Improving Software Effort Estimation Using Neuro-Fuzzy Model with SEER-SEM

a g e 52 Vol. 0 Issue 2 (Ve..0) Octobe 200 Global Jounal of Compute Science and Technology Impoving Softwae Effot Estimation Using Neuo-Fuzzy Model with SEER-SEM Abstact - Accuate softwae development effot estimation is a citical pat of softwae pojects. Effective development of softwae is based on accuate effot estimation. Although many techniques and algoithmic models have been developed and implemented by pactitiones, accuate softwae development effot pediction is still a challenging endeavo in the field of softwae engineeing, especially in handling uncetain and impecise inputs and collinea chaacteistics. In ode to addess these issues, pevious eseaches developed and evaluated a novel soft computing famewok. The aims of ou eseach ae to evaluate the pediction pefomance of the poposed neuo-fuzzy model with System Evaluation and Estimation of Resouce Softwae Estimation Model (SEER- SEM) in softwae estimation pactices and to apply the poposed achitectue that combines the neuo-fuzzy technique with diffeent algoithmic models. In this pape, an appoach combining the neuo-fuzzy technique and the SEER-SEM effot estimation algoithm is descibed. This poposed model possesses positive chaacteistics such as leaning ability, deceased sensitivity, effective genealization, and knowledge integation fo intoducing the neuo-fuzzy technique. Moeove, continuous ating values and linguistic values can be inputs of the poposed model fo avoiding the lage estimation deviation among simila pojects. The pefomance of the poposed model is accessed by designing and conducting evaluation with published pojects and industial data. The evaluation esults indicate that estimation with ou poposed neuo-fuzzy model containing SEER-SEM is impoved in compaison with the estimation esults that only use SEER- SEM algoithm. At the same time, the esults of this eseach also demonstate that the geneal neuo-fuzzy famewok can function with vaious algoithmic models fo impoving the pefomance of softwae effot estimation. Keywods softwae estimation, softwae management, softwae effot estimation, neuo-fuzzy softwae estimation, SEER-SEM T I. INTRODUCTION he cost and delivey of softwae pojects and the quality of poducts ae affected by the accuacy of softwae effot estimation. In geneal, softwae effot estimation techniques can be subdivided into expeience-based, paametic model-based, leaning-oiented, dynamics-based, egession-based, and composite techniques (Boehm, Abts, About - Wei Lin Du, the Depatment of Electical and Compute Engineeing, the Univesity of Westen Ontaio, London, Ontaio, Canada N6A 5B9(email: wdu6@uwo.ca) About 2 - Danny Ho, NFA Estimation Inc., Richmond Hill, Ontaio Canada L4C 0A2(email: danny@nfa-estimation.com) About 3 -D. Luiz Fenando Capetz, the Depatment of Electical and Compute Engineeing, the Univesity of Westen Ontaio, London, Ontaio, Canada N6A 5B9 (telephone: -59-66-2 ext. 85482 email: lcapetz@eng.uwo.ca) Wei Lin Du, Danny Ho 2, Luiz Fenando Capetz 3 GJCST Classification (FOR) D.2.9, K.6.3, K.6.4 and Chulani 2000). Amongst these methods, model-based estimation techniques involve the use of mathematical equations to pefom softwae estimation. The estimation effot is a function of the numbe of vaiables, which ae factos impacting softwae cost (Boehm 98). These model-based estimation techniques compise the geneal fom: E a Size b, whee E is the effot, size is the poduct size, a is the poductivity paametes o factos, and b is the paametes fo economies o diseconomies (Fischman, McRitchie, and Galoath 2005; Jensen, utnam, and Roetzheim 2006). In the past decades, some impotant softwae estimation algoithmic models have been published by eseaches, fo instance Constuctive Cost Model (COCOMO) (Boehm et al. 2000), Softwae Life-cycle Management (SLIM) (utnam and Myes 992), SEER- SEM (Galoath and Evans 2006), and Function oints (Albecht 979; Jones 998). Model-based techniques have seveal stengths, the most pominent of which ae objectivity, epeatability, the pesence of suppoting sensitivity analysis, and the ability to calibate to pevious expeience (Boehm 98). On the othe hand, these models also have some disadvantages. One of the disadvantages of algoithmic models is the lack of flexibility in adapting to new ccumstances. The new development envonment usually entails a unique situation, esulting in impecise inputs fo estimation by an algoithmic model. As a apidly changing business, the softwae industy often faces the issue of instability and hence algoithmic models can be quickly outdated. The outputs of algoithmic models ae based on the inputs of size and the atings of factos o vaiables (Boehm 98). Hence, incoect inputs to such models, esulting fom outdated infomation, cause the estimation to be inaccuate. Anothe dawback of algoithmic models is the stong collineaity among paametes and the complex non-linea elationships between the outputs and the contibuting factos. SEER-SEM appeals to softwae pactitiones because of its poweful estimation featues. It has been developed with a combination of estimation functions fo pefoming vaious estimations. Ceated specifically fo softwae effot estimation, the SEER-SEM model was influenced by the famewoks of utnam (utnam and Myes 992) and Doty Associates (Jensen, utnam, and Roetzheim 2006). As one of the algoithmic estimation models, SEER-SEM has two main limitations on effot estimation. Fst, thee ae ove 50 input paametes elated to the vaious factos of a poject, which inceases the complexity of SEER-SEM, especially fo managing the uncetainty fom these outputs. Second, the specific details of SEER-SEM incease the difficulty of discoveing the nonlinea elationship between the

