Estimating Development Time of Software Projects Using a Neuro Fuzzy Approach

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1 Estmatng Development Tme of Software Projects Usng a Neuro Fuzzy Approach Venus Marza, Amn Seyyed, and Luz Fernando Capretz Abstract Software estmaton accuracy s among the greatest challenges for software developers. Ths study amed at buldng and evaluatng a neuro-fuzzy model to estmate software projects development tme. The forty-one modules developed from ten programs were used as dataset. Our proposed approach s compared wth fuzzy logc and neural network model and Results show that the value of MMRE (Mean of Magntude of Relatve Error) applyng neuro-fuzzy was substantally lower than MMRE applyng fuzzy logc and neural network. Keywords Artfcal Neural Network, Fuzzy Logc, Neuro- Fuzzy, Software Estmaton I. INTRODUCTION ANY exstng research papers have proposed varous M estmaton technques, but no sngle software development estmaton technque s the best for all stuatons [1]. A careful comparson of the results of the several approaches s most lkely to choose the best one and produce realstc estmates [2]. The neural network research started n the 1940s, and the fuzzy logc research started n the 1960s, but the neuro-fuzzy research area s relatvely new [3]. The objectve of ths paper s to present a feasble way of combnng fuzzy logc and neural networks for achevng hgher accuracy. Neural network technques are based on the prncple of learnng from hstorcal data, whereas fuzzy logc s a method used to make ratonal decsons n an envronment of uncertanty and vagueness. However, fuzzy logc alone does not enable learnng from the hstorcal database of software projects. Once the concept of fuzzy logc s ncorporated nto neural network, the result s a neuro-fuzzy system that combnes the advantages of both technques [4]. A software tool (MATLAB 7.4) was used to process the fuzzy logc, neural network and neuro-fuzzy systems. The paper s organzed as follows: Secton 2 revews some related work n fuzzy logc and neural network doman, secton 3 dscusses fuzzy logc approach for tme estmaton n software development, secton 4 descrbes neural network technques for tme estmaton, secton 5 begns wth a bref dscusson of neuro-fuzzy model n general and ths s Venus Marza s an MSc student of computer engneerng, Islamc Azad Unversty of South Tehran Branch, Tehran, Iran (e-mal: venus.marza@gmal.com). Amn Seyyed s a member of Department of Computer Engneerng, Islamc Azad Unversty of Maku Branch, (e-mal: amseyyed@gmal.com). Luz Fernando Capretz s a professor at the Department of Electrcal and Computer Engneerng, Unversty of London, Ontaro, Canada N6A, Tel.: Fax: (e-mal: lcapretz@eng.uwo.ca). followed by comparson between three descrbed approaches, fnally secton 6 offers conclusons and a recommendaton for future research. II. RELATED WORK Estmaton accuracy s largely affected by modelng accuracy [5]. Fndng good models for software estmaton s very crtcal for software engneerng n bddng and plannng. In the recent years many software estmaton models have been developed [6], [7], [8], [9]. López Martín et al. [6] proposed a fuzzy logc model for development tme estmaton. Tng su et al. [7] descrbed an enhanced fuzzy logc model for the estmaton of software development effort whch had the smlar capabltes as the prevous fuzzy logc model n addton to enhancements n emprcal accuracy n terms of MMRE. Abbas Heat [8] used artfcal neural network technques lke RBF (Radal Bass Functon) and MLP (Mult-Layer Perceptron) for estmatng software development effort. Furthermore, Xsh Huang et al. [9] developed a novel neuro-fuzzy Constructve Cost Model (COCOMO) for software cost estmaton whch uses the desrable features of a neuro-fuzzy approach, such as learnng ablty and good nterpretablty, n COCOMO model. III. FUZZY LOGIC APPROACH Snce fuzzy logc foundaton by Zadeh n 1965, t has been