CN108510060A - A kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network - Google Patents
A kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network Download PDFInfo
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Abstract
The invention discloses a kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network, the model structure include four layers of neural network：First layer is the input layer of sample data, and initial input variable is passed to next layer of neuron by this layer of neuron by activation primitive；The second layer is membership function layer, and for realizing concept obfuscation, causal uncertainty between solving concept is rationally discussed in combination with section type-2 fuzzy sets；Third layer is corresponding with the second layer, quantifies the causality between concept by the mutual function of definition and carries out defuzzification process；4th layer is sample data drop type output layer, is a determining monodrome and output by the interval value drop type obtained after defuzzification.The model combined during calculating membership function section type-2 fuzzy sets rationally opinion come the uncertainty of correlation between describing concept so that novel Fuzzy Cognitive Map model is more healthy and strong and accurate.
Description
Technical field
The present invention relates to fuzzy neural networks and Fuzzy Cognitive Map field, and in particular to a kind of based on fuzzy neural network
Two type Fuzzy Cognitive Map model of section.
Background technology
Cognitive Map (cognitive map, CM) is causal graph model, node between concept in expression and inference system
And side indicates the causality between concept and concept respectively.It was proposed that Kelly will in nineteen fifty-five by Tloman in 1948 first
It is introduced into causal qualitative analysis, and Axelord was applied particularly in 1976 in Political Analysis.Due to Cognitive Map
Model is only capable of indicating the relationship of the concepts increase and reduces by two kinds of qualitative states, not energetic causal variation degree, therefore
Kosko introduced fuzzy mearue in 1986 between concept in causality, three values { -1,0,1 } logical relation between concept is expanded
Exhibition is the fuzzy relation of section [- 1,1], proposes Fuzzy Cognitive graph model (fuzzy cognitive map, FCM), is used for concept
Between FUZZY RELATION OF CAUSE AND EFFECT expression and reasoning.Fuzzy logic obviously can carry more information, therefore the table of FCM than three-valued logic
It is the mainstream of current Cognitive Map research up to stronger with inferential capability.
Fuzzy Cognitive Map is by multiple concepts and represents the causal side between concept and forms, and wherein C is concept, it
Or event, target, emotion and the trend etc. of system, attribute, feature, quality and the state of reaction system.C has certain
State, state value is fuzzy value or two-value { 0, l }, with the ON/OFF shape for indicating degree existing for concept status or being in
State.Side ωij, it is reason concept CiTo result concept CjInfluence degree, be fuzzy value, can also degenerate for three values { -1,0,1 }
Logic.If ωij＞ 0, then it represents that CiVariation cause CjThe degree of equidirectional variation；If ωij＜ O, then it represents that CiVariation draw
Play CjThe degree of changing inversely；If ωij=0, then it represents that concept CiWith CjThere is no causalities.
FCM is easy in expression system fuzzy relation and Degree of interaction between object, has stronger processing structure
Change the ability of information, reasoning process can be realized by simple matrix operation, but since its flexibility is poor, more difficult expression
Object and its causal dynamic and uncertainty, therefore their predictive ability is limited.And neural network is with stronger
The ability for handling multidate information, be fused to contribute to from complicated uncertain or subjective knowledge to obtain in FCM it is useful
Information.Secondly as in view of causal uncertainty between concept, the Fuzzy Set Theory for introducing two type of section combines
Into neural network.
The so-called set A given on domain u during section type-2 fuzzy sets close refers toAll specify a function
μA(u) ∈ [0,1] is corresponding to it, it is called membership functions of the u to A.
Given domain X and its element x ∈ X, type-2 fuzzy sets closeBy membership functionIt is expressed as：
Wherein u is time variable, JxFor main degree of membership, it is that master variable x correspondences are subordinate to angle value, usually an interval value；Given master variable x=x0, x is in x0The degree of membership at place is time variable u, then using u as horizontal axis withFor
The section of the longitudinal axis is exactly secondary membership function, i.e.,：
Secondary membership function is exactly a type fuzzy set.And the domain J of secondary membership functionxIt is then main degree of membership
Function.
Type-2 fuzzy sets closeMain membership function be generally limited within a belt-like zone, this belt-like zone
It is referred to as type-2 fuzzy sets conjunctionUncertain region (footprint of uncertainty), be denoted as FOU (A).Two patterns are pasted
SetUpper limit membership function and lower limit membership function be uncertain region boundary two type membership functions,
Upper limit membership functionForMaximum membership degree union, lower limit membership functionμ(x) it is that its minimum is subordinate to
The union of degree.Therefore, section type-2 fuzzy sets conjunction can be expressed completely by the upper and lower bound of its membership function.
