ANALYSIS OF SOFTWARE COST ESTIMATION USING FUZZY LOGIC

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1 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 NLYSIS OF SOFTWRE COST ESTIMTION USING FUZZY LOGIC BSTRCT Is Mlek 1 Ly Erhm 2 Smn Jodt 3 Irj Rmesh 4 14 Deprtment of Computer Engneerng Dehdsht Brnh Islm zd Unversty Dehdsht Irn 23 Deprtment of Computer Engneerng Sene nd Reserh Brnh Islm zd Unversty West zerjn Irn The growng pplton of softwre nd resoure onstrnts n softwre projets development need more urte estmte of the ost nd effort euse of the mportne n progrm plnnng oordnted shedulng nd resoure mngement nludng the numer of progrmmng's nd softwre desgn usng tools nd modern methods of modelng. Effetvely ontrol of nvestment for softwre development s heved y urte ost estmton.the urte Softwre Cost Estmton SCE s very dffult n the erly stges of softwre development euse mny of nput prmeters tht re effetve n softwre's effort re very vgue nd unertn n the erly stges. SCE tht s the ss of softwre projets development plnnng s onsdered to e of hgh ury euse f the estmte s less thn tul vlues onfdene ftor s redue nd ths s mens the posslty of flure n projet. Conversely f the projet s estmted t more thn the tul vlue t would e the onept of unhelpful nvestment nd wste of resoures. In the evluton of softwre projets s ommonly used determnst method. But softwre world s totlly dfferent from the lner vrles nd nowdys for performne nd estmton should e used nonlner nd non-prolst methods. In ths pper we hve studed the SCE Usng Fuzzy Log FL nd we hve ompred t wth COCOMO model. Results of nvestgtons show tht FL s performne model for SCE. KEYWORDS Softwre Cost Estmton COCOMO Fuzzy Log 1. INTRODUCTION The SCE s n ssue tht Longley engged softwre projet mnger's mnd. In generl t n e stted tht one of the mportnt tsks for mngers n the feld of softwre development s n ttempt to fnd orreltons etween the mpressve resoures n softwre development projets to urte estmton. lso n some ses softwre projets development ompnes due to norret estmtes led to the loss of resoures nd the lk from useful humn power. In softwre development proess flure s nevtle nd n the form of the osts mposed on the mngers who re dretly nvolved n the yle relted to softwre projets [1 2 3]. Ths prolem s onsdered s negtve ftor n the softwre produton nd development. Therefore t should e tken dvntge of dvned tehnques n order to vod the rsk of flure of softwre projets to otn urte estmtes. Most of softwre projets re eeuted n dynm nd omple envronments so tht lk onfdene nd ost s ther ntrns propertes [4]. Ths unertnty used tht mostly softwre projets do not heve notle suess n predetermned gols. Ths led to prolems suh s lk DOI: /jfst

2 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 of projet's development reduton n performne nd dsstsfton n ustomers. Currently there re severl ftors tht led to the derese of estmton ury whh n pont to the followngs [5 6]: Mngers who lk pproprte eperene Development tems tht do not hve sutle eperene wth progrmmng lnguges Customers who re ontnully demnd developments nd hnges. To estmte the ost nd effort of softwre projets dfferent lgorthm models suh s COCOMO I [7] COCOMO II [8] SLIM [9 10] nd FP [11] hs een used. The purpose of SCE s to nrese the prolty of projet suess nd ths s done through the dentfton nd evluton of systemt effort nd ost. urte estmton n the ntl phse of the projet s vtl for projet mngers nd softwre Development Compnes n order to e suessful n projets nd resonle n osts. In reent yers rtfl ntellgene models n omnton wth lgorthm models hd good performnes n SCE [12 13 nd 14]. lgorthm models suh s COCOMO re dependent on numer of ost ftors tht these ftors re used to lulte the non-funtonl hrtersts proess [7 8]. These models try to formulton the onneton etween fetures of efforts nd the sze of the projet. These models sed on rter suh s qunttes lke numer of Lne of Code LOC or the degree of effetve ftors n estmton. The sze of projets n e guged y these unts nd then the mount of requred effort nd osts re lulted. The generl trend of SCE nludes the followng ssumptons [5 15]: The use of prevous eperene to determne ftors n whh the ost nd effort estmton n e effetve for new projets for emple the numer of people on the projet. It should e noted tht the sze of the LOC vres n softwre projets nd lwys hs strong reltonshp wth effort nd ost. Evluton of the ury of estmton models Beuse estmton s omple nd unertn phenomenon due to unertnty nd mguty n determnng ftors of development nd underdevelopment the use of lgorthm models lke COCOMO n e neffetve. FL s formed due to nlyze of systems tht the dependenes etween vrles s very omple [16]. The estene of suh omplety n engneerng nd the other dfferent senes s ommon. n mportnt lnk whh onnets thngs of ths type s mpreson mguous nd unertn nture of relty. The struture of the pper s s follows: n Seton 2 we wll dsuss out SCE nd evluton rter; n Seton 3 we wll study the FL memershp funtons nd ther pplton n the SCE; n Seton 4 we wll dsusson the FL memershp funtons n SCE nd fnlly n Seton 5 we wll epln the onlusons nd future works. 2. SOFTWRE COST ESTIMTION Nturlly SCE for softwre projets nludes oordnton mong ll developmentl tvtes desgn produton montorng mntenne et. [1]. urte estmton of softwre projet uses tht nternl nd eternl proesses nd employee tvtes efforts nd osts to e oordnted. So efore desgn nd mplementton of softwre projets provdng the model for them s essentl nd n e the most dffult tsks n softwre projets development. In the proess of softwre projets produton to redue ost nd shedule nd prolst rsks estmte must e tken to vod projet flure [3 12]. The mportne of SCE s more evdent when we know eh evluton n the estmton of ost ontns the postve nd negtve onsequenes nd ts lnng t ny pont of tme s one of the most omple mngement 28

