Prediction of Dumping a Product in Textile Industry

Transcription

1 Int. J. Advanced Networkng and Applcatons Volue: 05 Issue: 03 Pages: (03) IN : Predcton of upng a Product n Textle Industry.V.. GANGA EVI Professor n MCA K..R.M. College of Engneerng Kadapa A.P. Inda Eal:svsgangadev_06@yahoo.co.n ABTRACT Fuzzy ecson Trees (FT s) are one of the ost popular choces for learnng and reasonng fro dataset. They have undergone a nuber of alteratons to language and easureent uncertantes. However they are poor n classfcaton accuracy. In ths paper Neuro -fuzzy decson tree ( a fuzzy decson tree structure wth neural lke paraeter adaptaton strategy) proves FT s classfcaton accuracy and extracts ore accuracy huan nterpretable classfcaton rules. In the forward cycle fuzzy decson tree s constructed and n the feedback cycle paraeters of fuzzy decson tree have been adapted usng stochastc gradent descent algorth by traversng back fro leaf to root nodes. In ths paper the syste ay predct whether a product n duped or not for the textle ndustry s explaned. Index Ters - Fuzzy ecson Tree Neuro-fuzzy decson tree Fuzzy I ate of ubsson: eceber 0 03 ate of Acceptance: January INTROUCTION Many early-warnng systes are avalable n our socety and n any other felds and found to be very benefcal. The textle ndustry also needs such a syste to reduce the rsks. At the present te ost of the exstng dupng and warnng systes are drectly based on huan coon sense and knowledge whch are soetes naccurate unrelable and ncoplete. FT s a successful ethod for accurate predcton. It facltates huan nspecton or understandng. But t s poor level of predctve accuracy. Neuro-Fuzzy ecson Trees [] s a Fuzzy ecson Tree structure wth neural lke paraeter adaptaton strategy. In the forward cycle we construct Fuzzy ecson Trees usng any of the standard nducton algorths lke fuzzy I3. In the feedback cycle paraeters of Fuzzy decson trees have been adapted usng stochastc gradent descent algorth by traversng back fro leaf to root nodes. Wth ths strategy durng the paraeter adaptaton stage keep the herarchcal structure of fuzzy decson trees ntact. Ths approach of applyng back propagaton algorth drectly on the structure of fuzzy decson trees proves ts learnng accuracy wthout coprosng the coprehensblty (nterpretablty).. FUZZY I3 ALGORITHM I3 algorth [] [3] apples to a set of data and generates a decson tree for classfyng the data. Fuzzy I3 algorth s extended to apply to a fuzzy set of data (several data wth ebershp grades) and generates a fuzzy decson tree usng fuzzy sets defned by a user for all attrbutes. A fuzzy decson tree conssts of nodes for testng attrbutes edges for branchng by test values of fuzzy sets defned by a user and leaves for decdng class naes wth certantes. Fuzzy I3 s very slar to I3 except I3 selects the test attrbute based on the nforaton gan whch s coputed by the probablty of ordnary data but ours by the probablty of ebershp value for data. Assue that we have a set of data where each data has θ nuercal values for attrbutes A A.A θ and one classfed class C {C C..C q } and Fuzzy ets f f. f n for the attrbute A (the value of vares on every C attrbute). Let k to be a fuzzy subset n whose class s C k and the su of the ebershp values n a fuzzy set of data [4]. Then an algorth to generate a fuzzy decson tree s n the followng:. Generate the root node that has a set of all data.e. a fuzzy set of all data wth the ebershp value.. If a node t wth a fuzzy set of data satsfes the followng condtons: () the proporton of a data set of a class C k s greater than or equal to a threshold θ r that s C k θ r () The nuber of a data set s less than a threshold θ n that s < θ n

