFor to this
Solution procedure is illustrated；
By matrixX?j=4 status index feature value vectorx 4=(-15.04,-115.43)T, then by attract (based on) domain matrixI ab , range domain matrixI cd And matrixM?h=2 attraction (based on) domain vector, range domain vector and point valueM i2 Vector is respectively as follows:
WheniWhen=1,x 14=-15.04, andc 12=-15.6,a 12=-14.6,b 12=-13.6,d 12=-12.6,M 12=-14.6, thus judge, this
Whenx 14?M 12Left side, andx 14∈, so selecting in formula (15),
Bringing β=1 and related data into above formula can obtain, reapply formula (5) and obtain=0.28, together
Li Ke getj=4,iThe relative defects vector of=1,2 pairs of 2 grades of water body isotope enrichment degree；
Similarly it can be obtainedj=1,2 ..., 10 pairs of ranksh=1,2,3,4 index relative defects matrix is respectively as follows:
2 by inspection are obtained according to certainty index importance sequence consistency theorem for the weight vector for determining 2 indexs
Item index importance sequence consistent guideline matrix are as follows:
By matrixFAbout the sequence of importance, field experience knowledge, indexx 1With indexx 2It compares, in " slightly " or " slightly
It is micro- " it is important between；
The non-normalized power of 2 evaluation indexes can be obtained using the relation table in pertinent literature between mood operator and relative defects
Vector are as follows:
The then normalization weight vector of index are as follows:
Nagqu basin, which is solved, using variable fuzzy assessment modular form (26) is respectively segmented being subordinate to relatively for water body isotope enrichment degree
Degree, now withjThe solution procedure is described for=4, is obtained by matrixj=4 index relative defects vector are as follows:
Take distance parameterp=1, model optimization criteria parameter α=2, when j=4, h=2, variable fuzzy assessment modular form:
Vector, substitution above formula are obtained, similarly, can be obtainedNagqu basin is segmented the same position of water body
The relative defects vector of plain enrichment degree:
It is rightIt carries out similar solution to calculate, obtains Nagqu basin segmentation water body isotope enrichment degree
Non-normalized relative defects matrix:
By matrixNormalization obtains relative defects matrix:
According to formula (30), the rank feature values vector that Nagqu basin is respectively segmented water body isotope enrichment degree is obtained:
Thus the evaluation result that Nagqu basin is respectively segmented water body isotope enrichment degree is obtained, as shown in the table:
| Evaluation region | Rank feature values | Opinion rating | Corresponding result |
| T-1 | 1.089 | 1 | Very dilution |
| M-1 | 1.03 | 1 | Very dilution |
| T-2 | 1.264 | 1 | Very dilution |
| T-3 | 1.005 | 1 | Very dilution |
| M-2 | 4 | 4 | Serious enrichment |
| T-4 | 2.624 | 2 | Compared with dilution |
| T-5 | 1.151 | 1 | Very dilution |
| M-3 | 3.248 | 3 | Compared with enrichment |
| T-6 | 1 | 1 | Very dilution |
| T-7 | 1.455 | 1 | Very dilution |
According to as a result, in 10 evaluation sections:
(1) 7 section is shown as isotope very dilution, shows that one's respective area water body has a large amount of precipitation recharges and snow melt supply, water
The serious dilution of heavy isotope in body；
(2) No. 4 tributaries Qushui River Mu Ge body shows as isotope compared with dilution, shows that this basin water body has a small amount of rainfall recharge, evaporation
Unobvious, water body heavy isotope dilution, rain or snowmelt import；
(3) mainstream downstream part is shown as isotope relatively enrichment, indicates that water body experience is evaporated to a certain degree, while having other water sources
Convergence；
(4) mainstream middle reaches are shown as isotope and are seriously enriched with, and indicate that this basin water body lives through explosive vaporization, water body is by fractionation
Water body is rich in heavy isotope.
