A soft computing approach for modeling of severity of faults in software systems

Transcription

1 Internatonal Journal of Physcal Scences Vol. 5 (), pp , February, 010 Avalable onlne at ISSN Academc Journals Full Length Research Paper A soft computng approach for modelng of severty of faults n software systems Ebru Ardl 1 and Parvnder S. Sandhu * 1 Department of Electrcal and Electroncs Engneerng, Fath Unversty, Istanbul, Turkey. Head of Computer Scence and Engneerng and Informaton Technology Department, Rayat and Bahra Insttute of Engneerng and Bo-Technology, Sahauran, Dstt. Mohal (Punjab) Inda. Accepted 5 January 010 As the majorty of faults are found n a few of ts modules so there s a need to nvestgate the modules that are affected severely as compared to other modules and proper mantenance need to be done n tme especally for the crtcal applcatons. In ths present work, hybrd fuzzy-genetc Algorthm and Partcle Swarm Optmzaton traned Neural Network technques are emprcally evaluated and earler publshed results of the Mamdan Based Fuzzy Inference System and Neuro-Fuzzy Based technques are also dscussed for the comparatve analyss n order to predct level of mpact of faults n NASA s publc doman defect dataset coded n Perl programmng language. The results are recorded n terms of accuracy, mean absolute error (MAE) and root mean squared error (RMSE). The results of Neuro- Fuzzy model are also convncng but Fuzzy-GA based hybrd model provde relatvely better predcton accuracy as compared to other models and hence, t s proposed for the mantenance severty predcton of the software systems. Key words: Fuzzy, neuro-fuzzy, genetc algorthm, partcle swarm optmzaton (PSO), accuracy, MAE, RMSE. INTRODUCTION When a software system s developed, the majorty of faults are found n a few of ts modules. In most of the cases, 55% of faults exst wthn 0% of source code. It s, therefore, much of nterest to fnd out fault-prone software modules at early stage of a project (Benlarb et al., 1999). Usng software complexty measures, the technques buld models, whch classfy components as lkely to contan faults or not. Qualty wll be mproved as more faults wll be detected. Predctng the mpact of the faults early n the software lfe cycle can be used to mprove software process control and acheve hgh software relablty. Tmely predctons of faults n software modules can be used to drect cost-effectve qualty enhancement efforts to modules that are lkely to have a hgh number of faults. Predcton models based on software metrcs can estmate number of faults n software modules. Predcton of severty of faults: *Correspondng author. E-mal: parvnder.sandhu@gmal.com. Tel: (1) Supports software qualty engneerng through mproved schedulng and project control. () Can be a key step towards steerng the software testng and mprovng the effectveness of the whole process. (3) Enables effectve dscovery and dentfcaton of defects. (4) Enables the verfcaton and valdaton actvtes focused on crtcal software components. (5) Used to mprove software process control and acheve hgh software relablty. (6) Can be used to drect cost-effectve qualty enhancement efforts to modules. In the lterature (Benlarb et al., 1999; Lanuble et al., 1995; Fenton et al., 1999; Denaro, 000; Deodhar, 00; Belln, 005) made predcton of fault prone modules n software development process and mostly used the metrc based approach wth machne learnng technques to model the fault predcton n the software modules. Khoshgoftaar et al. (001) used zero-nflated Posson regresson to predct the fault-proneness of software

2 Ardl and Sandhu 075 systems wth a large number of zero response varables. Munson et al. (1990) and Khoshgoftaar et al. (1990) also nvestgated the applcaton of multvarate analyss to regresson and showed that reducng the number of ndependent factors (attrbute set) does not sgnfcantly affect the Accuracy of software qualty predcton. Menzes et al. (003) compared decson trees, naïve Bayes and 1- rule classfer on the NASA software defect data. Eman et al. (001) compared dfferent case-based reasonng classfers and concluded that there s no added advantage n varyng the combnaton of parameters (ncludng varyng nearest neghbor and usng dfferent weght functons) of the classfer to make the predcton Accuracy better. Many modelng technques have been developed and appled for software qualty predcton (Hudepohl et al., 1996; Khoshgoftaar et al., 1996; Khoshgoftaar et al., 00; Selya et al., 005). The