Adaptive Group Organization Cooperative Evolutionary Algorithm for TSK-type Neural Fuzzy Networks Design

Transcription

1 Adaptve Group Organzaton Cooperatve Evolutonary Algorthm for TSK-type Neural Fuzzy Networs Desgn Sheng-Fuu Ln * and Jyun-We Chang Department of Electrcal Engneerng Natonal Chao Tung Unversty Hsnchu, Tawan Abstract Ths paper proposes a novel adaptve group organzaton cooperatve evolutonary algorthm (AGOCEA) for TSK-type neural fuzzy networs desgn. The proposed AGOCEA uses group-based cooperatve evolutonary algorthm and selforganzng technque to automatcally desgn neural fuzzy networs. The group-based evolutonary dvded populatons to several groups and each group can evolve tself. In the proposed self-organzng technque, t can automatcally determne the parameters of the neural fuzzy networs, and therefore some crtcal parameters have no need to be assgned n advance. The smulaton results are shown the better performance of the proposed algorthm than the other learnng algorthms. Keywords TSK-type Neural Fuzzy Networs; Evolutonary Algorthm; Group based Symbotc; Self Organzaton; System Identfcaton I. INTRODUCTION In the feld of artfcal ntellgence, neural fuzzy networ [1-3] refers to combnatons of neural networs and fuzzy logc. Because the advantages of neural fuzzy networs are powerful computaton ablty and human-le reasonng ablty from neural networs and fuzzy systems, respectvely, t has good performance for solvng complex nonlnear problems. The neural fuzzy networs can perform the nonlnear mappng once the system parameters are traned based on a sequence of nput and desred response pars, and t does not requre mathematcal descrptons of system. Therefore, the determnaton of parameters s a crtcal ssue for neural fuzzy networs. The bacpropagaton (BP) [4, 5] s a common method and wdely used for tranng neural fuzzy networs. It s well nown that BP s an approxmate steepest descent algorthm. The steepest descent algorthm s the smplest, and the mnmzaton method. The advantage of steepest decent algorthm s very smple, requrng calculaton only of the gradent, the dsadvantage of steepest descent algorthm s that tranng tme s generally longer than other algorthms; based on ntal weght values, t s often to fnd the local optmal soluton but not global optmal soluton. Besdes, BP tranng performance depends on the ntal values of the system parameters, and for dfferent networ topologes one has to derve new mathematcal expressons for each networ layer. Consderng the aforementoned dsadvantages one may be faced wth suboptmal performance even for a sutable neural fuzzy networ topology. Hence, the capablty of tranng parameters and fndng the global soluton whle optmzng the overall structure are mportant. The evolutonary methods usng for tranng the fuzzy model has become a popular research feld [6-0] because evolutonary methods smultaneously evaluate many ponts n the search space and are more lely to converge toward the global soluton. The evolutonary fuzzy model s a learnng process to generate a fuzzy model automatcally by ncorporatng evolutonary learnng procedures. Recently, several mproved evolutonary algorthms have been proposed [16-].In [16], Bandyopadhyay et al. used the varable-length genetc algorthm (VGA) that allows the dfferenta of lengths of chromosomes n a populaton. Carse et. al. [17] used the genetc algorthm to evolve fuzzy rule based controllers. In [18], Chen proposed an effcent mmune symbotc evoluton learnng algorthm for compensatory neuro-fuzzy controller. In [19], Ln presented a novel selfconstructng evolutonary algorthm to desgn a TSK-type fuzzy model. In [0], the group-based symbotc evoluton (GSE) was proposed to solve the ssue of the tradtonal genetc algorthm that all the fuzzy rules were encoded nto one chromosome. In [1], Ln proposed a hybrd evolutonary learnng algorthm to combne the compact genetc algorthm and the modfed varable-length genetc algorthm to perform structure/parameter learnng to construct a networ dynamcally. Hsu [] proposed a mult-groups cooperatonbased symbotc evoluton (MGCSE) to tran a TSK-type neural fuzzy networ (TNFN). Ther results showed that MGCSE can obtan better performance and convergence than symbotc evoluton. Although MGCSE beng a good approach for tranng