International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
DOI:10.5121/ijfcst.2...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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of project's deve...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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issues. Evaluatio...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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(1)
If a fuzzy se...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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Generalized Bell ...
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A new approach fo...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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Table 3. Evaluati...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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A new model based...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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Table 8. Evaluati...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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the goals. FL and...
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Table 13. Evaluat...
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COCOMO. Table (14...
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than COCOMO model...
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[11] A.J. Albrech...
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014
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[34] I. Attarzade...
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Analysis of software cost estimation using

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The growing application of software and resource constraints in software projects development need a
more accurate estimate of the cost and effort because of the importance in program planning, coordinated
scheduling and resource management including the number of programming's and software design using
tools and modern methods of modeling. Effectively control of investment for software development is
achieved by accurate cost estimation.The accurate Software Cost Estimation (SCE) is very difficult in the
early stages of software development because many of input parameters that are effective in software's
effort are very vague and uncertain in the early stages. SCE that is the basis of software projects
development planning is considered to be of high accuracy, because if the estimate is less than actual
values, confidence factor is reduce and this is means the possibility of failure in project. Conversely, if the
project is estimated at more than the actual value it would be the concept of unhelpful investment and
waste of resources. In the evaluation of software projects is commonly used deterministic method. But
software world is totally different from the linear variables and nowadays for performance and estimation
should be used nonlinear and non-probabilistic methods. In this paper, we have studied the SCE Using
Fuzzy Logic (FL) and we have compared it with COCOMO model. Results of investigations show that FL is
a performance model for SCE.

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Analysis of software cost estimation using

  1. 1. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 DOI:10.5121/ijfcst.2014.4303 27 ANALYSIS OF SOFTWARE COST ESTIMATION USING FUZZY LOGIC Isa Maleki1 , Laya Ebrahimi2 , Saman Jodati3 , Iraj Ramesh4 1,4 Department of Computer Engineering, Dehdasht Branch, Islamic Azad University, Dehdasht, Iran 2,3 Department of Computer Engineering, Science and Research Branch, Islamic Azad University, West Azerbaijan, Iran ABSTRACT The growing application of software and resource constraints in software projects development need a more accurate estimate of the cost and effort because of the importance in program planning, coordinated scheduling and resource management including the number of programming's and software design using tools and modern methods of modeling. Effectively control of investment for software development is achieved by accurate cost estimation.The accurate Software Cost Estimation (SCE) is very difficult in the early stages of software development because many of input parameters that are effective in software's effort are very vague and uncertain in the early stages. SCE that is the basis of software projects development planning is considered to be of high accuracy, because if the estimate is less than actual values, confidence factor is reduce and this is means the possibility of failure in project. Conversely, if the project is estimated at more than the actual value it would be the concept of unhelpful investment and waste of resources. In the evaluation of software projects is commonly used deterministic method. But software world is totally different from the linear variables and nowadays for performance and estimation should be used nonlinear and non-probabilistic methods. In this paper, we have studied the SCE Using Fuzzy Logic (FL) and we have compared it with COCOMO model. Results of investigations show that FL is a performance model for SCE. KEYWORDS Software Cost Estimation, COCOMO, Fuzzy Logic 1. INTRODUCTION The SCE is an issue that Longley engaged software project manager's mind. In general it can be stated that one of the important tasks for managers in the field of software development is an attempt to find correlations between the impressive resources in software development projects to accurate estimation. Also in some cases software projects development companies due to incorrect estimates lead to the loss of resources and the lack from useful human power. In software development process, failure is inevitable and in the form of the costs imposed on the managers who are directly involved in the cycle related to software projects [1, 2, 3]. This problem is considered as a negative factor in the software production and development. Therefore, it should be taken advantage of advanced techniques in order to avoid the risk of failure of software projects to obtain accurate estimates. Most of software projects are executed in dynamic and complex environments, so that lack confidence and cost is their intrinsic properties [4]. This uncertainty caused that mostly software projects do not achieve notable success in predetermined goals. This led to problems such as lack