the subject of mportant nvestgatons [10]. It s a mathematcal tool for dealng wth uncertanty and also t provdes a technque to deal wth mprecson and nformaton granularty [11]. The purpose n ths secton s not to dscuss fuzzy logc n depth, but rather to present these parts of the subject that are necessary for understandng of ths paper and for comparng t wth Neuro-Fuzzy model. Fuzzy logc offers a partcularly convenent way to generate a keen mappng between nput and output spaces thanks to fuzzy rules natural expresson [12]. There are some major modules: frst stage transformed the classfcaton tables nto a contnuous classfcaton, ths process s called Fuzzfcaton [13]. These are then processed n fuzzy doman by nference engne based on knowledge base (rule base and data base) suppled by doman experts [14]. Fnally the process of translatng back fuzzy numbers nto sngle real world values s named Defuzzfcaton [13]. Here, the development tme of forty-one modules and for each module, couplng (Dhama), complexty (McCabe), and lnes of code metrcs were regstered, all programs were wrtten n Pascal, hence, module categores belong to 575

2 procedures or functons. The development tme of each of the forty-one modules were regstered ncludng fve phases: requrements understandng, algorthm desgn, codng, complng and testng. The statstcs and a bref descrpton related to each module are depcted n Table Ι whch s prepared by Lopez-Martn et al. [6]. TABLE I MODULES DESCRIPTION AND METRICS Module Descrpton MC DC LOC DT (mn) 1 Calculates t value Inserts a new element n a lnked lst 3 Calculates a value accordng to normal dstrbuton equaton 4 Calculates the varance Generates range square root Determnes both mnmum and maxmum values from a stored lnked lst 7 Turns each lnked lst value nto ts z value 8 Copes a lst of values from a fle to an array 9 Determnes party of a number Defnes segment lmts From two lsts (X and Y), returns the product of all x and y values 12 Calculates a sum from a vector and ts average 13 Calculates q values Generates the sum of a vector components 15 Calculates the sum of a vector values square 16 Calculates the average of the lnked lst values 17 Counts the number of lnes of code ncludng blanks and comments 18 Prnts values non zero of a lnked lst 19 Stores values nto a matrx Generates range square root Returns the number of elements n a lnked lst 22 Calculates the sum of odd segments (Smpson s formula) 23 Calculates the sum of par segments (Smpson s formula) 24 Generates the standard devaton of the lnked lst values 25 Returns the sum of square roots of a lst values 26 Prnts a matrx Calculates the sum of odd segments (Smpson s formula) 28 Calculates the sum of par segments (Smpson s formula) 29 Calculates the average of lnked lst values 30 Returns the sum of a lst of values 31 Generates the standard devaton of lnked lst values Prnts a lnked lst Calculates gamma value (G) Calculates the average of vector components 35 Calculates the range standard devaton 36 Calculates beta 1 value Returns the product between values of two vectors and the number of these pars 38 Counts commented lnes Reduces fnal matrx (accordng to Gauss method) 40 Reduces a matrx (accordng to Gauss method) 41 Counts blank lnes MC: McCabe Complexty, DC: Dhama Couplng, LOC: Lnes of Code, DT: Development Tme(mnutes) Implementng a fuzzy system requres that the dfferent categores of the dfferent nputs be presented by fuzzy sets, whch n turn s presented by membershp functons. A natural membershp functon type that readly comes to mnd s the trangular membershp functons [15]. A trangular MF s a three-pont (parameters) functon, defned by mnmum (a), maxmum (c) and modal (b) values, that s MF(a, b, c) where a b c. Ther scalar parameters (a, b, c) are defned as follows [2]: MF(x) = 0 f x < a MF(x) = 1 f x = b MF(x) = 0 f x > c Based on the correlaton of the varables, fuzzy rules can be formulated. Correlaton