a TNFN, there s no systematc way to determne sutable groups for selectng chromosomes. Although the above evoluton learnng algorthms [16-] can mprove the tradtonal genetc algorthms, these algorthms may encounter one or more of the followng ssues: 1) all fuzzy rules represent one chromosome; ) the random group selecton of fuzzy rules; 3) the numbers of fuzzy rules and group numbers have to be assgned n advance. Recently, the data mnng approach has been wdespread used n several felds [3-30]. The data mnng can be regarded as a new way of data analyss. One goal of data mnng s to fnd assocaton rules among frequent tem sets n transactons. In [3], the authors proposed a mnng method of ascertan *Correspondng author: Sheng-Fuu Ln, Tel.: ext P a g e

2 large tem sets to fnd assocaton rules n transactons. Han et al. [4] proposed the frequent pattern growth (FP-Growth) to mne frequent patterns wthout canddate generaton. Wu et al. [30] proposed a data mnng method based on the genetc algorthm that effcently mprove the Tradtonal genetc algorthm by usng analyss support and confdence parameters. In order to solve aforementoned problems, ths paper proposes an adaptve group organzaton cooperatve evolutonary algorthm (AGOCEA) for desgnng a TSK-type neural fuzzy networ. The AGOCEA adopts the group symbotc evoluton (GSE). Each populaton n the GSE s dvded to several groups and each group represents a set of the chromosome that belongs to one sngle fuzzy rule. To solve the problem of random group selecton, a data mnng based group selecton method was used to select the better groups. The adaptve group organzaton was used to solve the some parameters have to be assgned n advance. Ths paper s organzed as follows. In the Secton II, a bref descrpton of TSK-type neural fuzzy networ s ntroduced. The proposed AGOCEA s descrbed n the Secton III. In the Secton IV, the smulaton results are presented. The conclusons are summarzed n the Secton V. II. THE CONCEPT OF THE TSK-TYPE NEURAL FUZZY NETWORKS A Taag-Sugeno-Kang (TSK) type neural fuzzy networ (TNFN) [1] employs dfferent mplcaton and aggregaton methods from the standard Mamdan fuzzy model[3]. Instead of usng fuzzy sets the concluson part of a rule, s a lnear combnaton of the crsp nputs. The fuzzy rule of TSK-type neural fuzzy networ s shown as followng equaton: IF x 1 s A 1 (m 1, 1 ) and x s A (m, ) and and x n s A n (m n, n ) THEN y=w 0 +w 1 x 1 + +w n x n. (1) where n s the number of the nput dmensons and s the number of the fuzzy rules. The structure of the TSK-type neural fuzzy networ s shown n Fg. 1. It s a fve-layer networ structure. The functons of the nodes n each layer are descrbed as follows: Layer 1 (Input Node): No functon s performed n ths layer. The node only transmts nput values to layer. That s u (1) x. () where m and σ are, respectvely, the center and the wdth of the Gaussan membershp functon of the th term of the th nput varable x. Layer 3 (Rule Node): The output of each node n ths layer s determned by the fuzzy AND operaton. Here, the product operaton s utlzed to determne the frng strength of each rule. The functon of each rule s u u exp (3) () u (1) m. (4) Layer 4 (Consequent Node): Nodes n ths layer are called consequent nodes. The nput to a node n layer 4 s the output delvered from layer 3, and the other nputs are the nput varables from layer 1 as depcted n Fg. 1. n (4) (3) u u ( w0 w x ) 1, (5) where the summaton s over all the nputs and where w are the correspondng parameters of the consequent part. Layer 5 (Output Node): Each node n ths layer corresponds to one output varable. The node ntegrates all the actons recommended by layers 3 and 4 and acts as a defuzzfer wth (5) M M M (4) (3) u u w0 w x M M (3) (3) u u 1 1 y u ( ) where M s the number of fuzzy rule., (6) Layer (Membershp Functon Node): Nodes n ths layer correspond to one lngustc label of the nput varables n layer 1; that s, the membershp value specfyng the degree to whch an nput value belongs to a fuzzy set s calculated n ths layer. For an external nput x, the followng Gaussan membershp functon s used: u () (1) u m exp, (3) Fg. 1. Structure of TSK-type neural fuzzy networ. P a g e