2 Int. J. Advanced Networkng and Applcatons Volue: 05 Issue: 03 Pages: (03) IN : () there are no attrbutes for ore classfcaton then t s a leaf node and assgned by the class nae (ore detaled ethod s descrbed below). 3. If t does not satsfy the above condtons t s not a leaf node and the test node s generated as follows: 3. For A ' s ( l) calculate the nforaton gans G(A ) to be descrbed below and select the test attrbute A ax that axzes the. 3. vde nto a fuzzy subsets. accordng to A ax where the ebershp value of the data n s the product of the ebershp value n and the value of f ax of the value of A ax n. 3.3 Generate new nodes t t t for fuzzy subsets. and label the fuzzy sets f ax to edges that connect between the nodes t and t. 3.4 Replace by (..) and repeat fro recursvely. G for the attrbute A by a fuzzy set of data s defned by The nforaton gan ( A ) G ( A ) I( ) E( A ) where I () n ( ) ( ) E p p k p k. log p k () ( A ) ( p. I( )) (3) C k k (4) q (5) As for assgnng the class nae to the leaf node we propose three ethods as follows: (a) (b) The node s assgned the class nae that has the greatest ebershp value that s other than the selected data are gnored. If the condton (a) n step n the algorth holds do the sae as the ethod (a). If not the node s consdered to be epty that s the data are gnored. (c) The node s assgned by all class naes wth ther ebershp values that s all data are taken nto account [5]. 3. NEURO-FUZZY ECIION TREE ue to the sze and perforance of FT s severely affected by fuzzness control paraeter (α-cut) and leaf selecton threshold ( th ) however gude rules of selectng α and th are very hard to fnd n the exstng fuzzy decson tree lterature. Neuro-FT ncorporates the erts of neural learnng algorths nto the feedback cycle of herarchcal FT. The ethod sgnfcantly proves the classfcaton accuracy of FT wthout coprosng the coprehensblty the FT structure has been kept ntact durng the paraeter adaptaton stage. Raen. B Bhatt and M. Gopal [] proposed back propagaton learnng to be appled drectly on FT structure by traversng back fro each leaf node to root node. Neuro-FT ncludes one forward cycle of FT nducton and then several back propagaton teratons of tunng the FT paraeters (ebershp functons and leaf certantes). Ths strategy doesn t dsturb the herarchcal structure of FT and effectvely tune the tree paraeters whle preservng the nterpretablty [6]. The fgure shows the basc Neuro-FT structure wth two sung nodes added to t to carry out nference. Fro all the leaf nodes certanty factors correspondng to class (Yes) are sued up to calculate y. ae way certanty factors correspondng to class (No) are sued up to calculate y. For an arbtrary pattern the frng strength of l th class at th leaf node s gven by µ (6) path l Each (...6) path s defned on the prese space coposed of nput features avalable n traversng fro root node to th leaf node where µ path s ebershp degree of path. Whch can be calculated as µ path 3 µ F ( s ) l (0 l ; l ) s the degree of certanty wth whch path can classfy the class l. In Fgure path 6 can classfy Yes wth the certanty of 6 and classfy No wth the certanty of 6. F s th varable s ebershp functon avalable on th path. (7)

3 Int. J. Advanced Networkng and Applcatons Volue: 05 Issue: 03 Pages: (03) IN : Frng strengths of all the leaf nodes for a partcular class l are sued up to calculate the predcton certanty l of the pattern through FT y l ( ) τ + l τ l η + n ( d y ) l l n µ path (3) y l 6 µ (8) path where 0 y l. For exaple n fgure predcton certantes for Yes (y ) No (y ) are to be calculated by y M path M path µ ; y µ When classfcaton to unque class s desred the class wth the hghest ebershp degree has to be selected.e. classfy gven pattern to class l 0 where (9) l arg ax 0 l { y } l The class correspondng to axu predcton certanty arg ax y y l0 wll be selected { } To fuzzfy nput attrbutes the ethod we select Gaussan ebershp functons out of any alternatves [7] due to ts dfferentable property. For th pattern ebershp degree of path can be calculated by ( ) ( ) s c µ path µ F s exp (0) σ where c and σ are center and standard devaton (wdth) of Gaussan ebershp of th nput attrbute on th path of F. The ethod defnes as the error functon of the FT a dfferentable functon lke the ean-square-error E q n E ( d y ) n l l () l Where n the total nuber of tranng patterns and d l and yl s the desred class of th pattern through Neuro-FT respectvely. The necessary condton for the nzaton of error s that ts dfferentatons wth respect to the paraeters Gaussan center locatons Gaussan wdths and certanty factors are all vansh. The leads to the paraeter update rule τ + τ δe () θ θ η δθ For FT structure wth Gaussan ebershp functons we obtan the followng update rules for the adaptaton of the paraeters centers wdths and certanty factors. 4. Constructon of Fuzzy ecson Tree: The export textle products dataset fro January to August n 0 are consdered. Fuzzy set of dataset shown n table. Table : Export Textle ataset M µ (%) 3 (%) C.0 Mddle Yes 0.8 Hgh No 3 0. Hgh No Low Yes 5.0 Hgh No Low No 7.0 Mddle No Mddle Yes M 3 represents respectvely onths producton capacty of port country arket share and chna s textle products export growth rate. Fuzzy sets low ddle and hgh n the attrbute 3 fuzzy sets sall ddle and bg n and fuzzy sets strong and weak n are defned as Low Mddle Hgh all 36 Mddle Bg trong 0.3 ddle low Weak low hgh