software qualty may be analyzed wth lmted fault proneness data (Munson et al., 199). In (Sandhu et al., 007), the author has used varous machne learnng technques for an ntellgent system for the software mantenance predcton and proposed the logstc model trees (LMT) and Complmentary Naïve Bayes (CNB) algorthms on the bass of Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Accuracy percentage. Soft-Computng algorthms have proven to be of great practcal value n a varety of applcaton domans. Not surprsngly, the feld of software engneerng turns out to be a fertle ground where many software development and mantenance tasks could be formulated as learnng problems and approached n terms of learnng algorthms. The Soft Computng (SC) paradgm also known as Computatonal Intellgence dffers from conventonal computng n that, technques belongng to t can be tolerant of mprecse, ncomplete or corrupt nput data. Some of them can solve problems wthout requrng the soluton steps or reasonng process to be explctly stated. Some soft computng systems develop the capablty to solve problems through repeated observaton and adaptaton. Some arrve at a soluton through a process smlar to evoluton n nature. In more than one ways, the human mnd s the role model for soft computng technques - for example, the ablty to solve problems expressed n vague terms, or solvng problems wthout makng use of explct soluton steps. Arrvng at a soluton through an evolutonary process s commonplace n nature. The predomnant SC methodologes found n current ntellgent systems are: (1) Artfcal Neural Networks (ANN). () Fuzzy Systems. (3) Genetc Algorthms (GA). Partcle Swarm Optmzaton (PSO) shares many smlartes wth evolutonary computaton technques such as genetc algorthms (GA). The system s ntalzed wth a populaton of random solutons and searches for optma by updatng generatons. However, unlke GA, PSO has no evoluton operators such as crossover and mutaton. In PSO, the potental solutons, called partcles, fly through the problem space by followng the current optmum partcles. Ths paper s the extenson of the earler work (Ardl et al., 009) n whch varous machne learnng algorthms ncludng Fuzzy and Neuro-Fuzzy based technques are expermented for the predcton of level of mpact of faults n the software modules. In ths present work, hybrd fuzzy-ga and PSO traned neural network technques are evaluated and results of the Fuzzy and Neuro-Fuzzy based technques are also dscussed for the comparatve analyss n order to predct level of mpact of faults n the software modules. In ths paper, secton two descrbes the methodology part of work done, whch shows the steps used n order to reach the objectves and carry out the results. In the secton three, results of the mplementaton are dscussed. In the last secton, on the bass of the dscusson varous conclusons are drawn and the future scope for the present work s dscussed. Fuzzy nference systems A fuzzy nference system (FIS) s a way of mappng an nput space to an output space usng fuzzy logc. A FIS tres to formalze the reasonng process of human language by means of fuzzy logc (that s, by buldng fuzzy IF-THEN rules). On wde categorzaton, followng are the basc types of fuzzy nference systems: (1) Mamdan fuzzy nference system. () Takag-sugeno fuzzy nference system. (3)Adaptve neuro-fuzzy nference system (ANFIS). Mamdan fuzzy nference system Mamdan's fuzzy nference method s the most commonly seen fuzzy methodology. Mamdan's method was among the frst control systems bult usng fuzzy set theory. It was proposed n 1975 by Mamdan et al. (1975) as an attempt to control a steam engne and boler combnaton by syntheszng a set of lngustc control rules obtaned from experenced human operators. Mamdan's effort was based on Lotf Zadeh's 1973 paper on fuzzy algorthms for complex systems and decson processes (Zadeh, 1973). Although the nference process descrbed n the next few sectons dffers somewhat from the methods descrbed n the orgnal paper, the basc dea s much the same. Mamdan-type nference expects the output member-