Global Jounal of Compute Science and Technology Vol. 0 Issue 2 (Ve..0) Octobe 200 a g e 53 paamete inputs and the coesponding outputs. Oveall, these two majo limitations can lead to a lowe accuacy in effot estimation by SEER-SEM. The estimation effot is a function of the numbe of vaiables, which ae factos impacting softwae cost (Boehm 98). These model-based estimation techniques compise the geneal fom: E a Size b, whee E is the effot, size is the poduct size, a is the poductivity paametes o factos, and b is the paametes fo economies o diseconomies (Fischman, McRitchie, and Galoath 2005; Jensen, utnam, and Roetzheim 2006). In the past decades, some impotant softwae estimation algoithmic models have been published by eseaches, fo instance Constuctive Cost Model (COCOMO) (Boehm et al. 2000), Softwae Life-cycle Model (SLIM) (utnam and Myes 992), SEER-SEM (Galoath and Evans 2006), and Function oints (Albecht 979; Jones 998). Model-based techniques have seveal stengths, the most pominent of which ae objectivity, epeatability, the pesence of suppoting sensitivity analysis, and the ability to calibate to pevious expeience (Boehm 98). On the othe hand, these models also have some disadvantages. One of the disadvantages of algoithmic models is the lack of flexibility in adapting to new ccumstances. The new development envonment usually entails a unique situation, esulting in impecise inputs fo estimation by an algoithmic model. As a apidly changing business, the softwae industy often faces the issue of instability and hence algoithmic models can be quickly outdated. The outputs of algoithmic models ae based on the inputs of size and the atings of factos o vaiables (Boehm 98). Hence, incoect inputs to such models, esulting fom outdated infomation, cause the estimation to be inaccuate. Anothe dawback of algoithmic models is the stong collineaity among paametes and the complex non-linea elationships between the outputs and the contibuting factos. SEER-SEM appeals to softwae pactitiones because of its poweful estimation featues. It has been developed with a combination of estimation functions fo pefoming vaious estimations. Ceated specifically fo softwae effot estimation, the SEER-SEM model was influenced by the famewoks of utnam (utnam and Myes 992) and Doty Associates (Jensen, utnam, and Roetzheim 2006). As one of the algoithmic estimation models, SEER-SEM has two main limitations on effot estimation. Fst, thee ae ove 50 input paametes elated to the vaious factos of a poject, which inceases the complexity of SEER-SEM, especially fo managing the uncetainty fom these outputs. Second, the specific details of SEER-SEM incease the difficulty of discoveing the nonlinea elationship between the paamete inputs and the coesponding outputs. Ou study attempts to educe the negative impacts of the above majo limitations of the SEER-SEM effot estimation model on pediction accuacy and make contibutions towads esolving the poblems caused by the disadvantages of algoithmic models. Fst, fo accuately estimating softwae effot the neual netwok and fuzzy logic appoaches ae adopted to ceate a neuo-fuzzy model, which is subsequently combined with SEER-SEM. The Adaptive Neuo-Fuzzy Infeence System (ANFIS) is used as the achitectue of each neuo-fuzzy sub-model. Second, this eseach is anothe evaluation fo effectiveness of the geneal model of neuo-fuzzy with algoithmic model poposed by the pevious studies. Thd, the published data and industial poject data ae used to evaluate the poposed neuo-fuzzy model with SEER-SEM. Although the data was collected specifically fo COCOMO 8 and COCOMO 87, they ae tansfeed fom COCOMOs to COCOMO II and then to the SEER-SEM paamete inputs, utilizing the guidelines fom the Univesity of Southen Califonia (USC) (Madachy, Boehm, and Wu 2006; USC Cente fo Softwae Engineeing 2006). Afte the tansfe of this data, the estimation pefomance is veified to ensue its feasibility. II. BACKGROUND Soft computing, which is motivated by the chaacteistics of human easoning, has been widely known and utilized since the 960s. The oveall objective fom this field is to achieve the toleance of incompleteness and to make decisions unde impecision, uncetainty, and fuzziness (Nauck, Klawonn, and Kuse 997; Nguyen, asad, Walke, and Walke 2003). Because of capabilities, soft computing has been adopted by many fields, including engineeing, manufactuing, science, medicine, and business. The two most pominent techniques of soft computing ae neual netwoks and fuzzy systems. The most attactive advantage of neual netwoks is the ability to lean fom pevious examples, but it is difficult to pove that neual netwoks ae woking as expected. Neual netwoks ae like black boxes to the extent that the method fo obtaining the outputs is not evealed to the uses (Chulani 999; Jang, Sun, and Mizutani 997). The obvious advantages of fuzzy logic ae easy to define and undestand an intuitive model by using linguistic mappings and handle impecise infomation (Gay and MacDonell 997; Jang, Sun, and Mizutani 997). On the othe hand, the dawback of this technique is that it is not easy to guaantee that a fuzzy system with a substantial numbe of complex ules will have a pope degee of meaningfulness (Gay and MacDonell 997). In addition, the stuctue of fuzzy if-then ules lacks the adaptability to handle extenal changes (Jang, Sun, and Mizutani 997). Although neual netwoks and fuzzy logic have obvious stengths as independent systems, the disadvantages have pompted eseaches to develop a hybid neuo-fuzzy system that minimizes these limitations. Specifically, a neuo-fuzzy system is a fuzzy system that is tained by a leaning algoithm deived fom the neual netwok theoy (Nauck, Klawonn, and Kuse 997). Jang s (Jang, Sun, and Mizutani 997; Nauck, Klawonn, and Kuse 997) ANFIS is one type of hybid neuo-fuzzy system, which is composed of a five-laye feed-fowad netwok achitectue. Soft computing is especially impotant in softwae cost estimation, paticulaly when dealing with uncetainty and with complex elationships between inputs and outputs. In the 990 s a soft computing technique was intoduced to build softwae estimation models and impove pediction pefomance (Damiani, Jain, and Madavio 2004). As a

