Analysis of software cost estimation using

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

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

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).

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 

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.

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.

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.

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.
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.

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.
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
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
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

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
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.

37
Table 13. Evaluation of PRED and MARE Criteria
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

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

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.

40
[11] A.J. Albrecht, J. Gaffney, “Software Function, Source Lines of Code, and Development Effort
Prediction: a Software Science Validation”, IEEE Transactions on Software Engineering SE, Vol. 9,
No. 6, pp. 639-648, 1983.
[12] I. Maleki, A. Ghaffari, M. Masdari, “A New Approach for Software Cost Estimation with Hybrid
Genetic Algorithm and Ant Colony Optimization”, International Journal of Innovation and Applied
Studies, Vol. 5, No. 1, pp. 72-81, 2014.
[13] F.S. Gharehchopogh, “Neural Networks Application in Software Cost Estimation: A Case Study”,
2011 International Symposium on Innovations in Intelligent Systems and Applications (INISTA
2011), pp. 69-73, IEEE, Istanbul, Turkey, 15-18 June 2011.
[14] Z.A. Khalifelu, F.S. Gharehchopogh, “Comparison and Evaluation Data Mining Techniques with
Algorithmic Models in Software Cost Estimation”, Elsevier, Procedia-Technology Journal, ISSN:
2212-0173, Vol. 1, pp. 65-71, 2012.
[15] P. Pandey, “Analysis of the Techniques for Software Cost Estimation”, Rohtak, pp. 16-19, IEEE,
2013.
[16] L. A. Zadeh, “Fuzzy sets”, Information and Control, Vol. 8, pp. 338-353, 1965.
[17] G. J. Klir, B. Yuan, “Fuzzy Sets and Fuzzy Logic”, Prentice Hall, Upper Saddle River, New Jersey,
1995.
[18] A. Malik, V. Pandey, A. Kaushik, “An Analysis of Fuzzy Approaches for COCOMO II”,
International Journal Intelligent Systems and Applications, Vol.5, pp. 68-75, 2013.
[19] Ziauddin, S. Kamal, S. khan, J.A. Nasir, “A Fuzzy Logic Based Software Cost Estimation Model”,
International Journal of Software Engineering and Its Applications, Vol. 7, No. 2, 2013.
[20] S. Ravishankar, P. Latha, “Software Cost Estimation using Fuzzy Logic”, International Conference
on Recent Trends in Computational Methods, Communication and Controls (ICON3C 2012), IJCA,
pp.38-42, 2012.
[21] S. Malathi, S. Sridhar, “Performance Evaluation of Software Effort Estimation using Fuzzy Analogy
based on Complexity”, International Journal of Computer Applications (IJCA), Vol. 40, No.3, pp. 32-
37, 2012.
[22] A. Hamdy, “Fuzzy Logic for Enhancing the Sensitivity of COCOMO Cost Model”, Journal of
Emerging Trends in Computing and Information Sciences, Vol. 3, No. 9, pp. 1292-1297, 2012.
[23] A. BalaKrishna, T.K.Rama Krishna, “Fuzzy and Swarm Intelligence for Software Effort Estimation”,
Advances in Information Technology and Management (AITM), Vol. 2, No. 1, pp. 246-250, 2012.
[24] E. Praynlin, P. Latha, “Estimating Development Effort of Software Projects using ANFIS”,
International Conference on Recent Trends in Computational Methods, Communication and Controls
(ICON3C), IJCA, pp. 15-20, 2012.
[25] R. Agarwa, Q. Alam, S. Sarwar, “Efficient Estimation of Software System Using Fuzzy Technique”,
International Journal of Electronics and Computer Science Engineering, Vol. 1, No. 3, pp. 1006-1012,
2012.
[26] P. Jha, K.S. Patnaik, “Comparative Analysis of COCOMO81 using Various Fuzzy Membership
Functions”, International Journal of Computer Applications (IJCA), Vol. 58, No. 14, pp. 220-27,
2012.
[27] R.R. Yager, D.P. Filev, “SLIDE: A Simple Adaptive Defuzzification Method”, IEEE transaction on
Fuzzy Systems, Vol. 1, No. 1, pp. 69-78, February 1992.
[28] R. Agarwal, I. Awasthi, S. Sarwar, “An Empirical Validation of Software Cost Estimation Model
Using Fuzzy Technique”, International Journal of Advances in Electrical and Electronics
Engineering, Vol. 1, No. 2, pp.188-194, 2012.
[29] J.N.V.R Swarup Kumar, A. Mandala, M.V. Chaitanya, G.V.S.N.R.V. Prasad, “Fuzzy logic for
Software Effort Estimation Using Polynomial Regression as Firing Interval”, International Journal
Computer Technology Application, Vol. 2, No. 6, pp. 1843-1847, 2011.
[30] M. Kazemifard, A. Zaeri, N. Ghasem-Aghaee, M.A. Nematbakhsh, F. Mardukhi, “Fuzzy Emotional
COCOMO II Software Cost Estimation (FECSCE) using Multi-Agent Systems”, Applied Soft
Computing, Vol. 11, pp. 2260-2270, Elsevier B.V, 2011.
[31] S. Rao.T, Prasad R.P.V.G.D, Hari Ch.V.M.K, “Fuzzy and Swarm Intelligence for Software Cost
Estimation”, Global Journal of Computer Science and Technology, Vol. 11, Issue 22, 2011.
[32] Prasad R.P.V.G.D, Sudha K. R, Rama S.P, “Application of Fuzzy Logic Approach to Software Effort
Estimation”, International Journal of Advanced Computer Science and Applications (IJACSA), Vol.
2, No. 5, pp. 87-92, 2011.
[33] A. Mittal, K. Parkash, H. Mittal, “Software Cost Estimation Using Fuzzy Logic”, ACM SIGSOFT
Software Engineering, Vol. 35, No. 1, pp. 1-7, 2010.

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.

Analysis of software cost estimation using

Recomendados

Recomendados

Más contenido relacionado

La actualidad más candente

La actualidad más candente (20)

Similar a Analysis of software cost estimation using

Similar a Analysis of software cost estimation using (20)

Más de ijfcstjournal

Más de ijfcstjournal (20)

Último

Último (20)

Analysis of software cost estimation using