3 076 Int. J. Phys. Sc. shp functons to be fuzzy sets. After the aggregaton process, there s a fuzzy set for each output varable that needs defuzzfcaton. It s possble and n many cases much more effcent, to use a sngle spke as the output membershp functons rather than a dstrbuted fuzzy set. Ths type of output s sometmes known as a sngleton output membershp functon and t can be thought of as a pre-defuzzfed fuzzy set. It enhances the effcency of the defuzzfcaton process because t greatly smplfes the computaton requred by the more general Mamdan method, whch fnds the centrod of a two-dmensonal functon. Rather than ntegratng across the twodmensonal functon to fnd the centrod, we use the weghted average of a few data ponts. Sugeno-type systems support ths type of model. In general, Sugenotype systems can be used to model any nference system n whch the output membershp functons are ether lnear or constant. Accordng to Abraham (005) NF computng s a popular framework for solvng complex problems. If one has knowledge expressed n lngustc rules, one can buld a fuzzy nference system (FIS) and f one has data, or can learn from a smulaton (tranng) then one can use artfcal neural networks (ANNs). For buldng a FIS, one has to specfy the fuzzy sets, fuzzy operators and the knowledge base. Smlarly, for constructng an ANN for an applcaton the user needs to specfy the archtecture and learnng algorthm. An analyss reveals that the drawbacks pertanng to these approaches seem complementary and therefore, t s natural to consder buldng an ntegrated system combnng the concepts. Whle the learnng capablty s an advantage from the vewpont of FIS, the formaton of lngustc rule base wll be advantage from the vewpont of ANN. In the smplest way, a cooperatve model can be consdered as a preprocessor wheren ANN learnng mechansm determnes the FIS membershp functons or fuzzy rules from the tranng data. Once the FIS parameters are determned, ANN goes to the background (Jang et al., 1995). The rule based s usually determned by a clusterng approach (self organzng maps) or fuzzy clusterng algorthms. Membershp functons (MF) are usually approxmated by neural network from the tranng data. In a concurrent model, ANN asssts the FIS contnuously to determne the requred parameters especally f the nput varables of the controller cannot be measured drectly. In some cases the FIS outputs mght not be drectly applcable to the process. In that case ANN can act as a postprocessor of FIS outputs (Abraham, 005). In fused NF archtecture, ANN learnng algorthms are used to determne the parameters of FIS. Fused NF systems share data structures and knowledge representatons. A common way to apply a learnng algorthm to a fuzzy system s to represent t n a specal ANN lke archtecture. However, the conventonal ANN learnng algorthms (gradent descent) cannot be appled drectly Fgure 1. Mamdan fuzzy nference system structure (Abraham, 005). to such a system as the functons used n the nference process are usually non dfferentable. Ths problem can be tackled by usng dfferentable functons n the nference system or by not usng the standard neural learnng algorthm. Some of the major woks n ths area are GARIC (Bherenj et al., 199), FALCON (Ln et al., 1991), ANFIS (Jang, 199), NEFCON, FUN (Sulzberger et al., 1993), SONFIN (Feng 1998), FINEST, EFuNN (Kasabov et al., 1999), dmefunn (Kasabov et al., 1999), evolutonary desgn of Neuro-Fuzzy systems and many others. Archtecture of Mamdan fuzzy nference system s llustrated n Fgure 1. The detaled functon of each layer s as follows: Layer-1 (Input layer): No computaton s done n ths layer. Each node n ths layer, whch corresponds to one nput varable, only transmts nput values to the next layer drectly. The lnk weght n layer 1 s unty. Layer- (Fuzzfcaton layer): Each node n ths layer corresponds to one lngustc label (excellent, good, etc.) to one of the nput varables n layer 1. In other words, the output lnk represents the membershp value, whch specfes the degree to whch an nput value belongs to a fuzzy set, s calculated n layer. A clusterng algorthm wll decde the ntal number and type of membershp functons to be allocated to each of the nput varable. The fnal shapes of the MFs wll be fne tuned durng network learnng. Layer-3 (Rule antecedent layer): A node n ths layer represents the antecedent part of a rule. Usually a T- norm operator s used n ths node. The output of a layer 3