3 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 ssues. Evluton of the estmtes performne hs lwys een the mportnt nd vlule tegory n softwre development projets. n ssue tht ould hs sgnfnt mpt on the future of softwre ompnes. So the more urte the rteron of evluton of softwre projets the etter estmte would e heved. Tle 1 shows the most mportnt SCE rter for softwre projets. Tle 1. SCE Evluton Crter Evluton Crter Desrpton t est Mgntude of Reltve Error MRE. MRE rter MRE 100 vlue error of estmted for eh of the projets t ompred to the tul model otns. n 1 Men Mgntude of Reltve Error MMRE. MMRE MMRE MRE s the rter error of the men vlue of the projet n 1 re onsdered. n 1 1 fmre Perentge Reltve Error Devton PRED. PRED PRED rter n order to use to estmte the ury of the n 1 0 otherwse models. n t est Men solute Reltve Error MRE. MRE MRE 100 / n rter n order to error of the men vlues of the 1 t ppled projets. t est Vrne solute Reltve Error VRE. VRE VRE Vr[ ] 100 rter n order to perent of vrne to estmte the t vlue of eh projet n e lulted. vr t est Vrne ount For VF. VF s used n the VF ontet of sttstl models whose mn purpose s vr est the predton of future outomes on the ss of other relted nformton. t est Blne Reltve Error BRE. BRE rter n order BRE to urtely estmte the error rte hs een used. mn t est Models for SCE should e ppled tht hve neessry performne n the evluton of estmte rter. The model whh hs lower MRE s etter thn the model whh hs hgher MRE. The model whh hs lower MMRE s etter thn the model whh hs hgher MMRE. The model whh hs hgher PRED s etter thn the model whh hs lower PRED. The model whh hs lower MRE s etter thn the model whh hs hgher MRE. The model whh hs lower VRE s etter thn the model whh hs hgher VRE. The model hs hgher VF s etter thn the model whh hs lower VF. The model tht hs lower BRE s etter thn the model whh hs hgher BRE. 3. FUZZY LOGIC FL theory ws presented n 1965 euse of the unertnty n dt nd nformton nd mpreson n the estene of vgueness [16]. FL s not rndom or unlkely method nd n ft ths method tself ntrodues spel system to del wth the mguous nd non-determnst stutons. The essentl hrterst of fuzzy theory s dsplyng unertn dt nd lso n e the operton nd pplton of mthemtl progrmmng. Eh fuzzy set n e shown wth memershp funton whh represents the memershp grde of element n the referene set X to fuzzy set. If the degree of memershp of n element s set to e zero tht memer s fully wthdrwn from the set nd f t wll e equl to 1 tht memer s qute n the set. If the degree of memershp of memer s etween 0 nd 1 ths numer represents the prtl memershp degree. In ths se fuzzy set s shown ordng to equton 1. 29

4 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My If fuzzy set ontns of dsrete elements the fuzzy set s shown ordng to equton 2. X n n / /... / / nd f the referene set wll e ontnuous the fuzzy set s shown ordng to equton 3. X n n / 3 Fuzzy sets n e defned nd mntned ts hrter sed on the memershp funton. The most mportne memershp funtons for fuzzy set nludes [16 17]: Trngulr Memershp Funton: Ths memershp funton wth three prmeters nd where << s defned ordng to equton 4. In the trngulr memershp funton f the vlue of the property s greter thn the enter of the memershp funton the enter of the memershp funton must e trnsferred to the left n order to go further wy of these hrtersts. The upper lmt of the memershp funtons should e moved to the left. lso for the se tht the vlue of the property s less thn the enter of the memershp funton the memershp funton of the men nd the lower lmt of memershp funton must e trnsferred to the rght. 0] m[mn 0 0 trngle 4 Trpezodl Memershp Funton: Ths funton wth the four prmeters d where <<<d s defned ordng to equton 5. 0] 1 m[mn d d d d d d d trpezod 5 Gussn Memershp Funton: Ths memershp funton wth two prmeters where represents wdth nd represents the enter of the memershp funton s defned ordng to equton e guss 6 [01]} ; { X