  2. 2. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 28 of project's development, reduction in performance and dissatisfaction in customers. Currently, there are several factors that lead to the decrease of estimation accuracy which can point to the followings [5, 6]:  Managers who lack appropriate experience  Development teams that do not have suitable experience with programming languages  Customers who are continually demand developments and changes. To estimate the cost and effort of software projects, different algorithmic models such as COCOMO I [7], COCOMO II [8], SLIM [9, 10] and FP [11] has been used. The purpose of SCE is to increase the probability of project success and this is done through the identification and evaluation of systematic effort and cost. Accurate estimation in the initial phase of the project is vital for project managers and software Development Companies in order to be successful in projects and reasonable in costs. In recent years, artificial intelligence models in combination with algorithmic models had good performances in SCE [12, 13, and 14]. Algorithmic models such as COCOMO are dependent on a number of cost factors that these factors are used to calculate the non-functional characteristics process [7, 8]. These models try to formulation the connection between features of efforts and the size of the project. These models based on criteria such as quantities like number of Line of Code (LOC) or the degree of effective factors in estimation. The size of projects can be gauged by these units and then the amount of required effort and costs are calculated. The general trend of SCE includes the following assumptions [5, 15]:  The use of previous experience to determine factors in which the cost and effort estimation can be effective for new projects, for example, the number of people on the project. It should be noted that the size of the LOC varies in software projects and always has a strong relationship with effort and cost.  Evaluation of the accuracy of estimation models Because, estimation is a complex and uncertain phenomenon, due to uncertainty and ambiguity in determining factors of development and underdevelopment, the use of algorithmic models like COCOMO can be ineffective. FL is formed due to analyze of systems that the dependencies between variables is very complex [16]. The existence of such complexity in engineering and the other different sciences is common. An important link which connects things of this type is imprecision, ambiguous and uncertain nature of reality. The structure of the paper is as follows: in Section 2, we will discuss about SCE and evaluation criteria; in Section 3, we will study the FL membership functions and their application in the SCE; in Section 4, we will discussion the FL membership functions in SCE and finally in Section 5, we will explain the conclusions and future works. 2. SOFTWARE COST ESTIMATION Naturally, SCE for software projects includes coordination among all developmental activities, design, production monitoring, maintenance, etc. [1]. Accurate estimation of software project causes that internal and external processes and employee activities, efforts and costs to be coordinated. So, before design and implementation of software projects providing the model for them is essential and can be the most difficult tasks in software projects development. In the process of software projects production to reduce cost and schedule and probabilistic risks estimate must be taken to avoid project failure [3, 12]. The importance of SCE is more evident when we know each evaluation in the estimation of cost contains the positive and negative consequences and its balancing at any point of time is one of the most complex management
  3. 3. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 29 issues. Evaluation of the estimates performance has always been the important and valuable category in software development projects. An issue that could has a significant impact on the future of software companies. So the more accurate the criterion of evaluation of software projects, the better estimate would be achieved. Table (1) shows the most important SCE criteria for software projects. Table 1. SCE Evaluation Criteria Evaluation Criteria Description 100   i ii act estact MRE Magnitude of Relative Error (MRE). MRE criteria value error of estimated for each of the projects compared to the actual model obtains.   n i iMRE n MMRE 1 1 Mean Magnitude of Relative Error (MMRE). MMRE as the criteria error of the mean value of the project are considered.       n i otherwise xifMRE n xPRED 1 ,0 ,11 )( Percentage Relative Error Deviation (PRED). PRED criteria in order to use to estimate the accuracy of the models. n act estact MARE n i i ii /)100( 1     Mean Absolute Relative Error (MARE). MARE criteria in order to error of the mean values of the applied projects. 100][    i ii act estact VarVARE Variance Absolute Relative Error (VARE). VARE criteria in order to percent of variance to estimate the value of each project can be calculated. 100) )var( )var( 1(    i ii est estact VAF Variance Account For (VAF). VAF is used in the context of statistical models whose main purpose is the prediction of future outcomes on the basis of other related information. ),min( ii ii estact estact BRE   Balance Relative Error (BRE). BRE criteria in order to accurately estimate the error rate has been used. Models for SCE should be applied that have necessary performance in the evaluation of estimate criteria. The model which has a lower MRE is better than the model which has higher MRE. The model which has a lower MMRE is better than the model which has higher MMRE. The model which has a higher PRED is better than the model which has lower PRED. The model which has a lower MARE is better than the model which has higher MARE. The model which has a lower VARE is better than the model which has higher VARE. The model has a higher VAF is better than the model which has lower VAF. The model that has a lower BRE is better than the model which has higher BRE. 3. FUZZY LOGIC FL theory was presented in 1965 because of the uncertainty in data and information and imprecision in the existence of vagueness [16]. FL is not a random or unlikely method and in fact, this method itself introduces a special system to deal with the ambiguous and non-deterministic situations. The essential characteristic of fuzzy theory is displaying uncertain data and also can be the operation and application of mathematical programming. Each fuzzy set can be shown with a membership function which represents the membership grade of element x in the reference set X to fuzzy set A. If the degree of membership of an element is set to be zero, that member is fully withdrawn from the set and if it will be equal to 1, that member is quite in the set. If the degree of membership of a member is between 0 and 1, this number represents the partial membership degree. In this case fuzzy set A is shown according to equation (1).