a g e 54 Vol. 0 Issue 2 (Ve..0) Octobe 200 technique containing the advantages of the neual netwoks and fuzzy logic, the neuo-fuzzy model was adopted fo softwae estimation. Reseaches developed some models with the neuo-fuzzy technique and demonstated the ability to impove pediction accuacy. Hodgkinson and Gaatt (Hodgkinson and Gaatt 999) intoduced the neuo-fuzzy model fo cost estimation as one of the impotant methodologies fo developing non-algoithmic models. The model did not use any of the existing pediction models, as the inputs ae size and duation, and the output is the estimated poject effot. The clea elationship between Function oints Analysis (FA) s pimay component and effot was demonstates by Aban and Robillad s study (Aban and Robillad 996). Huang et al. (Huang, Ho, Ren, and Capetz 2005 and 2006) poposed a softwae effot estimation model that combines a neuofuzzy famewok with COCOMO II. The paamete values of COCOMO II wee calibated by the neuo-fuzzy technique in ode to impove its pediction accuacy. This study demonstated that the neuo-fuzzy technique was capable of integating numeical data and expet knowledge. And the pefomance of RED(20%) and RED(30%) wee impoved by moe than 5% and % in compaison with that of COCOMO 8. Xia et al. (Xia, Capetz, Ho, and Ahmed 2008) developed a Function oint (F) calibation model with the neuo-fuzzy technique, which is known as the Neuo-Fuzzy Function oint (NFF) model. The objectives of this model ae to impove the F complexity weight systems by fuzzy logic, to calibate the weight values of the unadjusted F though the neual netwok, and to poduce a calibated F count fo moe accuate measuements. Oveall, the evaluation esults demonstated that the aveage impovement fo softwae effot estimation accuacy is 22%. Wong et al. (Wong, Ho, and Capetz 2008) intoduced a combination of neual netwoks and fuzzy logic to impove the accuacy of backfing size estimates. In this case, the neuo-fuzzy appoach was used to calibate the convesion atios with the objective of educing the magin of eo. The study compaed the calibated pediction model against the default convesion atios. As a esult, the calibated atios still pesented the invese cuve elationship between the pogamming languages level and the SLOC/F, and the accuacy of the size estimation expeienced a small degee of impovement. III. A NEURO-FUZZY SEER-SEM MODEL A. A Geneal Soft Computing Famewok fo Softwae Estimation This section descibes a geneal soft computing famewok fo softwae estimation, which is based on the unique achitectue of the neuo-fuzzy model descibed in the patent US-7328202-B2 (Huang, Ho, Ren, and Capetz 2008) and was built by Huang et al. (Huang, Ho, Ren, and Capetz 2006). The famewok is composed of inputs, a neuo-fuzzy bank, coesponding values of inputs, an algoithmic model, and outputs fo effot estimation, as depicted in Fig.. Among the components of the poposed famewok, the neuo-fuzzy bank and the algoithmic model ae the majo Global Jounal of Compute Science and Technology pats of the model. The inputs ae ating levels, which can be continuous values o linguistic tems such as Low, Nominal, o High. V,,Vn ae the non-ated values of the softwae estimation algoithmic model. On the othe hand, AI 0,, AI m ae the coesponding adjusted quantitative paamete values of the ating inputs, which ae the inputs of the softwae estimation algoithmic model fo estimating effot as the final output. Fig.. A Geneal Soft Computing Famewok. This novel famewok has attactive attibutes, paticulaly the fact that it can be genealized to many diffeent situations and can be used to ceate moe specific models. In fact, its genealization is one of the puposes of designing this famewok. Its implementation is not limited to any specific softwae estimation algoithmic model. The algoithmic model in the famewok can be one of the cuent popula algoithmic models such as COCOMO, SLIM o SEER-SEM. When vaious algoithmic models ae implemented into this famewok, the inputs and the nonating values ae diffeent. B. SEER-SEM Effot Estimation Model SEER-SEM stemmed fom the Jensen softwae model in the late 970s, whee it was developed at the Hughes Acaft Company s Space and Communications Goup (Fischman, McRitchie, and Galoath 2005; Galoath and Evans 2006; Jensen, utnam, and Roetzheim 2006). In 988, Galoath Inc. (GAI) stated developing SEER-SEM (Galoath and Evans 2006), and in 990, GAI tademaked this model. The SEER-SEM model was motivated by utnam s SLIM and Boehm s COCOMO (Fischman, McRitchie, and Galoath 2005; Galoath and Evans 2006; Jensen, utnam, and Roetzheim 2006). Ove the span of a decade, SEER-SEM has been developed into a poweful and sophisticated model, which contains a vaiety of tools fo pefoming diffeent estimations that ae not limited to softwae effot. SEER- SEM includes the beakdown stuctues fo vaious tasks, poject life cycles, platfoms, and applications. It also includes the most development languages, such as the thd and fouth geneation pogamming languages, in the estimation. Futhemoe, the uses can select diffeent knowledge bases (KBs) fo latfom, Application, Acquisition Method, Development Method, Development Standad, and Class based on the equements of the pojects. SEER-SEM povides the baseline settings fo paametes accoding to the KB inputs; thee ae ove 50 paametes that impact the estimation outputs. Among them, 34 paametes ae used by SEER-SEM effot estimation

Global Jounal of Compute Science and Technology Vol. 0 Issue 2 (Ve..0) Octobe 200 a g e 55 model (Galoath Incopoated 200 and 2006). Nevetheless, the SEER-SEM model contains some disadvantages. Fo instance, the effots spent on pespecification phases, such as equements collection, ae not included in the effot estimation. In SEER-SEM effot estimation, each paamete has sensitivity inputs, with the atings anging fom Vey Low (VLo-) to Exta High (EHi+). Each main ating level is divided into thee subatings, such as VLo-, VLo, VLo+. These atings ae tanslated to the coesponding quantitative value used by the effot estimation calculation. The SEER-SEM effot estimation is calculated by the following equations: E 0. 393469 Ctb K 2000 D 0.4 exp ( S C e te K ctbx 3.70945 ln 4. 