3 III. ADAPTIVE GROUP ORGANIZATION COOPERATIVE EVOLUTIONARY ALGORITHM The flowchart of the proposed adaptve group organzaton cooperatve evolutonary algorthm (AGOCEA) s shown n Fg.. The structure of chromosomes to construct a TNFN s shown n Fg. 3. The codng structure of chromosomes s shown n Fg. 4. The followng formulatons show how to generate the ntal chromosomes n each group: Devaton: Chr g, c [p]=random[, ] (7) mn where p=, 4,, n; g=1,,, M ; c=1,,, N C, Mean: Chr g, c [p]= random[ m, m ] (8) where p=1, 3,, n-1; mn Weght: Chr g, c [p]= random [ w, w ] (9) mn where p=n+1, n+,, n+(n+1), Fg.. The flowchart of the AGOCEA. Fg. 3. The structure of the chromosome n the AGOCEA. Fg. 4. The structure of the chromosome n the AGOCEA. The learnng process of the AGOCEA nvolves ten operators: ntalzaton, two phase self organzaton, data mnng based group selecton, ftness assgnment, reproducton, crossover, mutaton, calculaton of group smlarty, splttng process, and lumpng process. The whole learnng process s descrbed step-by-step as follows: A. Intalzaton Before the AGOCEA s desgned, ndvduals formng several ntal groups should be generated. The ntal groups of the AGOCEA are generated randomly wthn a fxed range. where Chr g, c represents cth chromosome n gth group; M represents rules that used to form a TNFN and N C s the total number of chromosomes n each group; p represents the pth gene n a Chr g, c ; and,, m, m, and mn wmn, w represent the range that are predefned to generate the chromosomes. B. Two phase self organzaton (TPSO) After every group s ntalzed, the AGOCEA adopts pervous research whch was TPSO [9, 31] to decde the sutable selecton tmes of each number of rules (n ths paper the number of rules le between [M, M mn ]); that s, t determnes the selecton tmes of M groups whch form a TNFN wth rules. After the TPSO, the selecton tmes of the sutable number of rules n a TNFN wll ncrease, and the selecton tmes of the unsutable number of rules wll decrease. The detals of the TPSO are lsted as follows: Step 0. mn Intalze the probablty vectors: V 0.5, where M M, M,, M M mn mn 1 (11) Accumulator = 0 (1) Step 1. Update the probablty vectors accordng to the followng equatons: V V ( Upt _ value * ), f Avg ft VM V ( _ * ), otherwse M Upt value M ) M M M M (13 M M / ( mn 1) (14 M Mmn Avg ft M M ) M Upt _ value ft ft (15 ) M M M M Mmn f FtnessM ( Best _ Ftness ) M ThresholdFtnessvalue (16) then ft ft Ftness M M M 3 P a g e

4 where V M s the probablty vector, s a predefne threshold value, Avg represents the average ftness value n the whole populaton, Best _ Ftness represents the best ftness value wth M rules, ft M s the sum of ftness value of TNFN wth M rules, Ftness M s the ftness value wth M rules, ThresholdFtnessvalue s a predefned threshold value. Step. Determne the selecton tmes accordng to the probablty vectors as follows: R ( Selecton _ Tmes)*( V / Total _ Velocy ), (17) pm V M Vmn M Total _ Velocy V, (18) M where Selecton_Tmes represents total selecton tmes n each generaton, Total_Velocy s summaton of the probablty vectors V M, Rp s the selecton tmes of M M groups that use to select chromosomes for constructng a TNFN. Step 3. After step, the selecton tmes of every numbers of rules n a TNFN are obtaned. Then the R tmes are used to select chromosomes form M groups to construct a TNFN. Step 4. In the proposed TPSO, for avodng sutable M groups may fall n the local optma soluton, the TPSO proposed two dfferent actons to update the V. Decde the deferent acton accordng to the followng equatons: If Accumulator TPSOTmes (19) Then do Step1, Step, and Step 3, If Best_Ftness g = Best_Ftness (0) Then Accumulator = Accumulator + 1, If Accumulator > TPSOTmes (1) Then do Step 0 and Accumulator = 0, where TPSOTmes s a predefned value; Best_Ftness g represents the best ftness value of the best combnaton of chromosomes n gth generaton; Best_Ftness represents the best ftness value of the best combnaton of chromosomes n current generatons. Eqs. (19)-(1) represents that f the ftness s not changed for a suffcent number of generatons, the sutable M groups may fall n the local optma soluton. C. Data mnng based group selecton (DMGS) After the TPSO step, the selecton tmes of each rule number n a TNFN s decded. The AGOCEA then performs selecton step. The selecton step n the AGOCEA can be dvded by selecton of groups and