  4. 4. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 30 (1) If a fuzzy set contains of discrete elements xi, the fuzzy set A is shown according to equation (2).   Xx iiAnnAAA i xxxxxxxxA /)(/)(.../)(/)( 2211  And if the reference set will be continuous, the fuzzy set A is shown according to equation (3).   Xx nnA i xxA /)( (3) Fuzzy sets can be defined and maintained its character based on the membership function. The most importance membership functions for fuzzy set includes [16, 17]: Triangular Membership Function: This membership function with three parameters a, b and c, where a<b<c is defined according to equation (4). In the triangular membership function if the value of the property is greater than the center of the membership function, the center of the membership function must be transferred to the left in order to go further away of these characteristics. The upper limit of the membership functions should be moved to the left. Also, for the case that the value of the property is less than the center of the membership function, the membership function of the mean and the lower limit of membership function must be transferred to the right. ]0),,max[min( 0 0 ),,|( bc xc ab ax cx cxb bc xc bxa ab ax ax cbaxtriangle                       (4) Trapezoidal Membership Function: This function with the four parameters a, b, c, d where a<b<c<d is defined according to equation (5). ]0),,1,max[min( 0 1 0 ),,,|( cd xd ab ax dx dxc cd xd cxb bxa ab ax ax dcbaxtrapezoid                         (5) Gaussian Membership Function: This membership function with two parameters c, where  represents width and c represents the center of the membership function is defined According to equation (6). 2 )(5.0 ),|(   cx ecxgauss    (6) ]}1,0[)(,));(,{(  xXxxxA AA 
  5. 5. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 31 Generalized Bell Membership Function: This membership functions with three parameters a, b, c where a is the width, b is the slope and c is the center of membership function. Bell membership function is shown according to equation (7). b a cx cbaxgbell 2 1 1 ),,|(    (7) Sigmoidal Membership Function: Sigmoidal membership function is defined according to equation (8). )]([ 1 1 ),|,( cxa e caxsig    (8) In equation (8), a value the amount of slope at the point x = c handles. Sigmoidal membership function will open from left to right based on parameter's a. Therefore, this type of membership function is good to represent concepts such as “very good” or “very bad”. 3.1. Fuzzy Logic for Software Cost Estimation In many engineering sciences lots of quality and quantity factors such as quality, price, flexibility, scalability and performance must be considered for decision-making. To do so would be to determine the factors and weights of fuzzy functions use and fuzzy numbers can be expressed in them. So FL tries to obtain convenient option for issues with estimates and decision making in environments with ambiguous and vague criteria. In recent years, FL has many applications in SCE due to the flexibility and high precision in the estimates. In this section, we review FL models and its applications and also the modeling results of proposed models that have been done by the researchers on the project software dataset. The SCE is analyzed using fuzzy functions [18]. Method of Triangular Membership Function, Trapezoidal Membership Function and Gaussian Membership Function are used for evaluating on the NASA93 dataset. The proposed method is combined with COCOMO II model. COCOMO II model includes 17 Effort Multipliers (EMs) and 5 Scale Factors (SFs). In Figure (1) is shown a hybrid model. Figure 1. FL hybrid model and COCOMO II Evaluation and results have been done on the 10 projects of NASA93 dataset. Their results show that fuzzy methods are more accurate in SCE and have less MRE error than the COCOMO II model. And also Gaussian Membership Function among Fuzzy functions has better performance than other models, and in most cases it has reduced MRE error's rate.