5 TURN ).2, C te C tb amadjustment ctbx ACA AEXAL MOD CA TOOL TERM (4) amadjustment LANGLEX TSYSTEX DSYSDEX SYSEX S IBRREUS MULT RDED RLOC DSVL SVL RV OL SEC TEST QUAL RHST(HOST) DIS ME MC TIMC RTIM SECR TSVL (5) whee, E is the development effot (in peson yeas), K is the total Life-cycle effot (in peson yeas) including development and maintenance, The elements included in equations (4) and (5) ae paametes o combined paametes; the fomulas fo calculating combined paametes ae shown below: AEXAL 0.82+(0.47*EX(-0.95977*(AEX/AL))) (6) LANGLEX +((.+0.085*LANG)-)*EX(-LEX/(LANG/3)) (7) TSYSTEX +(0.035+0.025*TSYS)*EX(-3*TEX/TSYS) (8) DSYSDEX +(0.06+0.05*DSYS)*EX(-3*DEX/DSYS) (9) (2) (3) () SYSEX (0.9^ SYS when SYS, when SYS SIBRREUS SIBR*REUS + 0.23 * SYS* EX(-3* EX /SYS))^0.833, 0 0 C. A Neuo-Fuzzy Model with SEER-SEM a) Oveview (0) () This section will descibe the poposed famewok of the neuo-fuzzy model with SEER-SEM, based on the geneal stuctue in the section III.A, as depicted in Fig. 2. The inputs consist of two pats: non-ating inputs and the ating levels of paametes, which include 34 technology and envonment paametes and complexity o staffing paamete. Among the technology and envonment paametes, thee is one paamete (SIBR), which is not ated by the linguistic tem. SIBR is decided by uses, though inputting the pecentage. Hence, simila to the input of size, SIBR is a non-ating value. While the othe paametes ae labeled as R to R 34, SIBR is labeled R 35. Fig.2. A Neuo-Fuzzy Model with SEER-SEM. Each paamete Ri (i,, 34) can be a linguistic tem o a continuous ating value. The linguistic inputs ae fom 8 ating levels (,, 8), which include Vey Low (VLo-), Vey Low (VLo), Vey Low+ (VLo+), Low, Low, Low+, Nominal- (Nom-), Nominal (Nom), Nominal+ (Nom+), High (Hi-), High (Hi), High+ (Hi+), Vey High (VHi-), Vey High (VHi), Vey High+ (VHi+), Exta High (EHi-), Exta High (EHi), and Exta High+ (EHi+). In these atings, thee ae 6 main levels, VLo, Low, Nom, Hi, VHi, and EHi, and each main ating level has thee sub-levels: minus, plus o neutal (Galoath Incopoated 2006 be 2005). NFi (i,, 34) is a neuo-fuzzy bank, which is composed of thty-fou NFi sub-models. The ating levels of each paamete Ri (i,, 34) ae the input of each NFi. Though these sub-models, the ating level of a paamete is tanslated into the coesponding quantitative value (i, i,, 34) as the inputs of the SEER-SEM effot estimation as intoduced in the section III.B, fom

age 56 Vol. 0 Issue 2 (Ve..0) Octobe 200 equations () to (). The output of the poposed model is the softwae effot estimation. b) Stuctue of NF i Global Jounal of Compute Science and Technology function; in ou poposed model, all the membeship functions of each node in Laye ae the same. In subsequent sections, the selected membeship function will be discussed in detail. O µ A ( R fo i, 2,, 34 ), 2,, 8 (2) i Fig.3. Stuctue of NF i. The neuo-fuzzy bank fulfills an impotant function in the poposed neuo-fuzzy model with SEER-SEM effot estimation model. NF i poduces fuzzy sets and ules fo taining datasets. It tanslates the ating levels of a paamete into a quantitative value and calibates the value by using actual poject data. Accoding to fuzzy logic techniques, linguistic tems can be pesented as a fuzzy set. Thee ae 8 ating levels fo each paamete in linguistic tems, which ae used to define a fuzzy set in this eseach. The selected membeship function tanslates the linguistic tems in this fuzzy set to membeship values. Each NF i uses the stuctue of the Adaptive Neuo-Fuzzy Infeence System (ANFIS), which is a five-laye hybid neuo-fuzzy system, as depicted in Fig. 3. Input and Output of NF i Thee is one input and one coesponding output fo each NF. The input of each NF i (R i, i,, 34) is the ating level of a paamete fo SEER-SEM effot estimation model, such as Vey Low (VLo) o High (Hi). On the othe hand, the output is the coesponding quantitative value of this paamete ( i, i,, 34), such as.30. Fuzzy Rule Based on the featues of ANFIS and the stuctue shown in Fig. 3, this wok efes to the fom of the fuzzy if-then ule poposed by Takagi and Sugeno (Takagi and Sugeno 986). The th fuzzy ule of the poposed model is defined as below: Fuzzy Rule : IF R i is A THEN i,, 2,, 8 whee A is a ating level of the fuzzy set that anges fom Vey Low- to Exta High+ fo the ith paamete and is chaacteized by the selected membeship function, and is the coesponding quantitative value of the th ating level fo the ith paamete. Futhemoe, with this fuzzy ule, the pemise pat is the fuzzy set and the consequent pat is the non-fuzzy value. Oveall, the fuzzy ules build the links between a linguistic ating level and the coesponding quantitative value of a paamete. Functions of Each Laye Laye : In this laye, the membeship function of fuzzy set A tanslates the input, R i, to the membeship gade. The output of this laye is the membeship gade of R i, which is the pemise pat of fuzzy ules. Also, the membeship function of the nodes in this laye is utilized as the activation whee O i is the membeship gade of A (VLo-, VLo, k VLo+, Low-, Low, Low+, Nom-, Nom, Nom+, Hi-, Hi, Hi+, VHi-, VHi, VHi+, EHi-, EHi, o EHi+) with the input R i o µ A continuous numbe x [ 0,9] ; is the membeship function of A. Laye 2: oducing the fing stength is the pimay function of this laye. The outputs of Laye ae the inputs of each node in this laye. In each node, Label Π multiplies all inputs to poduce the outputs accoding to the defined fuzzy ule fo this node. Consequently, the outputs of this laye ae the fing stength of a ule. The pemise pat in the defined fuzzy ule of ou poposed model is only based on one condition. Theefoe, the output of this laye, the fing stength, is not changed and is thus the same as the inputs, o membeship gade. 2 O w O ( R ) µ i (3) A Laye 3: The function of this laye is to nomalize the fing stengths fo each node. Fo each node, labeled "N", the atio of the th ule s fing stength to the sum of all ules fing stengths elated to Ri is calculated. The esulting outputs ae known as nomalized fing stengths. O 3 w 8 w w (4) Laye 4: An adaptive esult of i is calculated with the Laye 3 outputs and the oiginal input of i in the fuzzy ules by multiplying. The outputs ae efeed to as w consequent paametes. 4 (5) O w Laye 5: This laye aims to compute the oveall output with the sum of all easoning esults fom Laye 4. O 5 4 O i w (6) Membeship Function This section descibes the tiangula membeship function utilized in this wok; this paticula function is depicted in Fig. 4. Each ating level has the coesponding tiangula membeship function. This membeship function is a piecewise-linea function. Thoughout the leaning pocess, the membeship function is maintained in a fixed state. The following calculation defines the tiangula membeship function:

Global Jounal of Compute Science and Technology Vol. 0 Issue 2 (Ve..0) Octobe 200 a g e 57 x ( ), x µ ( x) ( + ) x, x + A (7) 0, othewise x [ 0,9] whee x R i o Membeshi p Degee fo, 2,, 8 0 Vl o- Vl o 2 Vl o+ 3 Low- 4 Low 5 Low+ 6 Nom- 7 Nom 8 Nom+ 9 Hi - 0 Hi Hi + 2 Vhi - 3 Vhi 4 Vhi + 5 Ehi - 6 Ehi 7 Ehi + 8 Thee ae seveal factos that influenced ou selection of the tiangula membeship function; fst, the natue of the NFi outputs was the most cucial eason. is a piecewise-linea intepolation y y x x 0 0 y y x x 0 0 between paamete values ( i, i8 ) of the ith paamete, i. Hence, the selection of the tiangula function can be deived fom the same esults as a linea intepolation. Secondly, one of the puposes of this eseach is to evaluate the extent to which Huang s poposed soft computing famewok can be genealized. Theefoe, it was impotant to use the same membeship function as that utilized in Huang s eseach in ode to pefom validation with a simila fuzzy logic technique (Huang 2003). Finally, the tiangula membeship function is easy to calculate. Leaning Algoithm With ANFIS, thee is a two-pass leaning cycle: the fowad pass and the backwad pass. The pass that is selected depends on the tained paametes in ANFIS. In ou poposed model, when the eo exists between the actual effot and the estimated effot, the outputs ae fixed and the inputs ae tained. Hence, the backwad pass is the type of leaning algoithm that this study uses. It is geneally a hybid method of Least Squae Estimate (LSE) and Back Fig.4. Tiangula Membeship Function opagation, which is calculated using a gadient decent algoithm that minimizes the eo. Fo the leaning algoithm, the paametes of the pemise pat and the consequent pat ae defined in two sets, as illustated below: X {x, x 2,..., xn} {R, R 2,..., R N, SIBR, Size} (8) {{, 2,, N }, { 2, 22,, N2 },, { M, 2M,, NM }} (9) whee N 34 and M 8; X epesents the inputs of the model, which ae the ating levels, SIBR and Size; and is the paamete values of the paametes. The output of each NF can be defined when substituting (3) and (4) into (6): f 8 ( ) ( ) w µ,..., i i, i2 i8 i NF i A fo i, 2,, 34 (20) i is the weighted sum of inputs X fo R i. In the section III.B, the equations fo the SEER-SEM Effot Estimation ae descibed in detail. The equations (), (2), (3), (4), and (5) can be e-witten as follows with the paametes symbols: x Effot.2 Size ctbx 3.70945 ln 4. exp 5 0 0.4 0.393469 34.2 amadjustment (2) 2000.2 ctbx 2-25 8 3 9 (22) amadjustment 23-4 3-6 24-5 26-7 35-22 2 2 27 30 33 32 (23).2

age 58 Vol. 0 Issue 2 (Ve..0) Octobe 200 Utilizing equations (8) to (2), the poposed neuo-fuzzy model can be witten: (24) If thee ae NN poject data points, the inputs and outputs can be pesented as (X n, E acn ), whee n, 2,, NN, X n contains 34 paametes as well as SIBR and Size, E aen is the actual effot with X n inputs fo poject n. The leaning pocedue involves adopting the gadient descent method to adjust the paamete values of ating levels that minimizes the eo, E. Accoding to LSE, the eo, E, on the output laye is defined as follows: (25) whee w n is the weight of poject n and E en is the estimation of the output fo poject n. (26) The following steps ae used to pefom gadient descent accoding to the Back opagation leaning algoithm. Accoding to the SEER-SEM effot estimation model pesented by equations (2) to (23), the esults of the patial deivative of E en with espect to, ( ) Effot f X, NF E E 2 NN w n n Effot E en E E acn f acn, ae diffeent. 2 ( X ) n n, en n NF E E E en NN wn 2 n Een E en i i en ( ) E Een E acn (27) fo i, 2,, 34 (28) i ( f E en ( NFi en ( f ( NF X n, n) ) i )) ( µ ( x A i ) ) µ ( x ) i A (29) Afte Global Jounal of Compute Science and Technology is calculated out, equation (30) is used to calculate the adjusted paamete values. l + l α E (30) whee α > 0 is the leaning ate and l is the cuent iteation index. Monotonic Constaints A monotonic function is a function that peseves the given ode. The paamete values of SEER-SEM ae eithe monotonic inceasing o monotonic deceasing. The elationship between the monotonic functions and the ating levels have been accepted by the pactitiones as a common sense pactice. Fo instance, the values of ACA ae monotonic deceasing fom VLo- to EHi+, which is easonable because the highe the analysts capability, the less spent on poject effots. As fo TEST, its values ae monotonic inceasing because the highe test level causes moe effot to be spent on pojects. Afte calibating paamete values by the poposed model, the tained esults of these values may contavene the monotonic odes, so that the tained values ae changed to a non-monotonic ode. Fo instance, the paamete value of the ACA ating Hi can be geate than the value of the coesponding ating, EHi. This discepancy can lead to uneasonable inputs fo pefoming estimation and can impact the oveall accuacy. Theefoe, monotonic constaints ae used by ou model in ode to maintain consistency with the ating levels. IV. EVALUATION Fo evaluating the neuo-fuzzy SEER-SEM model, in total, data fom 99 studies is collected, including 93 published COCOMO 8 pojects and 6 industy studies in the fomat of COCOMO 87 (Ho 996; anlilio-yap and Ho 2000). An algoithmic estimation model, E a Size b compises the geneal fom of COCOMO and SEER-SEM (Fischman, McRitchie, and Galoath 2005; Jensen, utnam, and Roetzheim 2006). Specifically, this model enables us to use the COCOMO database fo evaluating the poposed SEER- SEM model in spite of the diffeence between COCOMO and SEER-SEM. In fact, vaious studies have evealed the simila estimation pefomances of COCOMO and SEER- SEM (Madachy, Boehm, and Wu 2006; USC Cente fo Softwae Engineeing 2006).