chromosomes. In the selecton of groups, ths paper uses the DMGS to mprove the random selecton. In the DMGS, the groups are selected accordng to the frequent patterns found by FP-Growth. In the proposed DMGS, the FP-Growth fnds the frequent groups from a transacton (n ths paper a transacton means a set of the M group ndexes that perform well). After the frequent group ndexes have been found, the DMGS selects the M groups M M pm ndexes accordng to the frequent group ndexes. To avod the frequently-occurrng groups from fallng n the local optmal soluton, the DMGS uses three actons to select M groups. The three actons defned n ths paper are normal, search, and explore. The detal of the DMGS s shown as follows: f Step 0. The transactons are buldng as follow equaton: Ftness Best _ Ftness ThresholdFtnessvalue M M then Transacton [ ] TNFNRuleSet [ ] where 1,,, M 1,,, TransactonNum M () where the Ftness M represents the ftness value of TNFN wth M rules, TransactonNum s the total number of transactons Transacton [] represents the th tem n the th transacton, TNFNRuleSet [] represents th group ndex n M M group ndexes that are selected to form a TNFN wth M rules. For example, as shown n Table I, the frst transacton of the transacton set means the 3 rules TNFN that select from 1st group, 4th group, and 8th group has a well performance. TABLE I. TRANSACTIONS IN A FP-GROWTH. Transacton ndex Group ndexes 1 1, 4, 8, 4, 7, 10 TransactonNum 1, 3, 4, 6, 8, 9 Step 1. Normal acton: After buldng up the transactons, the DMGS selects group accordng to dfferent acton types. If the acton type s normal acton, the DMGS selects the group as followng equaton: f Accumulator NormalTmes then GroupIndex[ ] Random[1, P ] where 1,,, M ; M M, M,, M, sze mn mn1 (3) where Accumulator s defned n Eq. (0); GroupIndex[] represents selected th group ndex of the M group ndexes and P sze represents there are P sze groups n a populaton n the AGOCEA. Step. Fnd the frequent groups: If the acton s searchng or explorng acton, the DMGS uses the FP-Growth [4] to fnd frequent group ndexes n transactons. The frequent group ndexes are found accordng to the predefned Mnmum_Support. The Mnmum_Support means the mnmum fracton of transactons that contan an tem set. The FP-Growth algorthm can be vewed as two parts: constructon of the FP-tree and FP-growth. The sample transactons shown n Table II are taen as examples. Mnmum_Support = 3 s consdered n ths example. Frequent group ndexes generated by FP-growth shown n Table III are then thrown nto the pool that s named FrequentPool. 4 P a g e

5 TABLE II. SAMPLE TRANSACTIONS. Transacton ndex Group ndexes 1 {b, c, e, f, g, h, p} {a, b, c, f,, m, o} 3 {c, f,, m, o} 4 {b, c, e, s, p} 5 {a, b, c, d, f, m, o} f SearchngTmes Accumulator ExplorngTmes then GroupIndex[ ] w, where w Random[1, P ] and wfrequentitemset[ ]; sze FrequentItemSet[ ] Random[ FrequentPool]; (5) TABLE III. FREQUENT GROUP INDEXES GENERATED BY FP-GROWTH WITH MINIMUM_SUPPORT = 3. Suffx Cond. group Cond. Frequent group ndexes group base FP-tree B c:4 c:4 cb:4 F cb:3, c:1 c:4, cb:3 cf:4, bf:3, cbf:3 M cbf:, cf:1 cf:3 cm:3, fm:3, cfm:3 O cbfm:, cfm:1 cfm:3 co:3, fo:3, mo:3, cfo:3, cmo:3, fmo:3, cfmo:3 Step 3. Select the group ndexes accordng to dfferent actons: After obtanng the frequent tem sets, the DMGS selected group ndexes accordng to dfferent actons that descrbe as follows: In the searchng acton, the group ndexes are selected from the frequent tem as follow equatons: f then GroupIndex[ ] w, where NormalTmes Accumulator SearchngTmes w Random[1, P ] and wfrequentitemset[ q]; sze (4) 1,,, M ; M M, M,, M, mn mn 1 where ExplorngTmes s a predefned value that udge to perform explorng acton. Step 4. After selectng M group ndexes, the chromosomes are selected from M group as follows: ChromosomeIndex[ ] q, where q Random[1, N ] 1,,, c (6) where N c represents the number of chromosomes n each group; ChromosomeIndex[] represents the ndex of a chromosome that select from th group. The llustraton of the DMGS s shown n Fg. 5 wth smple descrptons as follows: suppose the TPSO determnes that 4 rules are expected, and 3 out of 7 groups, group, 3 and 6, are deemed as frequent groups. If the current acton type of the DMGS s normal acton, then 4 random groups wll