Since neural network has the ability of stronger processing multidate information, being fused in FCM contributes to from complexity
Useful information is obtained in uncertain or subjective knowledge.In FCM, when node state value changes, using nerve
Causality in neural network forecast FCM between each pair of node, and useless node and weight are eliminated by beta pruning, find iptimum relationship
Lu Jing.Four layers of neural network structure of construction are as follows：
First layer：Indicate input layer.This layer of neuron is by initial input variable x1,x2,…,xnIt is transmitted by activation primitive f
To next layer of neuron.The output of Hidden unit is：
In formula, wijIt is sigmoid functions for input layer i to the weights of output node layer j, f.
The second layer：Indicate membership function layer.Neuron input variable is mapped as Indistinct Input vector R={ μ by the layer1
(xi),μ2(xi),…,μR(xi) | 1≤i≤n } wherein μiIndicate the membership function used, generally Gaussian function.
Third layer：Indicate the rules layer and anti fuzzy method layer to fuzzy rule progress networking description.
Rule corresponding to i-th of neuron is：
Wherein, FijFor the output of second layer neuron, Y1For desired output.Second and third layer is responsible for each rule and is fitted
Response calculates.J-th of fuzzy rule RjOutput function be：
Wherein, X=(x1,x2,…xr)∈Rr；
Secondly it is anti fuzzy method layer, the activation primitive of this layer of neuron is to be compounded with fuzzy or operation membership function.
The number of nodes of this layer is identical with fuzzy rule number of nodes.J-th of anti fuzzy method node NjOutput variable be：
4th layer：Output layer.Each output variable by this layer node indicate, be all input variables superposition and：
Wherein, ωkIt is the connection weight of K rules in model.
Invention content
Two type of section based on fuzzy neural network that in view of the deficiencies of the prior art, it is an object of the present invention to provide a kind of
Fuzzy Cognitive graph model efficiently solves the causality uncertain problem between concept in Fuzzy Cognitive Map so that new
Type Fuzzy Cognitive Map model is more healthy and strong and accurate.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network, the model structure include four layers of nerve
Network：
First layer is the input layer of sample data, this layer of neuron passes to down initial input variable by activation primitive
One layer of neuron；
The second layer is that membership function layer is rationally discussed for realizing concept obfuscation in combination with section type-2 fuzzy sets
Solves causal uncertainty between concept；
Third layer is corresponding with the second layer, quantifies the causality between concept by the mutual function of definition and carries out solution mould
Gelatinization process；
4th layer is sample data drop type output layer, is a determination by the interval value drop type obtained after defuzzification
Monodrome and output.
Compared with prior art, the present invention having the following advantages that and advantageous effect：
It 1, can be by original Fuzzy Cognitive Map the present invention is based on two type Fuzzy Cognitive Map model of the section of fuzzy neural network
The problem of be dexterously transformed into fuzzy neural network, and rationally discuss in conjunction with section type-2 fuzzy sets so that model is with mould
It, can be well using the self-learning property of neural network come training parameter while pasting reasoning.Secondly as by two type of section
Fuzzy Set Theory is introduced into the blurring layer of neural network, efficiently solves the cause and effect in Fuzzy Cognitive Map between concept and closes
It is uncertain problem, in the model using fuzzy neural network, is described using mutual function (mutual subsethood)
Correlation between concept, and in the level of fuzzy neural network blurring, tied during calculating membership function
The Fuzzy Set Theory for having closed two type of section, the uncertainty for describing the correlation between concept so that novel fuzzy
It is more healthy and strong and accurate to recognize graph model.
2, the present invention is based on two type Fuzzy Cognitive Map model of the section of fuzzy neural network, increased using fuzzy neural network
Into learning ability so that FCM not only has inference mechanism, and includes the causality of membership function quantization, is established with this
FCM scale-model investigation systems, greatly reduce the intervention of domain expert, can realize the automatic structure according to data.
Description of the drawings
Fig. 1 is the structure chart of section two type Fuzzy Cognitive Map model of the embodiment of the present invention based on fuzzy neural network.
Fig. 2 is two pattern of section of section two type Fuzzy Cognitive Map model of the embodiment of the present invention based on fuzzy neural network
Paste collection membership function Gaussian Profile figure.
Fig. 3 is two pattern of section of section two type Fuzzy Cognitive Map model of the embodiment of the present invention based on fuzzy neural network
Paste membership function Uncertainty distribution figure.
Specific implementation mode
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Embodiment：
A kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network is present embodiments provided, the model
Structure chart is as shown in Figure 1, include four layers of neural network：
First layer is the input layer of sample data, and initial input variable is passed through activation primitive (i.e. Gauss by this layer of neuron
Function) pass to next layer of neuron；
The second layer is that membership function layer is rationally discussed for realizing concept obfuscation in combination with section type-2 fuzzy sets
Solve causal uncertainty between concept, the Gaussian Profile figure of section type-2 fuzzy sets membership function as shown in Fig. 2,
Uncertainty distribution figure is as shown in Figure 3；
Third layer is corresponding with the second layer, quantifies the causality between concept by the mutual function of definition and carries out solution mould
Gelatinization process；
4th layer is sample data drop type output layer, is a determination by the interval value drop type obtained after defuzzification
Monodrome and output.