s the degree of relaton between two pars of varables whch vares from -1.0 to The equaton of the Correlaton Coeffcent s the followng [16]: n[ ( X. Y)] ( X)( Y) r = (1) [ n( X ) ( X) ][ n( Y ) ( Y) ] The result of computng Correlaton as shows n Table ΙΙ s ndcated that there s an acceptable correlaton between development tme (DT) and the next three metrcs: McCabe complexty (MC), Dhama couplng (DC), and lnes of code (LOC), because ther absolute values are hgher than 0.5 [6]. TABLE ΙΙ CORRELATION BETWEEN VARIABLES Par r Par r MC_DC DT_MC MC_LOC DT_DC DC_LOC DT_LOC For example the absolute value of correlaton between DT and DC s hgher than 0.5, therefore f one of them be low another one should be low too. So by usng Table ΙΙ, sx rules are derved [6]: 1. If Complexty s low and Sze(LOC) s small then DT s low 2. If Complexty s average and Sze(LOC) s medum then DT s average 3. If Complexty s hgh and Sze(LOC) s bg then DT s hgh 4. If Couplng s low then DT s low 5. If Couplng s average then DT s average 576

3 6. If Couplng s hgh then DT s hgh (a). McCabe Complexty Plot (nput) (b). Dhama Couplng Plot (nput) (c). Physcal Lnes of Code Plot (nput) IV. NEURAL NETWORK MODEL In recent years, a number of studes have used neural networks n varous stages of software development [13]. Artfcal neural network are used n estmaton due to ts ablty to learn from prevous data. In addton, t has the ablty to generalze from the tranng data set thus enablng t to produce acceptable result for prevously unseen data [7]. Artfcal neural networks can model complex non-lnear relatonshps and approxmate any measurable functon so t s very useful n problems where there s a complex relatonshp between nputs and outputs [14], [9]. When lookng at a neural network, t mmedately comes to mnd that actvaton functons are look lke fuzzy membershp functon [3]. Generally the radal bass functon networks enjoy faster convergence than back-propagaton networks [3]. So Radal Bass Functon (RBF) model was used here. There are many technques for tranng a neural network. The man technques employed by neural networks are supervsed and unsupervsed learnng [8]. RBF s n supervsed category and fnds a surface that best fts to gven tranng data. Supervsed tranng works n much the same way as a human learns new sklls, by showng the network a seres of examples [8]. Dataset s randomly dvded nto two parts: 25 of them are for tranng and all of them are used for valdaton. By MATLAB 7.4, RBF network was created, data were normalzed between 0 and 1, and test data were appled nto network. The results of ths mplementaton are gathered n Table ΙΙΙ. V. NEURO-FUZZY SYSTEM The hybrdzaton of neural networks and fuzzy logc s the basc dea behnd the neuro-fuzzy system. Neuro-fuzzy hybrdzaton s done n two ways [17]: fuzzy neural networks (FNN) and neuro-fuzzy systems (NFS). FNN s a neural network equpped wth the capablty of handlng fuzzy nformaton. NFS s a fuzzy system augmented by neural networks to enhance some characterstcs lke flexblty and adaptablty [18], [19], [20]. Ths paper s based on the second approach. Here Takag-Sugeno neuro-fuzzy system was used whch makes use of a mxture of back propagaton to learn the membershp functons and least mean square estmaton to determne the coeffcents of the lnear combnaton n the rule s conclusons. The Takag-Sugeno neuro-fuzzy system schema s depcted n Fg. 2 [21]: (d). Development Tme Plot (output) Fg. 1 Inputs and Output Fuzzy Plots By usng trangular membershp functons, nput and output fuzzy membershp functons are shown n Fg