  6. 6. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 32 A new approach for the SCE has been proposed with a combination of Triangular Membership Function and COCOMO II model [19]. Evaluation has been conducted on 30 projects from NASA software projects. The hybrid model factors of EM, SF and KSLOC (Kilo Source Line of Code) are evaluated using fuzzification. In Figure (2) is shown the hybrid model. Figure 2. Hybrid Model COCOMO II and the Fuzzy Inference System Hybrid model inputs consist of 17 EMs, 5 SFs and KSLOC. Inference Engine part is the process of formulating the mapping from a given input to an output using the FL. Rule Base part is the selection of fuzzy rules. In the Database, used membership functions are defined in the fuzzy rules. And the Inference Engine, which includes inference try to give a reasonable output with the help of rules. Defuzzification part converts a fuzzy set to a number. Experimental results show that the accuracy of MMRE and MRE errors in the hybrid model is high when compared with other models. Such that the value of MMRE error in a hybrid model is equal to 7.512, and the MRE error on average for the 30 projects is equal to %63.33. Also in Table (2) is shown the PRED error for the projects. Table 2. Evaluation of MMRE, VAF and PRED Criteria Criterias Models [19] COCOMO II Hybrid MMRE 11.003% 7.512% VAF 95.86% 98.77% PRED(25) 93.33% 96.33% PRED(15) 63.33% 93.33% PRED(10) 50% 80% PRED(8) 40% 63.33% FL-COCOMO II hybrid model has proposed based on the membership functions of Triangular, Trapezoidal, Gaussian, Generalized Bell and Sigmoidal in the SCE [20]. Inputs hybrid model consists of 17 EMs, 5 SFs and KSLOC. Evaluation of a hybrid model has been done on 63 projects from NASA software projects. Performance of hybrid model based on the criteria MMRE and PRED (%25) is shown in Table (3). As it can be viewed sigmoidal membership function has less MMRE error value than the other functions.
  7. 7. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 33 Table 3. Evaluation of MMRE and PRED Criteria No. Membership Function Models [20] MMRE PRED (%25) 1 dsigmf 0.37127 33.33 2 gauss2mf 0.37625 34.92 3 gaussmf 0.35920 36.50 4 gbellmf 0.37442 36.50 5 pimf 0.35373 36.50 6 psigmf 0.34634 36.50 7 trapezoidalmf 0.35809 36.50 8 triangularmf 0.67596 33.33 Inaccurate estimation of software projects often lead to inaccurate cost estimates. The new model is based on FL has been proposed to evaluate SCE factors [21]. Evaluation is done on %30 of NASA93 software projects. Generalized Bell membership function is used in the proposed model. Experimental results show that the proposed model has less error in VARE and MARE criteria in comparison with the COCOMO model. Table (4) shows the results of evaluation. Table 4. Evaluation of MARE and VARE Criteria Models [21] VARE MARE GBellMF 32.59 23.78 COCOMO 47.22 46.89 To increase the accuracy of the COCOMO model is used FL to increase the rate of accuracy in estimate [22]. In the presented model Trapezoidal and Triangular membership functions are used. Evaluation is done on five software's dataset from the NASA93 and COCOMO81 dataset. The main objective of utilization of FL can be the performance of the EMs of the projects that includes 15 cost drivers. Experimental results show that the PRED value of the proposed model is more accurate than the COCOMO model. Also the MRE error of the proposed model is less than COCOMO model. The results of PRED (%25) are shown in Table (5). Table 5. Evaluation of PRED Criterion Dataset PRED (25%) Proposed Model [22] COCOMO 1 48.43% 47% 2 54.85% 47% 3 46% 47% 4 44.2% 47% The new methodology is based on FL and Particle Swarm Optimization (PSO) algorithm is proposed for the SCE [23]. SCE depends on the estimate of the size of the project and its parameters. Uncertainty in the size is set using the FL control and its parameters using the particles of the PSO algorithm. Triangular membership functions are used in the proposed model. Evaluation was done on the NASA dataset. The results of experiments show that the proposed model has less error in the evaluation of VARE and MARE criteria in comparison with other models.