In the present embodiment, it proposes to build model structure using four layers of neural network.In fuzzy neural network, input
It is expressed as fuzzy vector X with outputT=[x1,x2,…,xi,…xN] and YT=[y1,y2,…,yi,…yN], wherein N tables
Show input, output variable number.And in view of FCM definition, it is proposed that fuzzy neural network input, output become
Amount number and the number of concept node in Fuzzy Cognitive graph model are consistent.Secondly, input variable xiBy one group of semanteme collectionCharacterization, whereinIndicate semantic symbol (namely fuzzy set), such asEach it is expressed as input variable xiFuzzy set in domain.Similar, output variable yi
It is also divided into identical semantic collectionIt should be noted that input variable xi, output variable yiIt is needle
For same concept, therefore,Indicate identical semantic collection.
Specifically, each input node x of first layeriA concept C is indicated respectivelyi, this layer is by initial input variable XT
=[x1,x2,…,xi,…xN] next layer is passed to, wherein N indicates the number of variable, defines the input variable f of first layeri (1)、
Output variable xi (1)It is expressed as：
fi (1)=xi
xi (1)=fi (1)
Wherein, the subscript in formula indicates the number of plies of neural network.
Specifically, the semantic collection of the node on behalf input of the second layer, input variable xiN-thiThe member that a fuzzy semantics are concentrated
Element is expressed asWherein ni=1 ..., Ni, the node of this layer is divided into M groups, the former piece portion of one fuzzy rule of every group of expression
Point, the symmetrical two type membership function of section of each node on behalf one；According to the relationship of input variable and mean value, the node layer
Output using in the type-2 fuzzy sets of section do not know mark the upper bound and lower bound membership function be directly calculated, indicate such as
Under：
In formula,μ ijWithIt is lower bound and upper bound membership function respectively,It is membership function respectively with σ
Uncertain mean value and standard deviation, outputIt is input variable xi (1)Be subordinate to grade, it is by a lower limit and a upper limit
It determines.
Specifically, due to the input variable x in fuzzy neural networki, output variable yiIt is identical in corresponding Fuzzy Cognitive graph model
Concept Ci, then accordingly, output variable yiFuzzy semantics collectionWith input variable xiFuzzy semantics collectionIt is identical, and defined with symmetrical Gaussian function, mean value and variance are expressed as
Indicate uncertain due to introducing the fuzzy set of two type of section, corresponding mean value and variance all should be a moulds
Paste collection, is determined jointly by a upper and lower bound；
Node and result due to being concept node respectively the second layer and third layer of four layers of fuzzy neural network
Node, then concept node CiWith CjBetween causality, it will be able to be converted into second and third layer of correspondenceWith WithBetween weight W, wherein Indicate fuzzy semantics
CollectionWithSimilarity, in art of mathematics, the representation of concept similarity accumulated with Inner, mathematical definition
For：
Find out from above formula, ifWithFor the fuzzy semantics collection of two same concepts, i.e., as i=j,It is maximized 1, thenDefinition above apparent meets very much
Causality in FCM between concept, i.e.,：Since a concept cannot function as the causality condition of itself variation, he itself not
With causality, so the diagonal entry ω of weight matrix Wij=0；
The input variable and output variable of i-th node be respectivelyWithThen：
Specifically, each output variable in the 4th layerAll it is the semantic collection of outputBetween it is linear
Combination, the m of i-th of linguistic variableiThe weight of type isThis layer of input variable fj (4)And output variable
xj (4)For：
Causal performance indicator parameter is corresponding between output variable and node, DT(d1(τ),d2(τ),…,dN(τ))
For desired output, output variable Y is XT(x1(τ),x2(τ),…,xN(τ)) reality output, the study mould of fuzzy neural network
Type uses gradient descent algorithm, and when iterations are τ, defining mean square error function is：
Wherein, yj(τ) indicates j-th of element of output variable Y；Finally, feedback is gone to update by constantly algorithm iteration
μ and σ parameters in fuzzy neural network model continuously improve model so that being optimal state.
The above, patent preferred embodiment only of the present invention, but the protection domain of patent of the present invention is not limited to
This, any one skilled in the art is in the range disclosed in patent of the present invention, according to the skill of patent of the present invention
Art scheme and its patent of invention design are subject to equivalent substitution or change, belong to the protection domain of patent of the present invention.