be selected to form a TFS. If the search acton s taen, then frequent group, 3 and 6 wll be selected. The remanng one group wll be draw randomly from group 1, 4, 5 and 7. If the explore acton s taen, then the 4 non-frequent group 1, 4, 5 and 7 wll be selected n case of the problem of local optmum. FrequentItemSet[ q] Random[ FrequentPool]; q 1,,, FrequentPoolNum; 1,,, M ; M M, M,, M, ax mn mn 1 m where SearchngTmes s a predefned value that udge to perform searchng acton; FrequentPool represents the sets of frequent tem set that obtan from FP-Growth; FrequentPoolNum presents the total number of sets n FrequentPool and FrequentItemSet[] presents a frequent tem set that select from FrequentPool randomly. In Eq. (4), f M greater than the sze of FrequentItemSet[], the remanng groups are selected by Eq. (3). In the explorng acton, the group ndexes are selected accordng to the frequent tem as follow equatons: Fg. 5. The example of the DMGS. D. Ftness assgnment The ftness value of a rule (an ndvdual) s calculated by concatenatng ths ndvdual wth eltes of other groups selected by DMGS. The detals for assgnng the ftness value are descrbed as follows: Denote G 1, G,, G M, the M groups selected by the DMGS; G.p denotes the th ndvdual of the th group; y refers to the elte ndvdual of the th group. Then the ftness of the ndvdual G.p can be computed as follows: ftness( G p ) ftness( G y,, G p, G y,, G y ) (7) M M 5 P a g e

6 E. Reproducton To perform reproducton, elte-based reproducton strategy (ERS) [] s adopted n ths study. In ERS, every chromosome n the best combnaton of M groups must be ept by performng reproducton step. In the remanng chromosomes n each group, the roulette-wheel selecton method [3] s adopted for proceedng wth the reproducton process. Then the well-performed chromosomes n the top half of each group [14] proceed to the next generaton. The other half s generated by performng crossover and mutaton operatons on chromosomes n the top half of the parent ndvduals. F. Crossover In ths step, a two-pont crossover strategy [3] s adopted. Once the crossover ponts are selected, exchangng the ste s values between the selected stes of ndvdual parents can create new ndvduals. These ndvduals are offsprng whch nherent the parents merts. G. Mutaton The utlty of the mutaton step can provde some new nformaton to every group at the ste of an ndvdual by randomly alterng the allele of a gene. Thus mutaton can lead to search new space whch can avod fallng nto the local mnmal soluton. In the mutaton step, unform mutaton [33] s adopted, and the mutated gene s drawn randomly from the doman of the correspondng varable. H. Calculaton of group smlarty In order to acheve self adaptve group organzaton, t must determne the group smlarty frst. Ths paper nvolves the three measurements to determne the group smlarty: 1. group centers,. group dstance, and 3. group standard devaton. m 1 Group centers: y x l, 1,,, N C (8) m 1 Group dstance: d Group standard devaton: P sze y y y y (9) 1, 1 m 1 xl y p m p1 0 1,, n (30) where y s the center of the th group, m s the total number of th group, x s th chromosome n the th group, d s the l Eucldean dstance between the th group and th group, s the th bt standard devaton n the th group, s the largest standard devaton of th group. After calculatng above three measurements, t wll be used to adust the group organzaton of the neural fuzzy networ by followng two processes: splttng process and lumpng process. 0 I. Splttng process 0 If 0, where 0 s standard devaton splttng threshold, t means the chromosomes n the th group are very dssmlar, so the AGOCEA wll call Splttng process. The Splttng process wll dvde th group nto two groups, whch are + group and - group, by followng step: the top 50% (ftness value) chromosomes n the th group wll put nto + group, the other 50% chromosomes n the th group wll put nto - group. The other 50% n the + group and - group wll generate randomly. After Splttng process, the dssmlar group wll be separated nto dfferent groups, and total number of group wll ncrease Lumpng process If d d0, where d 0 s lumpng threshold, t means the chromosomes are very smlar between th group and th group, so the AGOCEA wll call Lumpng process. The Lumpng process wll merge th group