Global Jounal of Compute Science and Technology Vol. 0 Issue 2 (Ve..0) Octobe 200 age 59 Fig. 5 shows the main steps of ou evaluation. Fst, in ode to use both published COCOMO 8 and industial poject data in the evaluation, the infomation was tanslated into the coesponding fomat of SEER-SEM data. Second, thee ae fou cases fo evaluating the pediction pefomance of ou neuo-fuzzy model. ) efomance Evaluation Metics The following evaluation metics ae adapted to assess and evaluate the pefomance of the effot estimation models. Relative Eo (RE) ( EstimationEffot ActualEffot) RE ActualEffot The RE is used to calculate the estimation accuacy. Magnitude of Relative Eo (MRE) EstimationEffot ActualEffot MRE ActualEffot Mean Magnitude of Relative Eo (MMRE) The MMRE calculates the mean fo the sum of the MRE of n pojects. Specifically, it is used to evaluate the pediction pefomance of an estimation model. ediction Level (RED) k RED ( L) n whee L is the maximum MRE of a selected ange, n is the total numbe of pojects, and k is numbe of pojects in a set of n pojects whose MRE < L. RED calculates the atio of pojects MREs that falls into the selected ange (L) out of the total pojects. (e.g. n 00, k 80, whee L MRE < 30%: RED(30%) 80/00 80%) Fig.5. Main Evaluation Steps. 2) Dataset Thee ae two majo steps in tansfeing data fom COCOMO 8 to SEER-SEM: fst, infomation is conveted fom COCOMO 8 to COCOMO II and then fom COCOMO II to SEER-SEM. The main guidelines ae efeed to (Madachy, Boehm, and Wu 2006; Reife, Boehm, and Chulani 999). In the method of the second step, 20 of the 34 SEER-SEM technical paametes can be dectly mapped to 4 COCOMO II cost dives and scale factos, COCOMO 8 cost dive, and 2 COCOMO 87 cost dives. The emainde of the SEER-SEM paametes cannot be tansfeed to the COCOMO model, and as a esult, they ae set up as nominal in SEER-SEM. Afte tansfeing 93 COCOMO 8 poject data points, the estimation pefomance with tansfeed data ae evaluated with the estimation pefomance metics. Table pesents the details of the pediction pefomance of COCOMO 8, COCOMO II, and SEER-SEM. Table. Estimation efomance with Tansfeed Data. Cocomo 8 Cocomo II See-sem Mme (%) 56.46 48.63 84.39 ed(20%) 36.56 37.63 36.56 ed(30%) 5.6 54.84 45.6 ed(50%) 76.34 78.49 56.99 ed(00%) 92.47 94.62 8.72 # of Outlies 22 20 39 The data tansfeing fom COCOMO 8 to COCOMO II keeps the vey close pefomance with little impovement when doing COCOMO II estimation with the tansfeed data. The tansfeing fom COCOMO II to SEER-SEM causes the MMRE deceasing and the outlies inceasing. Most of the new outlies come fom the embedded pojects whose MREs ae lowe than 50% befoe being tansfeed to SEER-SEM. The RED is still stable and thee is not a huge change. Oveall, tansfeing fom COCOMO 8 to SEER- SEM is feasible fo ou evaluation, especially when the actual poject data in the fomat of SEER-SEM ae difficult to obtain. We use the online calculato of the USC Cente fo Softwae Engineeing to pefom COCOMO 8 and

a g e 60 Vol. 0 Issue 2 (Ve..0) Octobe 200 COCOMO II estimation. We do SEER-SEM effot estimation by two methods. One is pefomed by the SEEM- SEM tool (SEER-SEM fo Softwae 7.3) which is offeed by GAI, and the othe is done manually by Micosoft Excel with the equations of SEER-SEM effot estimation model as pesented in the section III.B. The SEER-SEM effot estimation model is also implemented as pat of ou eseach because it is pat of ou poposed model. The estimation pefomance by the SEER-SEM tool and Excel ae vey close. This is a way to make sue the algoithm of SEER- SEM effot estimation pesented in this pape to be coect. We select the esults done manually to avoid the impact fom othe paametes settings in the SEER-SEM tool. The dataset of 6industial poject data points is fom the COCOMO 87 model, which is slightly diffeent than COCOMO 8, as the effot multiplies RUSE, VMVH (Host Volatility), and VMVT (Taget Volatility) ae not used in COCOMO 8. Howeve, RUSE can be tansfeed to COCOMO II dectly because it is one of the COCOMO II cost dives, and VMVH and VMVT can be tansfeed to the SEER-SEM paametes DSVL and TSVL. The est of COCOMO 87 cost dives ae matched to the coesponding cost dives of COCOMO 8. Then, they ae tansfeed to COCOMO II and SEER-SEM. 3) Evaluation Cases Afte tansfeing the data, we conducted fou main case studies to evaluate ou model. These cases, which used diffeent datasets fom 93 pojects, wee utilized to pefom taining on the paamete values. The 93 poject data points and the 6 industial poject data points wee adopted fo testing puposes. The oiginal SEER-SEM paamete values ae tained in each case. The leaned paamete values of the fou cases ae diffeent. This eason causes the pediction pefomance diffeence amongst the cases and the SEER- SEM. In ode to assess the pediction pefomance of the neuo-fuzzy model, we compaed SEER-SEM effot estimation model with ou famewok. Seveal pefomance metics wee used fo the analysis of each case, including MRE, MMRE, and RED. Accodingly, Table 2 pesents the MMRE esults fom Cases to 4, and Table 3 shows the MMRE esults of the industial poject data points. Table 4 Global Jounal of Compute Science and Technology shows the RED esults of Cases, 2, and 3. The RED esults of Case 4 ae pesented in Table 5.In the tables pesenting the analysis esults, we have included a column named Change, which is used to indicate the pefomance diffeence between SEER-SEM effot estimation model and ou neuo-fuzzy model. Fo the MMRE, the pediction pefomance impoves as the value becomes close to zeo; theefoe, if the change fo these pefomance metics is a negative value, the MMRE fo the neuo-fuzzy model is impoved in compaison with SEER-SEM. Additionally, the RED(L) in Table 4 epesent the pediction level of the selected ange, efeing to the definition pesented in the section IV.A; a highe pediction level indicates a geate level of pefomance fo RED. Fo RED, a negative value fo the Change indicates that ou model shows a deceased level of pefomance as compaed to SEER-SEM. Finally, the esults fo both MMRE and RED ae shown in a pecentage fomat. Table 2. MMRE of 93 ublished Data oints. Case ID SEER-SEM Validation Change C 84.39 6.05-23.35 C2 84.39 59. -25.28 C3 84.39 59.07-25.32 C4-50.49 39.5-0.98 C4-2 42.05 29.0-3.04 Table 3. MMRE of Industial oject Data oints. Case ID MMRE (%) SEER-SEM Industial Aveage Change C 37.54 35.54-2 C2 37.54 47.57 0.03 C3 37.54 47.6 9.62 C4-37.54 33.20-4.34 C4-2 37.54 30.39-7.5 SEER-SEM Table 4. RED of Cases, 2 and 3. Neuo-Fuzzy Model RED(L) RED (%) C C2 C3 RED (%) Change RED (%) Change RED (%) Change RED(20%) 36.65 29.03-7.62 5.05-2.6 5.05-2.6 RED(30%) 45.6 37.63-7.53 8.28-26.88 8.28-26.88 RED(50%) 56.99 64.52 7.53 36.56-20.43 38.7-8.28 RED(00%) 8.72 92.47 0.75 97.85 6.3 97.85 6.3