4 aggmethod: max was mplemented and the results are gven at Table ΙΙΙ. The Valdaton results of our experments are assessed by Mean Magntude Relatve Error (MMRE) as estmaton accuracy. MMRE s defned as [23]: = n = n 1 T T 1 MMRE = ( ) = MRE (5) n = 1 T n = 1 Where there are n projects; T s the Actual Tme, and T s the Predcted Tme. Fg. 2 Takag-Sugeno Neuro_Fuzzy system Perhaps the frst ntegrated hybrd neuro-fuzzy model s ANFIS, and also due to Takag-Sugeno rules mplementaton n ANFIS, t has lowest Root Mean Square Error (RMSE) among the other Neuro-Fuzzy models. So ANFIS was used here for mplement neuro-fuzzy model and Its archtecture s very smlar to Fg. 2. In ANFIS, the adaptaton (learnng) process s only concerned wth parameter level adaptaton wthn fxed structures [21]. The objectve of the parameter-learnng phase s to adjust parameters of the fuzzy nference system (FIS) such that the error functon durng tranng dataset, reaches mnmum or s less than a gven threshold [22]. When Gaussan membershp functons were used, operatonally ANFIS can be compared wth a radal bass functon network. Our model was just traned at 20 epochs, also the prevous tranng and testng data were used. The detaled functonng of each layer s as follows [21]: layer1, 2, 3 functons the same way as Mamdan FIS. Every node n layer 4 (rule strength normalzaton) calculates the rato of -th rule s frng strength to the sum of all rules frng strength: w w =, 1,2,... w + w = (2) 1 2 Every node n layer 5 (rule consequent layer) s wth a node functon: w f = w ( p x + q x + r ) (3) 1 2 w s the output of layer 4, and { } Where p, q, r s the parameter set. A well-establshed way to determne the consequent parameters s usng the least means squares algorthm. The sngle node n layer 6 (rule nference layer) computes the overall output as the summaton of all ncomng sgnals: w f (4) Overall output = w f = w By MATLAB, the ANFIS structure wth type: sugeno, and method: prod, or method: max, mpmethod: prod and TABLE ΙΙΙ THE MRE AND MMRE COMPARISON BETWEEN ESTIMATION MODELS Module Actual Fuzzy Logc Neural Network Neuro-Fuzzy DT MRE MRE MRE Fuzzy Logc Neural Network Neuro -Fuzzy MMRE VI. CONCLUSIONS AND FUTURE RESEARCH The paper suggests a new approach for estmatng of software projects development tme. The major dfference between our work and prevous works s that neuro-fuzzy technque s used for software development tme estmaton and then t s valdated wth gathered data. Here, the 578

5 advantages of neural network and fuzzy logc are combned and learnng ablty and good generalzaton are obtaned. The man beneft of ths model s ts good nterpretablty by usng the fuzzy rules and another great advantage of ths research s that t can put together expert knowledge (fuzzy rules) project data and the learnng ablty of neural network model nto one general framework that may have a wde range of applcablty n software estmaton. The results showed that neuro-fuzzy system s much better than two other mentoned methods (fuzzy logc and neural network). In order to acheve more accurate estmaton, votng the estmated values of several technques and combne ther results maybe be useful. [19] D. Nauck, A Fuzzy Perceptron as a Generc Model for Neuro-Fuzzy Approaches, In Proceedngs of Fuzzy-Systeme 94, 2 nd GI-Workshop, Munch, Semen Corporaton, [20] M.O. Salu, Adaptve Fuzzy Logc Based Framework for Software Development Effort Predcton, A Thess Presented to the DEANSHIP OF GRADUATE STUDIES, Kng Fahd Unversty of Petroleum & Mnerals Dhahran, Aprl [21] A. Abraham, Adaptaton of Fuzzy Inference System Usng Neural Learnng, Sprnger-Verlag Berln Hedelberg, 2005, pp [22] Y. Sh, M. Mzumoto, N.Yubazak, M. Otan, A Learnng Algorthm for Tunng Fuzzy Rules Based on the Gradent Descent Method, Proceedngs of Ffth IEEE Internatonal Conference on Fuzzy Systems (FUZZ-IEEE'96), New Orleans, USA, Vol.1, 1996, pp [23] V. Xa, L. F. Capretz, D. Ho, A Neuro-Fuzzy Model for Functon Pont Calbraton, WSEAS Transactons on Informaton Scence & Applcatons, Vol. 5, Issue 1, 2008, pp REFERENCES [1] H. Park, S. Baek, An emprcal valdaton of a neural network model for software effort estmaton, Expert Systems wth Applcatons, [2] C. Lopez-Martn, C.Yanez-Marquez, A.Guterrez-Tornes, Predctve accuracy comparson of fuzzy models for software development effort of small programs, The journal of systems and software, Vol. 81, Issue 6, 2008, pp [3] J. Jantzen, Neuro-fuzzy modelng, Report no 98-H-874, [4] W. Xa, L.F. Capretz, D. Ho, F.Ahmed, A new calbraton for functon pont complexty weghts, Informaton and Software Technology, Vol.50, Issue 7-8, 2007, pp [5] M. Jorgensen, B. Faugl, T. Gruschke, Characterstcs of software engneers wth optmstc predcton, Journal of Systems and Software, Vol. 80, Issue. 