5 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 Generlzed Bell Memershp Funton: Ths memershp funtons wth three prmeters where s the wdth s the slope nd s the enter of memershp funton. Bell memershp funton s shown ordng to equton 7. 1 gell Sgmodl Memershp Funton: Sgmodl memershp funton s defned ordng to equton 8. 1 sg [ ] 1 e 8 In equton 8 vlue the mount of slope t the pont = hndles. Sgmodl memershp funton wll open from left to rght sed on prmeter's. Therefore ths type of memershp funton s good to represent onepts suh s very good or very d Fuzzy Log for Softwre Cost Estmton In mny engneerng senes lots of qulty nd quntty ftors suh s qulty pre flelty sllty nd performne must e onsdered for deson-mkng. To do so would e to determne the ftors nd weghts of fuzzy funtons use nd fuzzy numers n e epressed n them. So FL tres to otn onvenent opton for ssues wth estmtes nd deson mkng n envronments wth mguous nd vgue rter. In reent yers FL hs mny ppltons n SCE due to the flelty nd hgh preson n the estmtes. In ths seton we revew FL models nd ts ppltons nd lso the modelng results of proposed models tht hve een done y the reserhers on the projet softwre dtset. The SCE s nlyzed usng fuzzy funtons [18]. Method of Trngulr Memershp Funton Trpezodl Memershp Funton nd Gussn Memershp Funton re used for evlutng on the NS93 dtset. The proposed method s omned wth COCOMO II model. COCOMO II model nludes 17 Effort Multplers EMs nd 5 Sle Ftors SFs. In Fgure 1 s shown hyrd model. Fgure 1. FL hyrd model nd COCOMO II Evluton nd results hve een done on the 10 projets of NS93 dtset. Ther results show tht fuzzy methods re more urte n SCE nd hve less MRE error thn the COCOMO II model. nd lso Gussn Memershp Funton mong Fuzzy funtons hs etter performne thn other models nd n most ses t hs redued MRE error's rte. 31

6 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 new pproh for the SCE hs een proposed wth omnton of Trngulr Memershp Funton nd COCOMO II model [19]. Evluton hs een onduted on 30 projets from NS softwre projets. The hyrd model ftors of EM SF nd KSLOC Klo Soure Lne of Code re evluted usng fuzzfton. In Fgure 2 s shown the hyrd model. Fgure 2. Hyrd Model COCOMO II nd the Fuzzy Inferene System Hyrd model nputs onsst of 17 EMs 5 SFs nd KSLOC. Inferene Engne prt s the proess of formultng the mppng from gven nput to n output usng the FL. Rule Bse prt s the seleton of fuzzy rules. In the Dtse used memershp funtons re defned n the fuzzy rules. nd the Inferene Engne whh nludes nferene try to gve resonle output wth the help of rules. Defuzzfton prt onverts fuzzy set to numer. Epermentl results show tht the ury of MMRE nd MRE errors n the hyrd model s hgh when ompred wth other models. Suh tht the vlue of MMRE error n hyrd model s equl to nd the MRE error on verge for the 30 projets s equl to % lso n Tle 2 s shown the PRED error for the projets. Tle 2. Evluton of MMRE VF nd PRED Crter Crters Models [19] COCOMO II Hyrd MMRE % 7.512% VF 95.86% 98.77% PRED % 96.33% PRED % 93.33% PRED10 50% 80% PRED8 40% 63.33% FL-COCOMO II hyrd model hs proposed sed on the memershp funtons of Trngulr Trpezodl Gussn Generlzed Bell nd Sgmodl n the SCE [20]. Inputs hyrd model onssts of 17 EMs 5 SFs nd KSLOC. Evluton of hyrd model hs een done on 63 projets from NS softwre projets. Performne of hyrd model sed on the rter MMRE nd PRED %25 s shown n Tle 3. s t n e vewed sgmodl memershp funton hs less MMRE error vlue thn the other funtons. 32