4 Ardl and Sandhu 077 node represents the rng strength of the correspondng fuzzy rule. Layer-4 (Rule consequent layer): Ths node bascally has two tasks. To combne the ncomng rule antecedents and determne the degree to whch they belong to the output lngustc label (hgh, medum, low, etc.). The number of nodes n ths layer wll be equal to the number of rules. Layer-5 (Combnaton and defuzzfcaton layer): Ths node does the combnaton of all the rules consequents usng a T-conorm operator and fnally computes the crsp. Takag-Sugeno fuzzy nference system Abraham (005) dscussed Takag-Sugeno fuzzy nference systems make use of a mxture of back propagaton to learn the membershp functons and least mean square estmaton to determne the coeffcents of the lnear combnatons n the rule's conclusons and that makes t Takag-Sugeno neuro-fuzzy system. A step n the learnng procedure got two parts: In the frst part, the nput patterns are propagated and the optmal concluson parameters are estmated by an teratve least mean square procedure, whle the antecedent parameters (membershp functons) are assumed to be fxed for the current cycle through the tranng set. In the second part, the patterns are propagated agan and n ths epoch, back propagaton s used to modfy the antecedent parameters, whle the concluson parameters reman fxed (Jang et al., 004). Ths procedure s then terated. Archtecture of Takag-Sugeno neuro-fuzzy system s llustrated n Fgure. The detaled functonng (Abraham, 005) of each layer s as follows: Layers 1, and 3: These layers functons the same way as Mamdan FIS. Fgure. Tagak-Sugeno neuro-fuzzy system structure (Ardl et al., 009). Fgure 3. Archtecture of ANFIS mplementng Tsukamoto fuzzy nference system (Jang, 199). Layer-6 (Rule nference layer): The sngle node n ths layer computes the overall output as the summaton of all ncomng sgnals Overall output = X Layer 4 (Rule strength normalzaton): Every node n ths layer calculates the rato of the th rule's frng strength to the sum of all rules frng strength. OverallOut put ω f = ϖ = f ω (3) ω ω =, = 1,... ω + ω 1 Layer-5 (Rule consequent layer): Every node n ths layer s wth a node functon ω f = ω ( p x + q x + r ) () Where; s the output of layer 4 and {f ; q ; r } s the parameter set. A well establshed way s to determne the consequent parameters usng the least means squares algorthm. (1) Adaptve network based fuzzy nference system (ANFIS) ANFIS proposed by Jang (199), s perhaps the frst ntegrated hybrd neuro-fuzzy model and the archtecture s very smlar to Fgure, a modfed verson of ANFIS whch s shown n Fgure 3 s capable of mplementng the Tsukamoto fuzzy nference system as depcted n Fgure 4. Hence, ANFIS have non-lnear antecedent parameters and lnear consequent parameters. These consequent and antecedent parameters are learned usng hybrd learnng algorthm. More specfcally, n the forward pass

5 078 Int. J. Phys. Sc. Fgure 4. Tsukamoto fuzzy reasonng (Jang, 199). of the hybrd learnng algorthm, functonal sgnals go forward tll layer 4 and consequent parameters are dentfed by the least square estmates. In the backward pass, the error rates propagate backward and the premse parameters are updated by the gradent descent. In the Tsukamoto FIS, the overall output s the weghted average of each rules crsp output nduced by the rules frng strength (the product or mnmum of the degrees of match wth the premse part) and output membershp functons. The output membershp functons used n ths scheme must be monotoncally non-decreasng. The frst hdden layer s for fuzzfcaton of the nput varables and T-norm operators are deployed n the second hdden layer to compute the rule antecedent part. The thrd hdden layer normalzes the rule strengths followed by the fourth hdden layer where the consequent parameters of the rule are determned. Output layer computes the overall nput as the summaton of all n comng sgnals. In ANFIS, the adaptaton (learnng) process s only concerned wth parameter level adaptaton wth n fxed structures. The structure of ANFIS ensures that each lngustc term s represented by only one fuzzy set. In most fuzzy systems, fuzzy rules were obtaned from the human expert. However, every expert does not want to share hs knowledge and there s no standard method that exsts to utlze expert knowledge. As a result, ANNs were ncorporated nto fuzzy systems to be able to acqure knowledge automatcally by learnng algorthms. The learnng capablty of the NNs was used for automatc fuzzy f-then rules generaton (Czogala et al., 000). PROPOSE METHODOLOGY Fnd the structural code and desgn attrbutes The frst step s to fnd the structural code and desgn attrbutes of software systems that s, software metrcs. The real-tme defect data sets are taken from the NASA s MDP (Metrc Data Program) data repostory. The dataset s related to the safety crtcal software systems beng developed by NASA. Select the sutable metrc values as representaton of statement The sutable metrcs lke product module metrcs out of