  8. 8. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 34 A new model based on the combined FL and Adaptive Neuro Fuzzy Inference System (ANFIS) is proposed for the SCE [24]. In the proposed model membership functions of Triangular, Trapezoidal, Gaussian and Generalized Bell is used. Evaluation has been performed on the NASA93 and NASA63 dataset. Test results show that proposed model has less error in comparison with other models. In Table (6) Criterion MMRE is shown. As it can be seen, Trapezoidal membership function's MMRE error value is less than the other models. Table 6. Evaluation of MMRE Criterion Models [24] MMRE Gaussmf 0.51 Dsigmf 0.77 Gauss2mf 0.85 Gbellmf 0.50 Psigmf 0.85 Trapmf 0.45 Trimf 0.63 Cost and time criteria are the most critical features of software development projects. Gaussian membership function has been tested on the 10 projects of NASA software projects [25]. The experimental results show that the proposed model has less MMRE error in comparison with other models. Table (7) shows MMRE Criterion. Table 7. Evaluation of MMRE Criterion Models [25] MMRE Boehm Model 0.172 Halstead 2.927 Waslton 0.146 COCOMO (Base Organic) 0.104 COCOMO (Base Semidetached) 0.244 COCOMO (Base Embedded) 0.480 Proposed Model 0.038 COCOMO81 model is proposed for the SCE using fuzzy membership functions [26]. In the FL- COCOMO proposed model membership functions of Triangular, Trapezoidal, Gaussian and Generalized Bell are used. Evaluation has been conducted on 63 projects of NASA software projects. Also, for Defuzzification the Center of Area (COA) [27] method used which is defined according to equation (9). In equation (9) )(zA is the membership function's output of the system.    Z A Z A COA dzz zdzz Z )( )(   (9) In order to demonstrate the performance of proposed model MMRE and PRED (%25) criteria's were used. Table (8) shows the analysis of evaluation criteria. As it is evidence, Generalized Bell membership function is better than the other models.
  9. 9. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 35 Table 8. Evaluation of MMRE and PRED Criteria Models [26] Evaluation MMRE PRED(%25) COCOMO 81 0.39 0.47 FL-COCOMO-Triangular 0.54 0.65 FL-COCOMO-Trapezoidal 0.39 0.71 FL-COCOMO-Gaussian 0.28 0.73 FL-COCOMO-GBell 0.27 0.73 Due to uncertain factors in SCE, it should be used a model that has more accuracy in estimate and could reach the cost error to actual amount. Gaussian membership function is evaluated on the KEMERER dataset [28]. Experimental results show that the proposed model has less MMRE error in comparison with other models. In Table (9) shows MMRE criterion. Table 9. Evaluation of MMRE Criterion Models [28] MMRE Boehm Model 0.2818 Halstead 6.284 Waslton 0.2008 COCOMO (Base Organic) 0.186 COCOMO (Base Semidetached) 0.414 COCOMO (Base Embedded) 0.837 Proposed Model 0.094 In the early stages of the software development cycle, the most important feature for project managers is effort and cost. Therefore, for careful consideration of these criteria, FL Triangular membership functions are used [29]. Evaluation has been performed on the KEMERER dataset. Experimental results show that the proposed model has been able to minimize the error MARE in comparison with other models. The results of proposed model are shown in Table (10). Table 10. Evaluation of MARE Criteria Models [29] MARE% COCOMO81 (Base Model) 4532.4 Doty Model 8186.1 Bailey-Basili 1324.9 Walston 3225.4 Halsted 105605.2 Proposed Model 548.6 The new approach is based on FL called Fuzzy Emotional COCOMO II Software Cost Estimation (FECSCE) has been proposed for the SCE [30]. In COCOMO II model only software projects' factors is assessed. In FECSCE model in addition to project factors, individual's experiences, their skills, and ability level of individuals of software development group were also studied. In FECSCE model, Triangular and Trapezoidal membership functions are used. Evaluated on the EPEDC, CRRS and MECVX dataset has been done. In this model, the Multi- Agent System (MAS) is used for modeling of communication of the individuals in the team. The existence of an experienced team is an important element of complex software projects success. A project is similar to MAS in which individuals and cooperation's play a key role in achieving