7 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 Tle 3. Evluton of MMRE nd PRED Crter No. Memershp Funton Models [20] MMRE PRED %25 1 dsgmf guss2mf gussmf gellmf pmf psgmf trpezodlmf trngulrmf Inurte estmton of softwre projets often led to nurte ost estmtes. The new model s sed on FL hs een proposed to evlute SCE ftors [21]. Evluton s done on %30 of NS93 softwre projets. Generlzed Bell memershp funton s used n the proposed model. Epermentl results show tht the proposed model hs less error n VRE nd MRE rter n omprson wth the COCOMO model. Tle 4 shows the results of evluton. Tle 4. Evluton of MRE nd VRE Crter Models [21] VRE MRE GBellMF COCOMO To nrese the ury of the COCOMO model s used FL to nrese the rte of ury n estmte [22]. In the presented model Trpezodl nd Trngulr memershp funtons re used. Evluton s done on fve softwre's dtset from the NS93 nd COCOMO81 dtset. The mn ojetve of utlzton of FL n e the performne of the EMs of the projets tht nludes 15 ost drvers. Epermentl results show tht the PRED vlue of the proposed model s more urte thn the COCOMO model. lso the MRE error of the proposed model s less thn COCOMO model. The results of PRED %25 re shown n Tle 5. Tle 5. Evluton of PRED Crteron PRED 25% Dtset Proposed COCOMO Model [22] % 47% % 47% 3 46% 47% % 47% The new methodology s sed on FL nd Prtle Swrm Optmzton PSO lgorthm s proposed for the SCE [23]. SCE depends on the estmte of the sze of the projet nd ts prmeters. Unertnty n the sze s set usng the FL ontrol nd ts prmeters usng the prtles of the PSO lgorthm. Trngulr memershp funtons re used n the proposed model. Evluton ws done on the NS dtset. The results of eperments show tht the proposed model hs less error n the evluton of VRE nd MRE rter n omprson wth other models. 33

8 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 new model sed on the omned FL nd dptve Neuro Fuzzy Inferene System NFIS s proposed for the SCE [24]. In the proposed model memershp funtons of Trngulr Trpezodl Gussn nd Generlzed Bell s used. Evluton hs een performed on the NS93 nd NS63 dtset. Test results show tht proposed model hs less error n omprson wth other models. In Tle 6 Crteron MMRE s shown. s t n e seen Trpezodl memershp funton's MMRE error vlue s less thn the other models. Tle 6. Evluton of MMRE Crteron Models [24] MMRE Gussmf 0.51 Dsgmf 0.77 Guss2mf 0.85 Gellmf 0.50 Psgmf 0.85 Trpmf 0.45 Trmf 0.63 Cost nd tme rter re the most rtl fetures of softwre development projets. Gussn memershp funton hs een tested on the 10 projets of NS softwre projets [25]. The epermentl results show tht the proposed model hs less MMRE error n omprson wth other models. Tle 7 shows MMRE Crteron. Tle 7. Evluton of MMRE Crteron Models [25] MMRE Boehm Model Hlsted Wslton COCOMO Bse Orgn COCOMO Bse Semdethed COCOMO Bse Emedded Proposed Model COCOMO81 model s proposed for the SCE usng fuzzy memershp funtons [26]. In the FL- COCOMO proposed model memershp funtons of Trngulr Trpezodl Gussn nd Generlzed Bell re used. Evluton hs een onduted on 63 projets of NS softwre projets. lso for Defuzzfton the Center of re CO [27] method used whh s defned ordng to equton 9. In equton 9 z s the memershp funton's output of the system. Z CO Z z zdz Z z dz In order to demonstrte the performne of proposed model MMRE nd PRED %25 rter's were used. Tle 8 shows the nlyss of evluton rter. s t s evdene Generlzed Bell memershp funton s etter thn the other models. 9 34

9 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 Tle 8. Evluton of MMRE nd PRED Crter Models [26] Evluton MMRE PRED%25 COCOMO FL-COCOMO-Trngulr FL-COCOMO-Trpezodl FL-COCOMO-Gussn FL-COCOMO-GBell Due to unertn ftors n SCE t should e used model tht hs more ury n estmte nd ould reh the ost error to tul mount. Gussn memershp funton s evluted on the KEMERER dtset [28]. Epermentl results show tht the proposed model hs less MMRE error n omprson wth other models. In Tle 9 shows MMRE rteron. Tle 9. Evluton of MMRE Crteron Models [28] MMRE Boehm Model Hlsted Wslton COCOMO Bse Orgn COCOMO Bse Semdethed COCOMO Bse Emedded Proposed Model In the erly stges of the softwre development yle the most mportnt feture for projet mngers s effort nd ost. Therefore for reful onsderton of these rter FL Trngulr memershp funtons re used [29]. Evluton hs een performed on the KEMERER dtset. Epermentl results show tht the proposed model hs een le to mnmze the error MRE n omprson wth other models. The results of proposed model re shown n Tle 10. Tle 10. Evluton of MRE Crter Models [29] MRE% COCOMO81 Bse Model Doty Model Bley-Bsl Wlston Hlsted Proposed Model The new pproh s sed on FL lled Fuzzy Emotonl COCOMO II Softwre Cost Estmton FECSCE hs een proposed for the SCE [30]. In COCOMO II model only softwre projets' ftors s ssessed. In FECSCE model n ddton to projet ftors ndvdul's eperenes ther sklls nd lty level of ndvduls of softwre development group were lso studed. In FECSCE model Trngulr nd Trpezodl memershp funtons re used. Evluted on the EPEDC CRRS nd MECVX dtset hs een done. In ths model the Mult- gent System MS s used for modelng of ommunton of the ndvduls n the tem. The estene of n eperened tem s n mportnt element of omple softwre projets suess. projet s smlr to MS n whh ndvduls nd ooperton's ply key role n hevng 35