9, 2007, pp [6] C.L. Martn, J.L. Pasquer, M.C. Yanez, T.A. Guterrez, Software Development Effort Estmaton Usng Fuzzy Logc: A Case Study, IEEE Proceedngs of the Sxth Mexcan Internatonal Conference on Computer Scence (ENC 05), 2005, pp [7] M.T. Su, T.C.Lng, K.K.Phang, C.S.Lew, P.Y.Man, Enhanced Software Development Effort and Cost Estmaton Usng Fuzzy Logc Model, Malaysan Journal of Computer Scence, Vol. 20, No. 2, 2007, pp [8] A. Heat, Comparson of artfcal neural network and regresson models for estmatng software development effort, Informaton and Software Technology, Vol. 44, Issue 15, 2002, pp [9] X. Huang, Danny Ho, J. Ren, L.F. Capretz, Improvng the COCOMO model usng a neuro-fuzzy approach, Appled Soft Computng, Vol.7, Issue 1, 2007, pp [10] A. Idr, A.Abran, A Fuzzy Logc Based Set of Measures for Software Project Smlarty: Valdaton and Possble Improvements, Proceedngs of the seventh nternatonal software metrcs symposum (METRICS 01), 2001, pp [11] S.N. Svanandam, S. Sumath, S.N. Deepa, Introducton to fuzzy logc usng MATLAB, Sprnger, [12] A. Lotf Zadeh, From Computng wth Numbers to Computng wth Words From Manpulaton of Measurements to Manpulaton of Perceptons, IEEE Transactons on Crcuts and Systems, Fundamental Theory and Applcatons, Vol. 45, No 1, 1999, pp [13] M.R.Braz & S.R.Verglo, Usng Fuzzy Theory for Effort Estmaton of Object-Orented Software, Proceedngs of the 16 th IEEE nternatonal Conference on Tools wth Artfcal Intellgence (ICTAI 2004), 2004, pp [14] K.K.Aggarwal, Y.Sngh, P.Chandra, M.Pur, Senstvty Analyss of Fuzzy and Neural Network Models, ACM SIGSOFT Software Engneerng Notes, Vol. 30, Issue 4, 2005, pp [15] A.A. Moataz, O.S.Moshood, A.Jarallah, Adaptve fuzzy-logc-based framework for software development effort predcton, Informaton and Software Technology, Vol. 47, Issue 1, 2005, pp [16] W.S. Humphrey, A Dscplne for Software Engneerng, Addson Wesley, [17] S. Mtra, Y.Hayash, Neuro-Fuzzy Rule Generaton: Survey n Soft Computng Framework, IEEE Transactons on Neural Networks, Vol.11, No.3, 2000, pp [18] D. Nauck, F. Klawonn, R. Kruse, Foundatons of Neuro-Fuzzy Systems, Wley, Chchester, Venus Marza was born 1984, n Tehran, Iran. She got her BSc n software engneerng from Islamc Azad Unversty of North Tehran Branch, Tehran, Iran, n She s now an MSc student at the Azad Unversty of South Tehran Branch, Tehran, Iran. Luz F. Capretz has over 22 years of experence n the software engneerng feld as a practtoner, manager and educator. Before jonng the Unversty of Western Ontaro, n Canada, he has worked snce 1981 at both the techncal and manageral levels, taught and carred out research on the engneerng of software n Brazl, Argentna, England and Japan. He was the Drector of Informatcs and Coordnator of the computer scence program at two unverstes (UMC and COC) n the State of Sao Paulo/Brazl. He has authored and co-authored over 50 peer-revewed research papers on software engneerng n leadng nternatonal journals and conference proceedngs, and has co-authored the book, Object-Orented Software: Desgn and Mantenance, publshed by World Scentfc. Hs current research nterests are software engneerng (SE), human factors n SE, software estmaton, software product lnes, and software engneerng educaton. Dr. Capretz receved hs PhD from the Unversty of Newcastle upon Tyne (U.K.), MSc from the Natonal Insttute for Space Research (INPE-Brazl), and BSc from UNICAMP (Brazl). He s a senor member of IEEE. 579