  10. 10. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 36 the goals. FL and MAS was used to simulate the interaction between individual personal and social characteristics. The main purpose of the FECSCE model is reviewing team's features in order to improve accuracy of the COCOMO II model for SCE. Experimental results show that FECSCE model has better performance in estimating PM (Person/Month) than COCOMO II model. Hybrid Model of FL and PSO is proposed for the SCE [31]. Evaluation has been done on NASA software project dataset. Triangular membership function is used to fuzzification. In general, two major reforms were carried out in the Triangular membership functions that are:  Training membership functions in order to increase the detection rate  Removing un-suitable rules to reduce the number of fuzzy rules and to increase the precision and power of generalization The PSO algorithm is used to Defuzzification of membership function parameters. In the done implementations and different experiments, the rate of error is decreased and the necessary fuzzy rules number is decreased per different parameters and using PSO algorithm in the training of membership function and choice of suitable fuzzy rules. Test results show that the hybrid model has less MARE criterion in comparison with other models measure less. Table (11) is showed MARE criterion. Table 11. Evaluation of MARE Criterion Evaluation Models [31] Bailey-Basili Proposed Model MARE% 17.325 6.947 Application of FL is proposed due to more accurate SCE [32]. In the proposed model, Triangular membership functions and Generalized Bell membership functions are used. Evaluated is done on NASA93 software projects dataset. Test results show that MARE, MMRE and VARE criteria have smaller errors than the COCOMO model. Also PRED, VAF and BRE criteria are more accurate in estimate. In the proposed model with Generalized Bell membership function has better accuracy of BRE criteria. Table (12) shows the results of criteria's evaluation. Table 12. Evaluation of MARE, MMRE, VAF, VARE, BRE and PRED Criteria Models [32] Evaluation MARE MMRE VAF VARE Mean BRE PRED (30%) Fuzzy-Triangular 28.53 54.81 96.53 10.51 0.61 62 Fuzzy-GBell 23.78 63.16 95.90 32.59 0.59 65 COCOMO 47.22 59.50 33.65 46.89 0.78 53 A new model is proposed based on FL for SCE [33]. Triangular membership functions are used in the proposed model. Evaluation has been done on 15 projects of KEMERER software projects dataset. The experimental results show that the proposed model has lower error rate in comparison with other models. Table (13) shows PRED and MARE criteria. As you can see, the value of PRED of proposed model is more accurate in comparison with other models.
  11. 11. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 37 Table 13. Evaluation of PRED and MARE Criteria Models [33] Evaluation MARE PRED (40%) COCOMO 236.48 0 Bailey-Basili 101.92 46.15 Doty 629.67 0 Halstead 8123.48 0 Proposed 39.29 69.23 In order to reduce the error of COCOMO model is used FL for SCE [34]. Evaluation of the proposed model has been done on NASA93 software project dataset. Triangular membership function is used for fuzzification in the proposed model. And also for Defuzzification Mean of Maximum (MOM), COA and First of Maximum (FOM) evaluation techniques have been used. Inputs of the proposed model consists of 17 EMs, 5 SFs and KSLOC. Experimental results show that the value of MMRE error in COCOMO II model and the proposed model are equal to 0.41 and 0.36 respectively. Also the value of the PRED (%25) in the COCOMO II model and the proposed model are 39 % and 46 % respectively. FL different models based on fuzzification membership functions are presented for SCE [35]. Triangular and Gaussian membership functions are used in this model. Evaluation and the results have been done on COCOMO81 dataset. Projects in the proposed model are 15 cost drivers. Experimental results show that the proposed models have less MMRE error value than COCOMO model and also have more accurate PRED (%25). COCOMO model has many applications in SCE in the software industry. But this model is not more efficient to estimate alone. For this reason for increasing the accuracy of the COCOMO model Triangular and Gaussian membership functions are used [36]. Evaluation has been conducted on 63 projects of the NASA dataset. EM factor of 17 is used in the proposed model. Experimental results show that the proposed model has much smaller errors than the COCOMO model. Also Gaussian function is more accurate in the estimate in comparison with Triangular membership function. 