10 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 the gols. FL nd MS ws used to smulte the nterton etween ndvdul personl nd sol hrtersts. The mn purpose of the FECSCE model s revewng tem's fetures n order to mprove ury of the COCOMO II model for SCE. Epermentl results show tht FECSCE model hs etter performne n estmtng PM Person/Month thn COCOMO II model. Hyrd Model of FL nd PSO s proposed for the SCE [31]. Evluton hs een done on NS softwre projet dtset. Trngulr memershp funton s used to fuzzfton. In generl two mjor reforms were rred out n the Trngulr memershp funtons tht re: Trnng memershp funtons n order to nrese the deteton rte Removng un-sutle rules to redue the numer of fuzzy rules nd to nrese the preson nd power of generlzton The PSO lgorthm s used to Defuzzfton of memershp funton prmeters. In the done mplementtons nd dfferent eperments the rte of error s deresed nd the neessry fuzzy rules numer s deresed per dfferent prmeters nd usng PSO lgorthm n the trnng of memershp funton nd hoe of sutle fuzzy rules. Test results show tht the hyrd model hs less MRE rteron n omprson wth other models mesure less. Tle 11 s showed MRE rteron. Tle 11. Evluton of MRE Crteron Evluton Models [31] Bley-Bsl Proposed Model MRE% pplton of FL s proposed due to more urte SCE [32]. In the proposed model Trngulr memershp funtons nd Generlzed Bell memershp funtons re used. Evluted s done on NS93 softwre projets dtset. Test results show tht MRE MMRE nd VRE rter hve smller errors thn the COCOMO model. lso PRED VF nd BRE rter re more urte n estmte. In the proposed model wth Generlzed Bell memershp funton hs etter ury of BRE rter. Tle 12 shows the results of rter's evluton. Tle 12. Evluton of MRE MMRE VF VRE BRE nd PRED Crter Models [32] Evluton MRE MMRE VF VRE Men BRE PRED 30% Fuzzy-Trngulr Fuzzy-GBell COCOMO new model s proposed sed on FL for SCE [33]. Trngulr memershp funtons re used n the proposed model. Evluton hs een done on 15 projets of KEMERER softwre projets dtset. The epermentl results show tht the proposed model hs lower error rte n omprson wth other models. Tle 13 shows PRED nd MRE rter. s you n see the vlue of PRED of proposed model s more urte n omprson wth other models. 36

11 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 Tle 13. Evluton of PRED nd MRE Crter Models [33] Evluton MRE PRED 40% COCOMO Bley-Bsl Doty Hlsted Proposed In order to redue the error of COCOMO model s used FL for SCE [34]. Evluton of the proposed model hs een done on NS93 softwre projet dtset. Trngulr memershp funton s used for fuzzfton n the proposed model. nd lso for Defuzzfton Men of Mmum MOM CO nd Frst of Mmum FOM evluton tehnques hve een used. Inputs of the proposed model onssts of 17 EMs 5 SFs nd KSLOC. Epermentl results show tht the vlue of MMRE error n COCOMO II model nd the proposed model re equl to 0.41 nd 0.36 respetvely. lso the vlue of the PRED %25 n the COCOMO II model nd the proposed model re 39 % nd 46 % respetvely. FL dfferent models sed on fuzzfton memershp funtons re presented for SCE [35]. Trngulr nd Gussn memershp funtons re used n ths model. Evluton nd the results hve een done on COCOMO81 dtset. Projets n the proposed model re 15 ost drvers. Epermentl results show tht the proposed models hve less MMRE error vlue thn COCOMO model nd lso hve more urte PRED %25. COCOMO model hs mny ppltons n SCE n the softwre ndustry. But ths model s not more effent to estmte lone. For ths reson for nresng the ury of the COCOMO model Trngulr nd Gussn memershp funtons re used [36]. Evluton hs een onduted on 63 projets of the NS dtset. EM ftor of 17 s used n the proposed model. Epermentl results show tht the proposed model hs muh smller errors thn the COCOMO model. lso Gussn funton s more urte n the estmte n omprson wth Trngulr memershp funton. 4. DISCUSSION In the revewed ppers were presented effent model for estmtng ost nd tme of development of softwre projets under unertnty s fuzzy. The ost nludes plnnng stges desgn nlyss mplementton nd support. For eh softwre projet there re three nterrelted ftors tme ost nd mnpower. ddressng eh of the ftors uses the mpt of two other ftors. Inresng projet durton use nresng more osts nd hs the effet on projet pres. Sne n projet plnnng requred resoures should lredy e estmted so estmte of the tme nd ost of softwre projet development s vtl oth for the produer nd user. Resoures nd mngement re two ftors for softwre projets operton. If these two ftors re known then the tme nd ost of softwre development n e determned. In the revewed ppers the dvntges dsdvntges nd opertons of dfferent methods of SCE emned nd fnlly omnton of COCOMO nd FL methods s used for dtset of dt evluton. In the nvestgtons fuzzy models hve een proposed wth hngng nd omposton of estng models tht re usle n rel ondtons of softwre development. Effeny nd ury of these methods re hgh n omprson wth the models lke 37