and th group nto a new group. The new group conssts of the top 50% chromosomes from th group and the top 50% chromosomes from th group. After Lumpng process, the smlar groups wll be merged nto a new group, and total number of group wll decrease. IV. SIMULATION RESULTS The example used for dentfcaton of nonlnear dynamc system gven by Narendra and Parthasarathy [34] s descrbed as followng dfference equaton: y 3 y 1 u 1 y (31) The output of above equaton depends nonlnearly on both ts past value and the nput, but the effects of the nput and output values are not addtve. The tranng nput patterns are random value n the nterval [-, ]. To determne the performance of the algorthms, ths example adopts the root mean square error (RMSE). The defnton of the RMSE s: RMSE where s number of data. N yˆ y 1 N (3) ŷ s desred output, y() s model output, and N In order to determne performance of the dfference learnng algorthm, ths example s compared AGOCEA wth HESP [35], ESP [36], MCGSE [], SANE [37], and GA [6]. All algorthms were learned for 500 generatons and repeated for 50 trals. The ntal parameters of the AGOCEA are gven n Table IV. Fgure 6-11 show the output of all algorthms for u sn. the nput sgnal 5 In these fgures, the symbol o represents the desred output of the nonlnear dynamc system, and the symbol * represents the output of all algorthms. It can be seen from the Fg that the model output of AGOCEA has more accuracy than the other comparng learnng algorthms. 6 P a g e

7 TABLE IV. INITIAL PARAMETERS OF THE AGOCEA. Parameters Value P sze 30 N c 0 Selecton_Tmes 40 NormalTmes 10 Searchng Tmes 0 ExplorngTmes 30 Crossover Rate 0.6 Mutaton Rate 0.3 [M mn, M ] [5, 15] [m mn, m ] [-10, 10] [σ mn, σ ] [1,15] [w mn, w ] [-10, 10] σ 0 6 d 0 1 Fg. 8. Identfcaton Results Of The Desred Output And The ESP. Fg. 6. Identfcaton Results Of The Desred Output And The AGOCEA. Fg. 9. Identfcaton Results Of The Desred Output And The MCGSE. Fg. 7. Fgure 4. Identfcaton Results Of The Desred Output And The HESP. Fg. 10. Identfcaton Results Of The Desred Output And The SANE. 7 P a g e

8 Fg. 11. dentfcaton Results Of The Desred Output And The GA. Fgure 1 (a)-(f) show the dentfcaton error between the desred output and all algorthms output. As shown n Fg. 1 (a)-(f), the AGOCEA llustrated the smaller error than other algorthms. Fgure 13 provdes the learnng curve of the varous learnng algorthms, t can be seen from the learnng curve that the AGOCEA converge faster and better than the other learnng algorthms. Fg. 13. The Learnng Curve Of AGOCEA, HESP, ESP, MCGSE, SANE, And GA. Table V shows the results obtaned from a RMSE analyss of the varous learnng algorthms. There was a sgnfcant dfference between the proposed AGOCEA and the other learnng algorthms. No matter whch performance ndex s, the proposed AGOCEA has the better performance than the other learnng algorthms. TABLE V. RMSE COMPARISON OF VARIOUS LEARNING ALGORITHMS. (a) (b) Algorthm RMSE Mean Best Worst STD AGOCEA HESP ESP MCGSE SANE GA (c) (e) (d) Fg. 1. Identfcaton Errors Of The (A) AGOCEA, (B) HESP, (C) ESP (D) MCGSE, (E) SANE, And (F) GA. (f) V. CONCLUSIONS In ths paper, the AGOCEA s proposed for desgnng TSKtype neural fuzzy networ. The proposed AGOCEA not only determne the sutable number of fuzzy rules and group number but also effcently tune the free parameters n the TNFN. The AGOCEA adopts the GSE that each populaton s dvded to several groups and each group represents only one fuzzy rule. In order to solve the problem of random group selecton, a data mnng based group selecton method was used to select the better groups. Furthermore, the adaptve group organzaton was proposed to solve the some parameters have to be assgned n advance. The smulaton results show that the AGOCEA traned TNFN s superor to other methods. Although the proposed AGOCEA can obtan better results n comparson wth the other learnng algorthms, t stll has a lmtaton. The mportant lmtaton les n the fact that the proposed AGOCEA emphasze the networ parameter learnng and the group structure organzaton, t s a two level learnng structure. Whle the problems become more complex, there s possble that ncrease the levels of learnng structure. 8 P a g e

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