these data sets are consdered. The term product s used referrng to module level data. Analyze and refne metrc values In the next step, the metrcs are analyzed and refned and then used for modelng of software fault severty n software systems. Emprcal evaluaton of dfferent machne learnng algorthms In ths step, the am s to fnd the best algorthm for classfcaton of software components nto dfferent levels of mpact of fault. In order to model the polshed dataset of the prevous step, Hybrd Fuzzy- GA and PSO-traned neural network technques are explored along wth the earler expermented fuzzy and neuro-fuzzy technques as dscussed n (Sandhu et al., 007). Fuzzy and neuro-fuzzy technques Accordng to (Jang et al., 1995), a fuzzy system can be consdered to be a parameterzed nonlnear map, called f, whch can be expressed as (4): f ( x) m l n y µ ( x ) l= 1 = 1 = m n µ ( x ) l= 1 = 1 l A l A Where; y l s a place of output sngleton f Mamdan reasonng s appled or a constant f Sugeno reasonng s appled. The membershp functon µ A l (x ) corresponds to the nput x = [x 1, x, x 3, x m] of the rule l. The and connectve n the premse s carred out by a product and defuzzfcaton by the center-of-gravty method. Consder a Sugeno type of fuzzy system havng the rule base: (4)

6 Ardl and Sandhu 079 Rule1: If x s A1 and y s B1, then f1 = p1x + q 1y + 1 Rule: If x s A and y s B, then f = p x+ q y + r Let the membershp functons of fuzzy sets A, B, I = 1,, be, µ A, µ B. Evaluatng the rule premses results n w = µ A(x) * µ B (y) where = 1, for the rule rules stated above. Evaluatng the mplcaton and the rule consequences gves (5). f Let w w1 f 1 w1 + w w f = (5) + w w + 1 w = (6) Then f can be wrtten as (7). f w f w f = (7) The steps for desgnng of adaptve neuro-fuzzy system are already dscussed n secton II of the paper. PSO traned neural network system The followng are the steps for the hybrd PSO-neural network based modelng system: (1) Desgnng of neural network and perform tranng: In ths step the followng three sub steps are there: (a) Calculate the mnmum and maxmum values n the attrbute of nput and settng the varous parameters of feed-forward backpropagaton network by lke: () Sze of the feed-forward back-propagaton neural network. () Type of transfer functon of each layer to be used. () Type of back-propagaton network tranng functon. (v) Back-propagaton weght/bas learnng functon. (b)generate the neural network. (c) Perform the tranng of the neural network wth PSO technque dscussed after the testng phase usng the tranng dataset. () Testng phase: In ths step the PSO traned neural network s evaluated aganst the testng data on the dfferent crtera s dscussed n the next steps. PSO s ntalzed wth a group of random partcles (solutons) and then searches for optma by updatng generatons. In every teraton, each partcle s updated by the followng two "best" values. The frst one s the best soluton (ftness) t has acheved so far. (The ftness value s also stored.) Ths value s called pbest. Another "best" value that s tracked by the partcle swarm optmzer s the best value, obtaned so far by any partcle n the populaton. Ths best value s a global best and called gbest. When a partcle takes part of the populaton as ts topologcal neghbors, the best value s a local best and s called lbest (Web URL: After fndng the two best values, the partcle updates ts velocty and postons wth followng equatons (8) and (9). v [ ] = v[ ] + c 1 * rand( ) * (pbest[ ] - present[ ]) + c * rand( ) * (gbest[ ] - present[ ]) (8) present[ ] = persent[ ] + v[ ] (9) where; v[ ] s the partcle velocty, persent[ ] s the current partcle (soluton), pbest[ ] and gbest[ ] are defned as stated before, rand ( ) s a random number between (0,1) ans c 1, c are learnng factors usually c 1 = c =. As mentoned n (Web URL: the pseudo code of the procedure s as follows: For each partcle Intalze partcle END Do For each partcle Calculate ftness value. If the ftness value s better than the best ftness value (pbest) n hstory. set current value as the new pbest. End Choose the partcle wth the best ftness value of all the partcles as the gbest. For each partcle, Calculate partcle velocty accordng equaton (8). Update partcle poston accordng equaton (9). End Whle maxmum teratons or mnmum error crtera s not attaned. Partcles' veloctes on each dmenson are clamped to a maxmum velocty V max. If the sum of acceleratons would cause the velocty on that dmenson to exceed V max, whch s a parameter specfed by the