12 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 COCOMO. Tle 14 shows omprson nd evluton of fuzzy memershp funtons on dtset nd evluton rter. Tle 14. Comprson nd Evluton of FL Funtons on Dtset Projets pproh's Memershp Funton Dtset Evluton Crter [18] Trpezodl Trngulr NS93 MRE Gussn [19] [23] [30] [32] [33] Trngulr NS EPEDC CRRS MECVX NS93 MMRE MRE PRED MRE VF VRE BRE [20] Trngulr Trpezodl Gussn Generlzed Bell Sgmodl KEMERER NS63 [22] Trngulr Trpezodl NS93 COCOMO81 [24] [26] Trngulr Trpezodl NS63 [34] Gussn Generlzed NS93 MMRE PRED PRED MRE MMRE PRED Bell [25] [29] Gussn NS MMRE MRE KEMERER [21] [28] Generlzed Bell KEMERER MMRE VRE NS93 [31] Trpezodl Trngulr NS MRE [35] [36] Trngulr Gussn COCOMO81 MMRE PRED NS63 FL performne sgnfntly depends on the desgned fuzzy struture. In other words the sgnfnt seleton of ths struture n ffet ts performne. Ftors suh s type of memershp funtons the type of used fuzzy omposton the numer of fuzzy rules nd the numer of used ftors n the funtons re of these tegores. In SCE lgorthm models the vlue of softwre development defned s the lner progrm. Whle n the FL vlue of softwre development n e epressed n the form of spetrum nd n the form of degree of memershp for eh of the ftors n developed nd undeveloped softwre. The results of the evluton of fuzzy memershp funtons on dfferent dtset showed tht Gussn nd Sgmodl memershp funton hd etter performne thn memershp funtons of Trngulr Trpezodl nd Generlzed Bell n estmtng MMRE nd PRED rter. Trngulr nd Gussn memershp funtons re requre less omputng pltes nd lso hve not the lty to vod the dt's nose. Dtset dt re etter nlyzed nd evluted y usng the ove two funtons. Trngulr nd Gussn memershp funtons n MMRE nd VRE rter hve less error thn the other funtons. Bsed on the onduted surveys memershp funtons of Trngulr Trpezodl Gussn Sgmodl nd Generlzed Bell on NS93 dtset hve less MMRE error thn the NS63 dtset. Beuse the NS93 dtset hs more projets more omprsons n e done on the memershp funtons for fuzzfton nd Defuzzfton of estmtng effetve ftors. Generlzed Bell memershp funtons n PRED %30 rteron on the dtset NS63 hs etter preson thn COCOMO model nd Trngulr memershp funton. lso Trngulr memershp funton n PRED %40 rteron on the dtset KEMERER hs etter ury 38