4. DISCUSSION In the reviewed papers were presented efficient model for estimating cost and time of development of software projects under uncertainty as fuzzy. The cost includes planning stages, design, analysis, implementation and support. For each software project, there are three interrelated factors time, cost and manpower. Addressing each of the factors causes the impact of two other factors. Increasing project duration cause increasing more costs and has the effect on project prices. Since, in project planning required resources should already be estimated, so estimate of the time and cost of software project development is vital both for the producer and user. Resources and management are two factors for software projects operation. If these two factors are known, then the time and cost of software development can be determined. In the reviewed papers, the advantages, disadvantages and operations of different methods of SCE examined and finally a combination of COCOMO and FL methods is used for dataset of data evaluation. In the investigations, fuzzy models have been proposed with changing and composition of existing models that are usable in real conditions of software development. Efficiency and accuracy of these methods are high in comparison with the models like
  12. 12. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 38 COCOMO. Table (14) shows comparison and evaluation of fuzzy membership functions on dataset and evaluation criteria. Table 14. Comparison and Evaluation of FL Functions on Dataset Projects Approach's Membership Function Dataset Evaluation Criteria [18] Trapezoidal, Triangular, Gaussian NASA93 MRE [19] [23] [30] [32] [33] Triangular NASA, EPEDC, CRRS, MECVX, NASA93, KEMERER MMRE, MRE, PRED, MARE, VAF, VARE, BRE [20] Triangular, Trapezoidal, Gaussian, Generalized Bell, Sigmoidal NASA63 MMRE, PRED [22] Triangular, Trapezoidal NASA93, COCOMO81 PRED, MRE [24] [26] [34] Triangular, Trapezoidal, Gaussian, Generalized Bell NASA63, NASA93 MMRE, PRED [25] [29] Gaussian NASA, KEMERER MMRE, MARE [21] [28] Generalized Bell KEMERER, NASA93 MMRE, VARE [31] Trapezoidal, Triangular NASA MARE [35] [36] Triangular, Gaussian COCOMO81, NASA63 MMRE, PRED FL performance significantly depends on the designed fuzzy structure. In other words, the significant selection of this structure can affect its performance. Factors such as type of membership functions, the type of used fuzzy composition, the number of fuzzy rules and the number of used factors in the functions are of these categories. In SCE algorithmic models the value of software development defined as the linear program. While in the FL value of software development can be expressed in the form of a spectrum and in the form of degree of membership for each of the factors in developed and undeveloped software. The results of the evaluation of fuzzy membership functions on different dataset showed that Gaussian and Sigmoidal membership function had better performance than membership functions of Triangular, Trapezoidal and Generalized Bell in estimating MMRE and PRED criteria. Triangular and Gaussian membership functions are require less computing capabilities and also have not the ability to avoid the data's noise. Dataset data are better analyzed and evaluated by using the above two functions. Triangular and Gaussian membership functions in MMRE and VARE criteria have less error than the other functions. Based on the conducted surveys membership functions of Triangular, Trapezoidal, Gaussian, Sigmoidal and Generalized Bell on NASA93 dataset have less MMRE error than the NASA63 dataset. Because the NASA93 dataset has more projects, more comparisons can be done on the membership functions for fuzzification and Defuzzification of estimating effective factors. Generalized Bell membership functions in PRED (%30) criterion on the dataset NASA63 has better precision than COCOMO model and Triangular membership function. Also Triangular membership function in PRED (%40) criterion on the dataset KEMERER has better accuracy
  13. 13. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 39 than COCOMO model. In Table (15), fuzzy membership functions in terms of Accuracy, Transient Response and Oscillations are evaluated. As you can see the performance of each of the functions are different from each other. Based on investigations, we concluded that it should be considered the performance of the functions for estimate. Table 15. Evaluation of the Performance of Fuzzy Functions Membership Function Accuracy Transient Response Oscillations Triangular High Normal Normal Trapezoidal Medium Normal High Gaussian High Normal Normal Generalized Bell Medium Normal Normal Sigmoidal High High Normal 5. CONCLUSIONS AND FUTURE WORKS In this paper, SCE was investigated