user, then the velocty on that dmenson s lmted to V max. Hybrd fuzzy-ga based approach Genetc algorthms are a part of evolutonary computng, whch s a rapdly growng area of artfcal ntellgence. As you can guess, genetc algorthms are nspred by Darwn's theory of evoluton. Smply sad, problems are solved by an evolutonary process resultng n a best (fttest) soluton (survvor) - n other words, the soluton s evolved. Rosenberg ntroduced evolutonary computng n the 1960s n hs work "Evoluton strateges" (Evolutons strateges n orgnal). Other researchers then developed hs dea. Genetc algorthms (GAs) were nvented by John Holland and hs students and colleagues. These lead to Holland's book" Adapton n Natural and Artfcal Systems" publshed n In 199, John Koza used genetc algorthms to evolve programs to perform certan tasks. He called hs method "genetc programmng" (GP). The steps of the hybrd fuzzy-ga algorthm are: (1) Read the nput as the metrc values. () Fnd the nearest match wth example data usng Eucldean Dstance. (3) Calculate the output of the fuzzy nference system correspondng to the Input set.

7 080 Int. J. Phys. Sc. Types of Modules Number of Modules Mantenance Severty Level Types of Fgure 5. Graphcal representaton of detals of the type of modules n the dataset. (4) Treat FIS value and the nearest match value as chromosome and convert the values nto bnary after multplyng the values wth 100. (5) Perform the sngle pont cross over at randomly generated pont n the selected parents. (6) Get the offsprngs from the prevous step and generate the output by dvdng the offsprng wth 100. (7) Repeat the process up to 100 generatons or the error reduces to certan mnmum level. (8) The model generated s evaluated aganst the testng data on the dfferent crtera s dscussed n the next steps. Comparson crtera The comparsons of machne learnng algorthms are made on the bass of the least value of MAE and RMSE values. Accuracy value of the predcton model s also used for the comparson. The best algorthm s pcked up after the 10 fold cross valdaton results and tested for the testng dataset. The Accuracy of the model s compared wth the results of Mamdan based FIS and neuro-fuzzy based systems. The detals of the MAE and RMSE are: Mean absolute error: Mean absolute error, MAE s the average of the dfference between predcted and actual value n all test cases; t s the average predcton error (Bherenj et al., 199). The formula for calculatng MAE s gven n equaton shown below: a1 c1 a c n a n cn Assumng that the actual output s a, expected output s c. (10) Root mean-squared error: RMSE s frequently used measure of dfferences between values predcted by a model or estmator and the values actually observed from the thng beng modeled or estmated (Challagulla et al., 005). It s just the square root of the mean square error as shown n equaton gven below: ( ) + ( ) ( ) a c a c a n c n 1 1 (11) n Conclusons drawn The conclusons are made on the bass of the comparson made n the prevous secton. RESULTS AND DISCUSSION The real-tme defect data set used s taken from the NASA s MDP (Metrc Data Program) data repostory, the detals of that dataset contans 60 modules of Perl Programmng language wth dfferent values of software fault severty labeled as 1,, 3, 4 and 5. The fault severty level-1 means the fault s havng hghest severty level and that need urgent attenton to be removed as t falls n the category of major faults. The fault severty level- means the fault s havng hgh severty level and that need less urgent attenton as compared to level-1 faults. The fault severty level-3 means the fault s havng medum severty level and that requre less attenton as compared to level- faults. The fault severty level-4 means the fault s less severe and that need low attenton to be removed. The faults of ths level belongs to category of mnor faults and fault severty level-5 means the fault s least severe means havng neglgble effect of the performance of system and belongs to the category of the purely mnor faults or no faults category. Graphcal detals of the type of modules n the dataset are shown n Fgure 5. The detals of the modules present n the dataset are shown n Table 1. The frst step s to fnd the structural code and desgn attrbutes of software systems that s, software metrcs. As most of the values of the other metrcs are zero or metrcs are redundant n nature. So, selected fve metrcs representng nput attrbutes are: - Branch_Count. - Cyclometrc_Complexty. - Desgn_Complexty.