13 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 thn COCOMO model. In Tle 15 fuzzy memershp funtons n terms of ury Trnsent Response nd Oslltons re evluted. s you n see the performne of eh of the funtons re dfferent from eh other. Bsed on nvestgtons we onluded tht t should e onsdered the performne of the funtons for estmte. Tle 15. Evluton of the Performne of Fuzzy Funtons Memershp ury Trnsent Oslltons Funton Response Trngulr Hgh Norml Norml Trpezodl Medum Norml Hgh Gussn Hgh Norml Norml Generlzed Bell Medum Norml Norml Sgmodl Hgh Hgh Norml 5. CONCLUSIONS ND FUTURE WORKS In ths pper SCE ws nvestgted usng the FL nd the pltes of COCOMO model. Nowdys the use of FL s new pproh n nlyzng softwre engneerng ssues suh s SCE hs mproved. One of the ssues tht helps the orret use of softwre nd prevent the softwre projets from flure s the urte estmte of ost. urte estmtes helps the developmentl ompnes tht hve etter nlyze of softwre projets feslty nd effetvely mnge softwre development proess. Inurte estmtes used ddtonl udget nd dum estmtes uses tht softwre projets development hs not enough progress nd the ntended softwre hs not re produed. Therefore ths pper nlyzes the FL n SCE usng memershp funtons of Trngulr Trpezodl Gussn Generlzed Bell nd Sgmodl. Funtons tested nd evluted on set of softwre projets dtset nd showed tht they hve etter performne thn COCOMO model etter. We hope n the future wth presentng ths pper gve performed models for SCE usng the fuzzy systems. REFERENCES [1] P.C. Pendhrkr Prolst Estmton of Softwre Sze nd Effort Epert Systems wth ppltons Vol. 37 pp [2] T.R. Benl R. Mll P. Srkvy M.V. HrPry Softwre Effort Estmton Usng Dt Mnng Tehnques dvnes n Intellgent Systems nd Computng Vol. 248 pp Sprnger [3] F.S. Ghrehhopogh I. Mlek S.R. Khze Novel Prtle Swrm Optmzton pproh for Softwre Effort Estmton Interntonl Journl of dem Reserh Prt Vol. 6. No. 2 pp [4] G. Svngeswr Ro Ch. V. Phn Krshn K. Rjsekhr Ro Mult Ojetve Prtle Swrm Optmzton for Softwre Cost Estmton dvnes n Intellgent Systems nd Computng Vol. 248 pp Sprnger [5]. Trendowz Why Softwre Effort Estmton? The Frunhofer IESE Seres on Softwre nd Systems Engneerng pp. 3-7 Sprnger [6] W. Zhng Y. Yng Q. Wng Study on Softwre Effort Predton Usng Mhne Lernng Tehnques Communtons n Computer nd Informton Sene Vol. 275 pp Sprnger [7] B.W. Boehm Softwre Engneerng Eonoms Prente-Hll Englewood Clffs New Jersy [8] B.W. Boehm Softwre Cost Estmton wth COCOMO II Prente Hll PTR Englewood Clffs New Jersy [9] S.D. Conte H.E. Dunsmore V.Y. Shen Softwre Engneerng Metrs nd Models The Benjmn/Cummngs Pulshng Compny In Menlo Prk C p [10] V.P. Cot B. Olgny N. Rvrd Softwre Metrs: n Overvew of Reent Results the Journl of Systems nd Softwre Vol. 8 pp