using the FL and the capabilities of COCOMO model. Nowadays, the use of FL as a new approach in analyzing software engineering issues such as SCE has improved. One of the issues that helps the correct use of software and prevent the software projects from failure is the accurate estimate of cost. Accurate estimates helps the developmental companies that have better analyze of software projects feasibility and effectively manage software development process. Inaccurate estimates caused additional budget and dumb estimates causes that software projects development has not enough progress and the intended software has not are produced. Therefore, this paper analyzes the FL in SCE using membership functions of Triangular, Trapezoidal, Gaussian, Generalized Bell and Sigmoidal. Functions tested and evaluated on a set of software projects dataset and showed that they have better performance than COCOMO model better. We hope in the future with presenting this paper give performed models for SCE using the fuzzy systems. REFERENCES [1] P.C. Pendharkar, “Probabilistic Estimation of Software Size and Effort”, Expert Systems with Applications, Vol. 37, pp. 4435-4440, 2010. [2] T.R. Benala, R. Mall, P. Srikavya, M.V. HariPriya, “Software Effort Estimation Using Data Mining Techniques”, Advances in Intelligent Systems and Computing, Vol. 248, pp. 85-92, Springer, 2014. [3] F.S. Gharehchopogh, I. Maleki, S.R. Khaze, “A Novel Particle Swarm Optimization Approach for Software Effort Estimation”, International Journal of Academic Research, Part A, Vol. 6. No. 2, pp. 69-76, 2014. [4] G. Sivanageswara Rao, Ch. V. Phani Krishna, K. Rajasekhara Rao, “Multi Objective Particle Swarm Optimization for Software Cost Estimation”, Advances in Intelligent Systems and Computing, Vol. 248, pp. 125-132, Springer, 2014. [5] A. Trendowicz, “Why Software Effort Estimation?”, The Fraunhofer IESE Series on Software and Systems Engineering, pp. 3-7, Springer, 2013. [6] W. Zhang, Y. Yang, Q. Wang, “A Study on Software Effort Prediction Using Machine Learning Techniques”, Communications in Computer and Information Science, Vol. 275, pp. 1-15, Springer, 2013. [7] B.W. Boehm, “Software Engineering Economics”, Prentice-Hall, Englewood Cliffs, New Jersy, 1981. [8] B.W. Boehm, “Software Cost Estimation with COCOMO II”, Prentice Hall PTR, Englewood Cliffs, New Jersy, 2000. [9] S.D. Conte, H.E. Dunsmore, V.Y. Shen, “Software Engineering Metrics and Models”, The Benjamin/Cummings Publishing Company, Inc, Menlo Park, CA, p. 214, 1986. [10] V.P. Cot, B. Oligny, N. Rivard, “Software Metrics: an Overview of Recent Results”, the Journal of Systems and Software, Vol. 8, pp. 121-131, 1988.
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  15. 15. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol.4, No.3, May 2014 41 [34] I. Attarzadeh, S.H. Ow, “Soft Computing Approach for Software Cost Estimation”, International Journal of Software Engineering (IJSE), Vol. 3 No. 1, 2010. [35] V. Sharma, H.K. Verma, “Optimized Fuzzy Logic Based Framework for Effort Estimation in Software Development”, IJCSI International Journal of Computer Science Issues, Vol. 7, Issue 2, No. 2, pp. 30-39, 2010. [36] Ch. Satyananda Reddy, K.V.S.V.N Raju, “An Improved Fuzzy Approach for COCOMO’s Effort Estimation using Gaussian Membership Function”, Journal of Software, Vol. 4, No. 5, pp. 452-459, 2009. Authors Isa Maleki is a Lecturer and Member of The Research Committee of The Department of Computer Engineering, Dehdasht Branch, Islamic Azad University, Dehdasht, Iran. He Also Has Research Collaboration with Dehdasht Universities Research Association NGO. He is a Member of Editorial Board and Review Board in Several International Journals and International Conferences. He has Published over 30 Papers in International journals and Conference Proceedings. His Interested Research Areas Are in the Software Cost Estimation, Machine Learning, Data Mining, Optimization and Artificial Intelligence. Laya Ebrahimi is a M.Sc. Student in Department of Computer Engineering, Science and Research Branch, Islamic Azad University, West Azerbaijan, Iran. Her Interested Research Areas are in Software Cost Estimation, Machine Learning, Data Mining and Optimization. Saman Jodati is a M.Sc. Student in Department of Computer Engineering, Science and Research Branch, Islamic Azad University, West Azerbaijan, Iran. His Interested Research Areas are in the Software Cost Estimation, Software Development, Machine Learning and Data Mining.

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