Claims (2)
1. a kind of river isotope enrichment degree evaluation method based on Variable Fuzzy theory, it is characterised in that: this method passes through
Variation model and its parameter reasonably determine out the differentiation grade of hydrogen in sampled water, oxygen heavy isotope enrichment degree, raising pair
The confidence level of water body isotope enrichment intensity grade evaluation, specifically includes the following steps:
Step 1, data acquire
Watershed carry out the acquisition of river water sample, is fitted into vial at once, the bottle cap of vial be seal threaded cap, and with seal
Membrana oralis is sealed, to prevent isotope fractionation caused by evaporation；
Step 2, variable fuzzy sets theory
Variable Fuzzy theory and method are the further development of engineering fuzzy set theory and method, and opposite as its core is subordinate to
The concept of function, relative different function and Variable Fuzzy Set and definition be mathematical linguistics when describing things quantitative change, qualitative change and
Quantification tool provides new thinking for the necessity of engineering field variation model and model parameter and possibility, to increase evaluation
The confidence level and reliability of identification and decision；
Definition: domain is setOn a fuzzy concept, rightIn arbitrary element, in the continuum of Relative Subordinate Function
On number axis any point,Property is attracted to expressionRelative defects be, property is repelled to expressionOpposite person in servitude
Category degree isIf:
(1)
Referred to asIt is rightRelative difference；
Mapping
(2)
Referred to asIt is rightRelative different function；
According to
(3)
Then
(4)
Or
(5)
Definition: it enables
(6)
(7)
(8)
(9)
In formula:Referred to as Variable Fuzzy Set,、、It is referred to as Variable Fuzzy SetDomain of attraction, region of rejection and gradually
Variant qualitative change circle；
Definition: it setsIt isVariable factor collection, it may be assumed that
(10)
In formula:For variable model collection,For variable model parameter set,For in addition to model and its parameter can be changed other because
Subset；
It enables
(11)
12)
It is collectively referred to as Variable Fuzzy SetAbout variable factor collectionVariable domain；
It enables
(13)
(14)
It is collectively referred to as Variable Fuzzy SetAbout variable factor collectionQuantitative change domain；
Relative different function model: it setsFor Variable Fuzzy Set on real axisDomain of attraction, i.e.,Section,For comprisingA certain Lower and upper bounds range domain section；
According to Variable Fuzzy SetKnown to definitionWithIt isRegion of rejection, i.e.,
Section, ifFor domain of attraction sectionInMidrange,ForThe magnitude of arbitrary point in section, thenIt falls intoRelative different function model when point left side can are as follows:
(15)
It falls intoWhen point right side, relative different function model can are as follows:
(16)
(17)
In formula (15) and formula (16)It is usually desirable for non-negative exponent, i.e. relative different function model is linear function,
Formula (15) and formula (16) meet: (1) whenWhen,；(2) whenWhen,；
WhenWhen,；Meet relative different function definition,After determination, according to formula (5)
Relative defects can be solved；
Step 3, variable fuzzy assessment model
Water body stable isotope enrichment degree work is identifiedA sample set:
(18)
TheThe characteristic of a sample is usedA index feature value indicates:
(19)
Then sample set is availableRank index feature value matrix indicates:
(20)
In formula:For sampleIndexCharacteristic value；Sample
Collect foundationA index is pressedThe criterion characteristic value of a rank is identified then haveRank criterion characteristic value square
Battle array:
(21)
In formula:For sampleIndexCharacteristic value,；
Water body isotope enrichment variable degrees set is determined referring to the actual conditions of criterion value matrix and area to be evaluated
Attract domain matrix and range domain matrix:
(22)
23)
It is divided into according to water body isotope enrichment degreeThe actual conditions of a rank determine domain of attractionInPoint valueMatrix:
(24)
According to formula (22) ~ formula (24) judgement sample characteristic value?The left side or right side of point, select formula (15) ~ formula accordingly
(17) diversity factor is calculated, then by formula (5) parameter pairThe relative defects of gradeMatrix:
(25)
According to fuzzy evaluation model
(26)
In formula:For non-normalized synthesis relative defects；For model optimization criteria parameter；For index weights；
For distinguishing indexes number；For distance parameter,For Hamming distances,For Euclidean distance；
Non-normalized synthesis relative defects matrix can be obtained by formula (26):
(27)
Formula (27) normalized is obtained into comprehensive relative defects matrix:
(28)
In formula:
(29)
Application level characteristic value
(30)
Level evaluation is carried out to sample.
2. a kind of river isotope enrichment degree evaluation method based on Variable Fuzzy theory according to claim 1,
It is characterized in that: in the step 1,WithValue is measured in ambient stable isotopic laboratory, and measurement result is with corresponding
Thousand points of deviations of Vienna Copenhagen water standard indicate:
In formula:、Indicate the ratio of heavy isotope and light isotope,Refer to sample
Thousand point deviations of the Stable isotope ratio of certain element relative to the corresponding ratio of standard in product；It is worth smaller, shows light isotope
More it is enriched with.
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