14 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 [11].J. lreht J. Gffney Softwre Funton Soure Lnes of Code nd Development Effort Predton: Softwre Sene Vldton IEEE Trnstons on Softwre Engneerng SE Vol. 9 No. 6 pp [12] I. Mlek. Ghffr M. Msdr New pproh for Softwre Cost Estmton wth Hyrd Genet lgorthm nd nt Colony Optmzton Interntonl Journl of Innovton nd ppled Studes Vol. 5 No. 1 pp [13] F.S. Ghrehhopogh Neurl Networks pplton n Softwre Cost Estmton: Cse Study 2011 Interntonl Symposum on Innovtons n Intellgent Systems nd ppltons INIST 2011 pp IEEE Istnul Turkey June [14] Z.. Khlfelu F.S. Ghrehhopogh Comprson nd Evluton Dt Mnng Tehnques wth lgorthm Models n Softwre Cost Estmton Elsever Proed-Tehnology Journl ISSN: Vol. 1 pp [15] P. Pndey nlyss of the Tehnques for Softwre Cost Estmton Rohtk pp IEEE [16] L.. Zdeh Fuzzy sets Informton nd Control Vol. 8 pp [17] G. J. Klr B. Yun Fuzzy Sets nd Fuzzy Log Prente Hll Upper Sddle Rver New Jersey [18]. Mlk V. Pndey. Kushk n nlyss of Fuzzy pprohes for COCOMO II Interntonl Journl Intellgent Systems nd ppltons Vol.5 pp [19] Zuddn S. Kml S. khn J.. Nsr Fuzzy Log Bsed Softwre Cost Estmton Model Interntonl Journl of Softwre Engneerng nd Its ppltons Vol. 7 No [20] S. Rvshnkr P. Lth Softwre Cost Estmton usng Fuzzy Log Interntonl Conferene on Reent Trends n Computtonl Methods Communton nd Controls ICON3C 2012 IJC pp [21] S. Mlth S. Srdhr Performne Evluton of Softwre Effort Estmton usng Fuzzy nlogy sed on Complety Interntonl Journl of Computer ppltons IJC Vol. 40 No.3 pp [22]. Hmdy Fuzzy Log for Enhnng the Senstvty of COCOMO Cost Model Journl of Emergng Trends n Computng nd Informton Senes Vol. 3 No. 9 pp [23]. BlKrshn T.K.Rm Krshn Fuzzy nd Swrm Intellgene for Softwre Effort Estmton dvnes n Informton Tehnology nd Mngement ITM Vol. 2 No. 1 pp [24] E. Prynln P. Lth Estmtng Development Effort of Softwre Projets usng NFIS Interntonl Conferene on Reent Trends n Computtonl Methods Communton nd Controls ICON3C IJC pp [25] R. grw Q. lm S. Srwr Effent Estmton of Softwre System Usng Fuzzy Tehnque Interntonl Journl of Eletrons nd Computer Sene Engneerng Vol. 1 No. 3 pp [26] P. Jh K.S. Ptnk Comprtve nlyss of COCOMO81 usng Vrous Fuzzy Memershp Funtons Interntonl Journl of Computer ppltons IJC Vol. 58 No. 14 pp [27] R.R. Yger D.P. Flev SLIDE: Smple dptve Defuzzfton Method IEEE trnston on Fuzzy Systems Vol. 1 No. 1 pp Ferury [28] R. grwl I. wsth S. Srwr n Emprl Vldton of Softwre Cost Estmton Model Usng Fuzzy Tehnque Interntonl Journl of dvnes n Eletrl nd Eletrons Engneerng Vol. 1 No. 2 pp [29] J.N.V.R Swrup Kumr. Mndl M.V. Chtny G.V.S.N.R.V. Prsd Fuzzy log for Softwre Effort Estmton Usng Polynoml Regresson s Frng Intervl Interntonl Journl Computer Tehnology pplton Vol. 2 No. 6 pp [30] M. Kzemfrd. Zer N. Ghsem-ghee M.. Nemtkhsh F. Mrdukh Fuzzy Emotonl COCOMO II Softwre Cost Estmton FECSCE usng Mult-gent Systems ppled Soft Computng Vol. 11 pp Elsever B.V [31] S. Ro.T Prsd R.P.V.G.D Hr Ch.V.M.K Fuzzy nd Swrm Intellgene for Softwre Cost Estmton Glol Journl of Computer Sene nd Tehnology Vol. 11 Issue [32] Prsd R.P.V.G.D Sudh K. R Rm S.P pplton of Fuzzy Log pproh to Softwre Effort Estmton Interntonl Journl of dvned Computer Sene nd ppltons IJCS Vol. 2 No. 5 pp [33]. Mttl K. Prksh H. Mttl Softwre Cost Estmton Usng Fuzzy Log CM SIGSOFT Softwre Engneerng Vol. 35 No. 1 pp

15 Interntonl Journl n Foundtons of Computer Sene & Tehnology IJFCST Vol.4 No.3 My 2014 [34] I. ttrzdeh S.H. Ow Soft Computng pproh for Softwre Cost Estmton Interntonl Journl of Softwre Engneerng IJSE Vol. 3 No [35] V. Shrm H.K. Verm Optmzed Fuzzy Log Bsed Frmework for Effort Estmton n Softwre Development IJCSI Interntonl Journl of Computer Sene Issues Vol. 7 Issue 2 No. 2 pp [36] Ch. Stynnd Reddy K.V.S.V.N Rju n Improved Fuzzy pproh for COCOMO s Effort Estmton usng Gussn Memershp Funton Journl of Softwre Vol. 4 No. 5 pp uthors Is Mlek s Leturer nd Memer of The Reserh Commttee of The Deprtment of Computer Engneerng Dehdsht Brnh Islm zd Unversty Dehdsht Irn. He lso Hs Reserh Collorton wth Dehdsht Unverstes Reserh ssoton NGO. He s Memer of Edtorl Bord nd Revew Bord n Severl Interntonl Journls nd Interntonl Conferenes. He hs Pulshed over 30 Ppers n Interntonl journls nd Conferene Proeedngs. Hs Interested Reserh res re n the Softwre Cost Estmton Mhne Lernng Dt Mnng Optmzton nd rtfl Intellgene. Ly Erhm s M.S. Student n Deprtment of Computer Engneerng Sene nd Reserh Brnh Islm zd Unversty West zerjn Irn. Her Interested Reserh res re n Softwre Cost Estmton Mhne Lernng Dt Mnng nd Optmzton. Smn Jodt s M.S. Student n Deprtment of Computer Engneerng Sene nd Reserh Brnh Islm zd Unversty West zerjn Irn. Hs Interested Reserh res re n the Softwre Cost Estmton Softwre Development Mhne Lernng nd Dt Mnng. 41