模糊聯(lián)想記憶FUZZYASSOCIATIVEMEMMORIESⅡ

1、模糊聯(lián)想記憶FUZZY ASSOCIATIVE MEMMORIESPresented by Yang BaishengE.E. Dept.Xidian UniversityOUTLINEwFuzzy Hebb FAMs（續(xù)） 6.Binary Input-Output FAMs 7. Multiantecedent FAM Rules 8. Adaptive Decompositional InferencewAdaptive FAMs (Product-Space Clustering in FAM Cells) 1.Adaptive FAM-Rule Generation 2.Adapti

2、ve BIOFAM Clustering 3.Adaptive BIOFAM Example: Inverted PendulumBinary Input-Output FAMsBIOFAMs map system-variable to control, classification, or other output data.For example: A BIOFAM maps traffic densities to screen (and red) light durations. In inverted-pendulum example, the system maps the sy

3、stem-variable ( ) to control data ( ).dvvd,fMultiantecedent FAM Rules (多前提FAM規(guī)則)1.Consider the FAM rule: “IF X is A, THEN C is Z,” or for short. 2.The rule is “IF X is A AND Y is B, THEN C is Z,” or for short.CTAACM);,(CBA),( CAWhat to do?Multiantecedent FAM Rules (多條件FAM規(guī)則)2 Single-antecedent FAMs:

4、Multiantecedent FAM Rules:),(BCACMBMABAFACMAACCBCACCBCMBBCCTBBCM),( CB),( CACTAACM);,(CBADefuzzify it to yield the exact output.Multiantecedent FAM Rules Suppose we present the exact inputs , to the single-FAM-rule system that stores(A,B;C).We present the unit bit vectors and to as nonfuzzy set inpu

5、ts.Thenix),(),(jYiXjiIIFyxFBCjYACiXMIMICbCajiCbaji),min(jyFiXIjYIFProperty of Hebb MatrixMultiantecedent FAM RuleswRepresenting with its membership function wFor all in :z)(),min(zmbaCjiZCmCBIOFAM prescriptionMultiantecedent FAM RulesAlso, We can get the FAM rules:),;,(DCBA),(CBICAIyxFTjYTiXjiCbCaji

6、Cbaji),min()(),min(zmbaCjiIF we encode : and with correlation-product encoding, decompositional inference gives the BIOFAM version of correlation-product inference:),(CA),( CBCorrelation-Product EncodingAdaptive Decompositional InferencewLet define an arbitrary neural-network system that maps fuzzy

7、subset of to fuzzy subsets of . can define a different neural-network. qnXIIN:)()(),(BNANBAFYXBACCCqpYIIN:AXCZThe neural-network change with time.Adaptive FAMs(Product-Space Clustering in FAM Cells)wAdaptive FAM-Rule GenerationwAdaptive BIOFAM ClusteringwAdaptive BIOFAM Example: Inverted PendulumAda

8、ptive FAM-Rule GenerationLet denote quantization vectors in the input-output product space .We count the number of quantizing vectors in each FAM cell . ijkkkijij1521kkkijFkmm,1kpnII Adaptive BIOFAM Clustering Through neural-network learning algorithm, learn to distribute input-output data in the in

9、put-output product space. Data clusters reflect FAM rules, such as the steady-state FAM rule ”IF is ZE AND is ZE, THEN is ZE.”f確定狀態(tài)變量（條件變量）和控制變量 （結(jié)論變量）收集相應(yīng) 的 訓(xùn)練樣本(大量的有代表性的)根據(jù)訓(xùn)練樣本的分布區(qū)間，劃分為相應(yīng)的模糊數(shù)，并賦于模糊語言量。自適應(yīng)DCLAVQ對樣本聚類。統(tǒng)計(jì)落在每 個(gè)可能單元中的突觸矢量個(gè)數(shù)，計(jì)算每個(gè)規(guī)則的權(quán)值據(jù)區(qū)間劃分進(jìn)行規(guī)則合并 產(chǎn)生規(guī)則庫，建立FAM系統(tǒng)BIOFAM聚類提取規(guī)則的過程Inverted Pend

10、ulum1、確定狀態(tài)變量和控制變量 狀態(tài)變量：擺線與垂直方向的 夾角 擺線的運(yùn)動角速度 控制變量：馬達(dá)作用于擺線的力 2、訓(xùn)練樣本 在這里我是利用MATLAB工具包里的倒立擺模型生成了 1000個(gè)倒立擺軌跡樣本作為訓(xùn)練樣本。45,45s150,150fMembership Function-40-200204000.20.40.60.81-150 -100 -50050100 15000.20.40.60.81-10-5051000.20.40.60.81fFAM Bank & Synaptic Histogram02040600100200300400FAM Rules00),(),

11、(),();,(iBCACBCACaAMBMABAFMCBMCAMCBAmnnnmiiimmACcacacacacacacacacacacacaCAM21212221212111FAM Rulesw去模糊 按照質(zhì)心法解模糊得馬達(dá)作用力為-2.18。（20，-30）PS，NS ZEPS，ZE NS（0.83，0.31）（0.83，0.22） 0.31)(FmFZE)(FmFNS 0.22CbaCbCaBAFjiji),min(),(仿真演示系統(tǒng)小車軌跡scopeFAM RulesFAM RulesREFERENCEw基于FAM模糊控制器的研究中南大學(xué) 蔡自興，文敦偉 2003.08w單級倒立擺的模糊控制及仿真山東師范大學(xué) 趙 莉 2004.09w二級倒