Claims (5)
1. a kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network, which is characterized in that the model structure packet
Include four layers of neural network：
First layer is the input layer of sample data, and initial input variable is passed to next layer by this layer of neuron by activation primitive
Neuron；
The second layer is membership function layer, and for realizing concept obfuscation, in combination with section type-2 fuzzy sets, rationally opinion solves
Causal uncertainty between concept；
Third layer is corresponding with the second layer, quantifies the causality between concept by the mutual function of definition and carries out defuzzification
Process；
4th layer is sample data drop type output layer, is a determining list by the interval value drop type obtained after defuzzification
It is worth and exports.
2. a kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network according to claim 1, feature
It is, each input node x of first layeriA concept C is indicated respectivelyi, this layer is by initial input variable XT=[x1,
x2,…,xi,…xN] next layer is passed to, wherein N indicates the number of variable, defines the input variable f of first layeri (1), output become
Measure xi (1)It is expressed as：
fi (1)=xi
xi (1)=fi (1)
Wherein, the subscript in formula indicates the number of plies of neural network.
3. a kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network according to claim 1, feature
It is, the semantic collection of the node on behalf input of the second layer, input variable xiN-thiThe element representation that a fuzzy semantics are concentrated isWherein ni=1 ..., Ni, the node of this layer is divided into M groups, the former piece part of one fuzzy rule of every group of expression, Mei Gejie
Point represents a symmetrical two type membership function of section；According to the relationship of input variable and mean value, the output profit of the node layer
It is directly calculated, is indicated as follows with the upper bound of uncertain mark and lower bound membership function in the type-2 fuzzy sets of section：
In formula,μ ijWithIt is lower bound and upper bound membership function respectively,It is the uncertain of membership function respectively with σ
Mean value and standard deviation, outputIt is input variable xi (1)Be subordinate to grade, it is determined by a lower limit and a upper limit.
4. a kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network according to claim 1, feature exist
In due to the input variable x in fuzzy neural networki, output variable yiIdentical concept C in corresponding Fuzzy Cognitive graph modeli, that
Accordingly, output variable yiFuzzy semantics collectionWith input variable xiFuzzy semantics collectionPhase
Together, and with symmetrical Gaussian function it defines, mean value and variance are expressed asAll it is mould
Paste collection, is determined jointly by a upper and lower bound；
Node and result node due to being concept node respectively the second layer and third layer of four layers of fuzzy neural network, that
Concept node CiWith CjBetween causality, it will be able to be converted into second and third layer of correspondenceWith With
Between weight W, wherein Indicate fuzzy semantics collection
WithSimilarity, in art of mathematics, the representation of concept similarity accumulated with Inner, mathematical definition is：
Find out from above formula, ifWithFor the fuzzy semantics collection of two same concepts, i.e., as i=j,
It is maximized 1, thenThe diagonal entry ω of weight matrix Wij=0；
The input variable and output variable of i-th node be respectivelyWithThen：
5. a kind of two type Fuzzy Cognitive Map model of section based on fuzzy neural network according to claim 1, feature
It is, each output variable in the 4th layerAll it is the semantic collection of outputBetween linear combination, i-th
The m of linguistic variableiThe weight of type isThis layer of input variableAnd output variableFor：
Causal performance indicator parameter is corresponding between output variable and node, DT(d1(τ),d2(τ),…,dN(τ)) it is it is expected
Output, output variable Y are XT(x1(τ),x2(τ),…,xN(τ)) reality output, the learning model of fuzzy neural network uses
Gradient descent algorithm, when iterations are τ, defining mean square error function is：
Wherein, yj(τ) indicates j-th of element of output variable Y；Finally, the fuzzy god of feedback update is gone by constantly algorithm iteration
Through μ the and σ parameters in network model, model is continuously improved so that being optimal state.
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| CN109492760A (en) * | 2018-12-21 | 2019-03-19 | 北京航空航天大学 | Interpretable prediction technique based on Depth Blur cognition graph model |
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| CN109492760A (en) * | 2018-12-21 | 2019-03-19 | 北京航空航天大学 | Interpretable prediction technique based on Depth Blur cognition graph model |
| EP3903245A4 (en) * | 2018-12-28 | 2023-01-11 | Meraglim Holdings | Method and system for predictive analytics through the use of fuzzy cognitive maps in a computing with words architecture |
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| CN112987741A (en) * | 2021-02-24 | 2021-06-18 | 武汉理工大学 | Uncertain interference-oriented ship course intelligent control method |
| CN113746663A (en) * | 2021-06-07 | 2021-12-03 | 西安交通大学 | Performance degradation fault root cause positioning method combining mechanism data and dual drives |
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| CN115754008A (en) * | 2022-09-28 | 2023-03-07 | 哈尔滨工业大学（威海） | Combined monitoring method and system for structural damage, computer equipment and storage medium |
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Application publication date: 20180907 |