8 Ardl and Sandhu 081 Table 1. Detals of the type of modules n the dataset. Label Count Fgure 6. Mamdan based FIS nference system. - Essental_Complexty. - Number_Of_Lnes. When analyzng performance of all the WEKA project (Web URL WEKA: algorthms, Logstc Model Trees (LMT) and smple logstc algorthms have outperformed all the other algorthms used n the comparatve study wth Accuracy, MAE and RMSE values as 65, and respectvely when the 10 fold cross valdaton s performed. When LMT and smple logstc algorthms are tested for the ffteen exemplar nputs 86.66% accuracy s obtaned. In the Mamdan based fuzzy nference system model (Mamdan et al, 1975) fve metrcs are consdered as nput attrbutes and one attrbute named as software mantenance severty level s used as output attrbute as shown n Fgure 6. Each nput and output attrbute s represented wth ffteen fuzzy sets and the membershp functon value of the each attrbute s shown n Fgure 7. In Fgure 8, ffteen rules used for the nference of the Mamdan based FIS are shown. Durng the testng phase of the Mamdan based fuzzy nference system (Mamdan et al., 1975), ffteen nputs are used and t shows 0.183, and 80% as MAE, RMSE and Accuracy values respectvely. As performance of adaptve neuro-fuzzy nference system s found to be the best out of all the hybrd NF systems (Abraham, 001) and the extra complexty n structure and computaton of Mamdam based adaptve NF nference system wth max-mn composton does not necessarly mply better learnng capablty or approxmaton power (Jang et al., 004). Hence, n MATLAB 7.4, the Sugeno based adaptve neuro-fuzzy nference system s used for modelng of software mantenance severty. The deal nference system for the evaluaton of software components should be less complex and more precson. The nference system, whch s already traned, wll get the metrc values from the earler stages and estmate the software mantenance severty value of the software components or modules. The followng s the nformaton regardng the structure of the adaptve neuro-fuzzy based nference system and pctorally represented n Fgure 9: - Number of nodes: 3. - Number of lnear parameters: 1. - Number of nonlnear parameters: 0. - Total number of parameters: 3. - Number of tranng data pars: Number of checkng data pars: 0. - Number of fuzzy rules:. The graphcal representaton of the nput exemplars for the NF system s shown n Fgure 10. The NF system s traned usng a hybrd learnng algorthm usng both least squares method and backpropagaton. In the forward pass, the consequent para-

9 08 Int. J. Phys. Sc. Fgure 7. Membershp functons of the nput and output attrbutes. Fgure 8. Ffteen rules of the Mamdan based FIS. Fgure 9. Structure of adaptve neuro-fuzzy nference system.

10 Ardl and Sandhu 083 Fgure 10. Tranng data for the neuro-fuzzy system. meters are dentfed usng least squares and n the backward pass the premse parameters are dentfed usng back-propagaton. The traned NF system s then tested for the ffteen nputs and t shows , and as MAE, RMSE and Accuracy values respectvely. PSO-neural network results In the mplementaton of the PSO traned neural network partcle swarm optmzaton toolbox for matlab (Brge, 003) s used. Sze of the feed-forward back-propagaton neural network s set as [5 5 1] means there are 5 neurons n the nput layer, 5 neurons n the hdden layer and one neuron n the output layer of the network. The lnear transfer functon s the type of transfer functon used for the last layer and hyperbolc tangent sgmod transfer functon s used for the rest of layer of the desgned neutral network. Gradent descent wth momentum weght and bas learnng functon s used as backpropagaton weght/bas learnng functon. TRAINPSO type of back-propagaton network tranng functon s used as TRAINPSO s a network tranng functon that updates weght and bas values accordng to partcle swarm optmzaton. The followng are the addtonal parameters values used: (1) Maxmum teratons: 000; () Populaton sze: 5; (3) Acceleraton constants (for type = 0): [,]; (4) Inerta weghts (for type = 0): [0.9,0.4]; (5) Mnmum error gradent: 1e-9; (6) Iteratons at error grad value before ext: floor (0.