Global Jounal of Compute Science and Technology Vol. 0 Issue 2 (Ve..0) Octobe 200 a g e 6 Case (C): Leaning with poject data points excluding all outlies This case involved taining the paametes of pojects whee the MREs ae lowe than o equal to 50%. Thee ae 54 pojects that meet this equement. Since we wanted to pefom leaning without any impact fom the outlies, the leaning was done with 54 poject data points, while 93 pieces of poject data and the 6 industial poject data points wee used fo testing. When using the neuo-fuzzy model, the MMRE deceased fom 84.39% to 6.05%, with an oveall impovement of 23.35%. Afte testing data fom the 93 pojects, we used the 6 industial poject data points to pefom testing. The esults of this evaluation pesent the same tendency as the testing esults with the 93 poject data points: the MMRE of the neuo-fuzzy model is lowe than the MMRE of SEER-SEM by 2%. With the neuo-fuzzy model, RED(20%) and RED(30%) deceased by 7.62% and 7.53% in compaison to the same values using SEER-SEM; howeve, RED(50%) and RED(00%) impoved with the neuofuzzy model by a facto of 7.53% and 0.75% espectively, which indicates that the MRE of the neuo-fuzzy model, in compaison with that of SEER-SEM, contained moe outlies that wee less than 00% o 50%. Futhemoe, the MMRE was significantly impoved with the neuo-fuzzy model due to the incease of outlies that wee less than 00%. By integating the esults fom the MMRE, RED, and the industial poject data points, this calibation demonstates that the neuo-fuzzy model has the ability to educe lage MREs. Case 2 (C2): Leaning with all poject data including all outlies In Case 2, we used the data points fom all 93 pojects to calibate the neuo-fuzzy model without emoving the 39 outlies. The testing was pefomed with the same poject dataset used in the taining and with the 6 industial poject data points. In compaison to Case, this test attempted to ascetain the pediction pefomance when the leaning involved the outlies as well as the effects of the outlies on the calibation. the MMRE using SEER-SEM compaison to the MMRE using SEER-SEM. Nevetheless, the industial poject data points caused the MMRE to wosen with the neuo-fuzzy model by 0.03%. The esults of RED demonstate that RED(20%), RED(30%), and RED(50%) deceased by moe than 20%, while RED(00%) inceased by 6.3% with the neuo-fuzzy model. Moeove, these esults also indicate that the neuo-fuzzy model is effective fo impoving the MREs that ae geate than 00%. As a esult, the MMRE in all of the datasets ae impoved when the neuofuzzy model is utilized. In Cases and 2, the esults of RED and the 6 industial poject data points show that the neuofuzzy model causes lage inceases in small MREs while educing lage MREs. Hence, the decease of lage MREs leads to the oveall impovement of the MMRE, thus showing the effectiveness of the neuo-fuzzy model. Case 3 (C3): Leaning with poject data excluding pat of outlies Afte taining, which included and then excluded all of the outlies, Case 3 calibated the neuo-fuzzy model by emoving the top 2 of 39 outlies whee the MRE is moe than 50%. In this case, 87 poject data points ae used to pefom taining, and the 93 poject data points and the 6 industial poject data points ae used fo testing. The esults of Case 3 ae almost identical to the esults of MMRE and RED as demonstated in Case 2. Specifically, fo the neuo-fuzzy model, the MMRE of industial poject data points is wosened by 9.62%. Oveall, as compaed to Case 2, calibation excluding the top 2 outlies does not make a significant diffeence in the pefomance of the model. Case 4 (C4): Leaning with pat of poject data points In the pevious thee cases, all data points fom the 93 pojects wee used fo testing. Howeve, in Case 4, we used pat of this dataset to calibate the neuo-fuzzy model, and the est of the data points, along with the 6 industial poject data points, wee used fo testing. The objective of this case was to detemine the impact of the taining dataset size on the calibation esults. Table 2, Table 3, and Table 5 pesent the esults. Case 4 - (C4-): Leaning with 75% of poject data points and testing with 25% of poject data points This sub-case pefomed taining with 75% of the 93 poject data points and testing with the emaining 25% of these points. The poject numbes fo the taining data points anged fom 24 to 93, while those fo the testing points anged fom to 23 and also included the 6 industial poject data points. To analyze the esults, we compaed the pefomance of SEER- SEM to that of the neuo-fuzzy model fo ojects to 23. In this case, the neuo-fuzzy model impoved the MMRE by 0.98%. Futhemoe, RED(30%) and RED(00%) with ou model impoved by 4.35% and 8.70% espectively. Finally, with the neuo-fuzzy model, the MREs of all 23 poject data points wee within 00%. In this case, the testing esults of the industial poject data points ae impoved fom the pevious tests by 4.34%. These esults demonstate the effective pefomance of the neuo-fuzzy model in educing lage MREs. Case 4-2 (C4-2): Leaning with 50% of poject data points and testing with 50% of poject data points Case 4-2 divided the 93 poject data points into two subsets. The fst subset included 46 poject data points that ae numbeed fom to 46 and wee used to pefom testing. On