4 Int. J. Advanced Networkng and Applcatons Volue: 05 Issue: 03 Pages: (03) IN : Note that we can defne fuzzy sets of the contnuous ebershp functons. Frst we calculate the nforaton I(). nce we have 5.5 C C. and 3. 3 we have I ( ) log log Next we calculate the expected nforaton for all A ' s. For 3 usng the step 3. n the algorth we have the fuzzy sets of data low ddle 3 hgh shown n table. () () or (3)n the step n the algorth. For ths data we have the fuzzy decson tree shown n fgure. Tale : Fuzzy ets data M Low d Hgh 3 (%) C Yes No No Yes No No No Yes Fgure : Fuzzy ecson Tree Then we ay get neuro-fuzzy decson tree usng the ethod []. For the export textle products dataset to classfy gven pattern to ether Yes or No Yes represents dupng and No represents no dupng. It shows n fgure. Usng the pseudo code of the Neuro-FT strategy to tran and get degree of certanty shown below. The ebershp value s calculated by the product of µ n and the ebershp value of the fuzzy sets low ddle and hgh of the value of the 3 n. C Ten for low we have low 3 low C.96 and I 3 low ( ) log log hgh C ddle C 3 ddle 3 ddle 0.85 and I ( ) ddle C for hgh we have hgh C.34 and I ( ) hgh 3 hgh 3 hgh Now we can calculate the expected nforaton after testng by the 3 as 3.. E ( 3 ) Thus we have the nforaton gan for the attrbute 3 as G I E ( ) ( ) ( ) 3 3 By slar analyss for and we have G( ) 0.8 G( ) nce we select the attrbute that axze the gan we have as the test attrbute. We apply the sae process untl t holds the leaf condton Fgure : FT for back propagaton

5 Int. J. Advanced Networkng and Applcatons Volue: 05 Issue: 03 Pages: (03) IN : CONCLUION Ths paper proposed a ethod for the early warnng syste ay predct whether a product n duped or not. The ethod s ore valdated for predctng a product to dup than other ethods. Neuro-FT has any advantages such as farly sple but powerful strategy for provng the classfcaton accuracy of FT wthout coprosng the coprehensblty. REFERENCE [] Raen B. Bhatt and M. Gopal Neuro- Fuzzy ecson Trees World centfc Publshng Copany Vol.6 pp [] J.R. Qunlan scoverng Rules by Inducton fro large collectons of Exaples n.mche (ed.): Expert ystes n the Mcro Electroncs Age Ednburgh Unversty Press Japan 979. [3] J.R. Qunlan Inducton of ecson Trees Machne Learnng Vol. pp [4] T. Tan and M. akoda Fuzzy Orented Expert yste to eterne Heater Outlet Teperature Applyng Machne Learnng 7 th Fuzzy yste yposu pp [5]. akura and. Arak Applcaton of Fuzzy Theory to Knowledge Acquston 5 th Intellgent yste yposu pp [6] X.Z. Wang.. Yeung and E.C.C.Tsang A coparatve study on heurstc algorths for generatng Fuzzy ecson Trees IEEE Transactons on MC-B3 pp [7] R.B. Bhatt and M. Gopal On the structure and ntal paraeter dentfcaton of Gaussan RBF networks Neural systes Vol.4 pp [8] K.H. yao and J.Y. Hu Fnancal Farly-warnng Analyss Based on ecson Tree ystes Engneerng Chna Vol.3 pp [9] Bryants M. A cased-based reasonng approach to bankruptcy predcton odel Intellgent systes n Accountng fnance and Manageent Vol.6 pp [0] Beaver W. Fnancal ratos as predctors of falure uppleent to Journal of Accountng Research pp