*tranParam.maxt); (7) Error goal: 0; (8) Type of PSO: Trelea. After the tranng, the archtecture of feed forward neural network s shown n Fgure 11 where the Brght Green lne shows more postve weght, brght red lne shows more negatve weght and dashed whte lne shows zero weght Fgure 11. Archtecture of feed forward neural network. that s, no connecton between the neurons. In the testng phase MAE, RMSE and Accuracy values of the system are 0.578, and respectvely as shown n Table. The plot of Global best value (Gbest) versus Iteratons s shown n fgure 1. As Gbest value s tracked by the partcle swarm optmzer s the best value, obtaned so far by any partcle n the populaton. The Gbest value obtaned s The fuzzy-ga hybrd system s also mplemented n Matlab 7.4. Durng the testng of the developed system, 0.10, and 100 are calculated as MAE, RMSE and Accuracy values for the testng dataset as shown n

11 084 Int. J. Phys. Sc. Table. Results of the proposed systems for the fault severty predcton. Performance Crtera Mamdan based fuzzy nference system Predcton model Neuro-fuzzy system PSO traned neural network Fuzzy-GA system MAE RMSE Accuracy Table. Fgure 1. Graph between gbest value and Iteraton ndex. Concluson and future drecton On comparng varous WEKA s machne learnng algorthms as mentoned n (Ardl et al., 009), t s observed that logstc model trees and smple logstc algorthms are better technques n predcton of fault severty level for NASA s publc doman defect dataset coded n Perl programmng language. Both the algorthms use same classfcaton algorthm that s, logstc classfer and have shown least mean absolute error and root mean square error values: and among other algorthms lsted n WEKA s project. Durng the testng phase, LMT and smple logstc algorthm has shown 86.66% Accuracy. When expermented wth Mamdan based fuzzy nference system (Mamdan et al., 1975), the testng phase results are comparatvely equvalent as that of the logstc model trees and smple logstc algorthm wth 0.183, and 80% as mean absolute error, root mean square error and accuracy values. The performance of feed forward neural network traned wth partcle swarm optmzaton algorthm s not promsng as the testng phase MAE, RMSE and Accuracy values of the developed system are 0.578, and % respectvely. The bad performance of ths technque could be due to the ncapablty of the PSO to tran the neural network desgned. The predcton Accuracy percentage s the lowest among Mamdan based fuzzy nference system, logstc model trees and smple logstc algorthms Accuracy values. Fuzzy GA hybrd algorthm s proved to be best as compared to the other algorthms consdered n ths work wth 0.10, and 100 as MAE, RMSE and Accuracy values respectvely for the testng dataset. In such data search applcaton the desgn and developed fuzzy GA code has shown ts superorty because t ncludes the advantages of fuzzy as well as genetc algorthms. Fuzzy provdes a robust nference mechansm wth no learnng and adaptablty whle on the other hand, the genetc algorthms provde an effcent data modfcaton n the wake of optmzaton objectves of gven applcaton. Neuro -fuzzy algorthm s defntely superor to fuzzy algorthm as t nherts adaptablty and learnng. The performance of neuro -fuzzy algorthm s somewhat satsfactory and better than fuzzy system. From the smulaton and the result obtaned, t has been shown that the percentage average error s least n the case of fuzzy- GA algorthms and maxmum n the case of PSO traned neural network algorthms. Neuro-fuzzy algorthm has yelded accuracy lyng between the accuracy levels as n the case of fuzzy and fuzzy-ga algorthms. It s therefore, the best algorthm for classfcaton of the software components nto dfferent level of severty of mpact of the fault s found to be fuzzy-ga based technque. The algorthm can be used to develop model that can be used for dentfyng modules that are heavly affected by the faults and those modules can be debugged tmely. Hence, for non lnear and complex engneerng applcatons nvolvng control, nference and analyss by and large fuzzy-ga s an effcent technque. The future work can be extended n followng drectons: )The performance of the PSO based technque can further be nvestgated by ncreasng the number of hdden layers and changng the populaton sze. )Ths work can be extended to other programmng language datasets. ) More algorthms can be evaluated and then we can

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