a g e 62 Vol. 0 Issue 2 (Ve..0) Octobe 200 Global Jounal of Compute Science and Technology the othe hand, the second subset contained 47 poject data points, numbeed fom 47 to 93, which wee used to tain the neuo-fuzzy model. In compaison to Case 4-, this test contains fewe taining data points and moe testing data points. Accodingly, we analyzed the pefomance esults of the 46 poject data points as estimated by both SEER-SEM and the neuo-fuzzy model. In this case, the MMRE impoved by 3.04% when using the neuo-fuzzy model. Specifically, the esults of RED showed impovement fom those in Case 4-; not only wee the MREs of all 46 poject data points within 00%, but the MREs of most poject data points wee also less than 50%. Futhemoe, in the testing that involved the 6 industial poject data points, the esults wee bette than those in Case 4-. Using the neuo-fuzzy appoach, the MMRE of the 6 industial poject data points impoved by 7.5%, which was the geatest impovement among all of the cases in this study. impovement. Howeve, the aveage of RED(00%) is inceased by 2.4%, which indicates that the neuo-fuzzy model impoves the pefomance of the MMRE by educing the lage MREs. Table 5. Summay of RED Aveage. SEER- SEM Aveage Validation RED(20%) 39.76% 27.48% RED(30%) 49.27% 36.46% of Change - 2.28% - 2.8% RED(50%) 62.02% 55.35% -6.67% RED(00%) 85.55% 97.69% 2.4% 4) EVALUATION SUMMARY In this section, we summaize the evaluation esults by compaing the analysis of all of the cases as pesented in the pevious sections. Fig. 6 shows the validation summay fo the mme acoss all of the cases. Specifically, the mme impoves in all of the cases, with the geatest impovement being ove 25%. 20.00% 00.00% 80.00% 60.00% 40.00% Summay of RED Validation SEER-SEM Validation 0.00% Summay of MMRE Validation 20.00% 0.00% RED(20%) Aveage RED(30%) Aveage RED(50%) Aveage RED(00%) Aveage MMRE and Change 90.00% 70.00% 50.00% SEER-SEM Validation 30.00% Change 0.00% -0.00% -30.00% C C2 C3 C4- C4-2 Aveage Fig.6. Summay of MMRE Validation. Fig.7. Summay of RED Validation Fig. 8 pesents the MMREs of industial poject data points fom all of the cases. The MMRE fom Cases and 4 demonstate an impovement of no moe than 7.5%. The calibations with the outlies in Cases 2 and 3 lowe the pediction pefomance of these two cases. Thus, fo the neuo-fuzzy model, the impovement of the MMRE of industial pojects is minimal. Table 6 illustates the RED aveages fo SEER-SEM in all of the cases, and Fig. 7 shows the RED aveages fo all of the cases using the neuo-fuzzy model. Compaed to the REDs fom SEER-SEM, the aveages of RED(20%), RED(30%), and RED(50%) with the neuo-fuzzy model do not show

Global Jounal of Compute Science and Technology Vol. 0 Issue 2 (Ve..0) Octobe 200 a g e 63 Fig.6. MMRE of Industial oject Data oints. V. CONCLUSION Oveall, ou eseach demonstates that combining the neuofuzzy model with the SEER-SEM effot estimation model poduces unique chaacteistics and pefomance impovements. Effot estimation using this famewok is a good efeence fo the othe popula estimation algoithmic models. The neuo-fuzzy featues of the model povide ou neuo-fuzzy SEER-SEM model with the advantages of stong adaptability with the capability of leaning, less sensitivity fo impecise and uncetain inputs, easy to be undestood and implemented, stong knowledge integation, and high tanspaency. Fou main contibutions ae povided by this study: a) ANFIS is a popula neuo-fuzzy system with the advantages of neual netwok and fuzzy logic techniques, especially the ability of leaning. The poposed neuo-fuzzy model can successfully manage the nonlinea and complex elationship between the inputs and outputs and it is able to handle input uncetainty fom the data. b) The involvement of fuzzy logic techniques impoves the knowledge integation of ou poposed model. Fuzzy logic has the ability to map linguistic tems to vaiables. Accodingly, the inputs of ou model ae not limited to linguistic tems and can also wok with numeical values. The defined fuzzy ules ae an effective method fo obtaining the expets undestanding and expeience to poduce moe easonable inputs. c) Thee ae two techniques intoduced in this eseach: the tiangula membeship function and the monotonic constaint. Tiangula Membeship Functions ae utilized to tanslate paamete values to membeship values. Futhemoe, monotonic constaints ae used in ode to peseve the given ode and maintain consistency fo the ating values of the SEER-SEM paametes. These techniques povide a good genealization fo the poposed estimation model. d) This eseach poves that the poposed neuo-fuzzy stuctue can be used with othe algoithmic models besides the COCOMO model and pesents futhe evidence that the geneal soft computing famewok can wok effective with vaious algoithmic models. The evaluation esults indicate that estimation with ou poposed neuo-fuzzy model containing SEER- SEM is moe efficient than the estimation esults that only use SEER-SEM effot estimation model. Specifically, in all fou cases, the MMREs of ou poposed model ae impoved ove the ones whee only SEER-SEM effot estimation model is used, and thee is moe than a 20% decease as compaed to SEER-SEM. Accoding to these esults, it is appaent that the neuo-fuzzy technology impoves the pediction accuacy when it is combined with the SEER-SEM effot estimation model, especially when educing the outlies of MRE >00%. Although seveal studies have aleady attempted to impove the geneal soft computing famewok, thee is still oom fo futue wok. Fst, the algoithm of the SEER-SEM effot estimation model is moe complex than that of the COCOMO model. io eseach that combines neuo-fuzzy techniques with the COCOMO model demonstates geate impovements in the pediction pefomance. Hence, the poposed geneal soft computing famewok should be evaluated with othe complex algoithms. Secondly, the datasets in ou eseach ae not fom the oiginal pojects whose estimations ae pefomed by SEER-SEM. When the SEER-SEM estimation datasets ae available, moe cases can be completed effectively fo evaluating the pefomance of the neuo-fuzzy model. VI. REFERENCES ) Aban, A. and Robillad,. N. (996) Function oints Analysis: An Empical Study of Its Measuement ocesses. Jounal of Systems and Softwae, Vol. 22, Issue 2: 895 90 2) Albecht, A. J. (979) Measuing Application Development oductivity. oceedings of the Joint SHARE, GUIDE, and IBM Application Development Symposium: 83 92 3) Boehm, B. W. (98) Softwae Engineeing Economics. entice Hall, Englewood Cliffs, NJ 4) Boehm, B. W., Abts, C., Bown, A. W., Chulani, S., Clak, B. K., Hoowitz, E., Madachy, R., Reife, D., and Steece, B. (2000) Softwae Cost Estimation with COCOMO II. entice Hall, Uppe Saddle Rive, NJ 5) Boehm, B. W., Abts, C., and Chulani, S. (2000) Softwae Development Cost Estimation Appoaches A Suvey. Annuals of Softwae Engineeing: 77 205 6) Chulani, S. (999) Bayesian Analysis of Softwae Cost and Quality Models. Dissetation, Univesity of South Califonia

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