Software Effort Estimation Using Fuzzy Logic: A Review

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Software Effort Estimation Using Fuzzy Logic: A Review

Rahul Kumar Yadav Mewar University Gangrar, Chhittorghara, India

Dr. S. Niranjan

PDM School of Technology & Management, Bahadurgarh, India.


One of the major problems with software project management is the difficulty to predict accurately the required effort for developing software applications. This is due to the reason that most of the software estimates should be performed at the beginning of the life cycle, when we do not yet know the problem we are going to solve. The task of effort estimation is challenging and is an important area of research in the field of Software Project Management. Though a number of estimation models exist for effort prediction, still many newer models are being proposed and active research is going on to obtain more accurate estimation models. In this paper we survey the most common and widely used effort estimation techniques using fuzzy logic. The survey shows that fuzzy logic effort estimation can be coupled with other techniques such as neural network, Bayesian Network and Particle Swarm Optimization technique. Recent trends on effort estimation have also been discussed at length.

Keywords- Software Development Effort, Effort Estimation, Fuzzy Logic Techniques, Estimation Models.

  1. Introduction

    It is ideally desirable that the improvement in estimation techniques currently available to project managers would facilitate increased control of time and overall cost benefit in software development life cycle. Furthermore, any improvement in the accuracy of predicting the development effort can significantly reduce the costs from errors, such as estimating inaccurately, inappropriate tendering bids, and disabling the monitoring progress. Software

    development effort estimates are the basis for project bidding and planning. The consequences of poor budgeting and planning can be disastrous: if they are too pessimistic, business opportunities can be gone astray, while optimism may be followed by significant loss. Software effort estimation has even been identified as one of the three most demanding challenges in software application areas [1]. During the development process, the cost and time estimates are useful for the initial rough validation and monitoring of the projects completion process. And in addition, these estimates may be useful for project productivity assessment phases. Software effort estimation models are divided into two main categories: viz., algorithmic and non-algorithmic. The most popular algorithmic estimation models include Boehms COCOMO [2], Putnams SLIM[3] and Albrechts Function Point[4]. Non-algorithmic techniques include Price-to-Win [1],Parkinson [1], expert judgment [1] and machine learning approaches[5]. Machine learning is used to group together a set of techniques that embodies some of the facets of human mind [5]. For example, fuzzy systems, analogy, regression trees, rule induction and neural networks are among the machine learning approaches, and fuzzy systems and neural networks are considered to belong to the soft computing paradigm.

    1. Algorithmic models

      Some of the famous algorithmic models are: Boehms COCOMO81, II (Boehm et al., 2000), Albrechts Function Point (Boehm et al., 2000; Boehm, 1995) and Putnams (1978) SLIM. All of them require inputs, accurate estimate of specific attributes, such as Line of Code (LOC), number of user screen, interfaces and complexity, which are not easy to acquire during

      the early stage of software development life cycle process. Models based on historical data have limitations. Understanding and the calculation using these models are difficult due to inherent complex relationships between the related attributes, which are unable to handle categorical data as well as lack of reasoning capabilities [6]. Besides, attributes and relationships used to predict software development effort those could change with the passage of time and/or differ for software development environments (Srinivasan and Fisher, 1995). The limitations of the algorithmic models led to the exploration of the nonalgorithmic techniques visualised through soft computing philosophy.

    2. Non-Algorithmic models

      In 1990s non-algorithmic model was conceptualized and have been proposed to project cost estimation. Software researchers have turned their attention to new approaches those are based on soft computing methodologies such as based on artificial neural networks and fuzzy logic models and genetic algorithms based implementations. Neural networks are able to generalize from trained data set. A set of training data, a specific learning algorithm makes a set of rules that fit the data and fits previously unseen data in a rational manner as well. Some of the early works show that neural networks are adequately applicable to cost estimation phases as presented in the works of Venkatachalam [7] and Krishna and Satsangi [8]. Fuzzy logic offers a powerful linguistic representation that is sufficiently accommodate the imprecision in inputs and outputs, while providing a more realistic knowledge based approach to model building. Contemporary research establishes to some extent that fuzzy logic model achieved good performance index, being outperformed in terms of accuracy only by neural network model with considerably more input variables. Hodgkinson and Garratt in their works presented that estimation by expert judgment was better than all regression based models [9].

    3. Fuzzy logic models

      A fuzzy model is used when the systems are not suitable for analysis by conventional approach or when the available data is uncertain, inaccurate or vague [10]. The fuzzy model uses the fuzzy logic concepts introduced by Lofti A. Zadeh [11]. Fuzzy reasoning consists of three main components [12]: fuzzification process, inference from fuzzy rules and defuzzification process. Fuzzification process is where the objective term is transformed into a fuzzy concept. The membership functions are applied to the actual values

      of variables to determine the confidence factor or membership value (MV). Fuzzification allows input and output to be expressed in linguistic terms. Inferencing involves defuzzification of the conditions of the rules and propagation of the confidence factors of the conditions to the conclusion of the rules. Defuzzification process refers to the translation of fuzzy output into objective terms.

      A system based on Fuzzy Logic has a direct relationship with fuzzy concepts (such as fuzzy sets, linguistic Variables etc.) and fuzzy logic. The popular fuzzy logic systems can be categorised into three types: pure fuzzy logic systems, Takagi and Sugenos fuzzy system, fuzzy logic systems with fuzzification and defuzzification [12]. Since most of the engineering applications produce crisp data as input and expects crisp data as output, the last type i.e., fuzzy logic system with fuzzification and defuzzification is most widely used one and was first proposed by Mamdani. It has been successfully applied to a variety of industrial processes and consumer products [12].

      1.3.1 Fuzzy Logic in Software Effort Estimation

      A fuzzy set theoretic model is a modelling construct featuring two main properties [13]: (1) It operates at a level of linguistic terms (fuzzy sets), and (2) it represents and processes uncertainty. Fuzzy logic offers a particularly convenient way to generate a keen mapping between input and output spaces thanks to the natural expression of fuzzy rules. In software development effort estimation, two considerations justify the deciion of implement–ing a fuzzy model:1) it is impossible to develop a precise mathematical model of the domain [14]; second, metrics only produce estimations of the real complexity. Thus, according to the previous assertions, formulating a tiny set of natural rules describing underlying interactions between the software metrics and the effort estimation could effortlessly reveal their intrinsic and wider correlations.

  2. Review of Software Estimation Based On Fuzzy Logic Techniques

    During the last decade, many methodologies have been developed in the areas of software cost estimation for improving estimation accuracy. Here we present a tabular view (Table 1) of works of various authors on software development effort estimation based on Fuzzy Logic techniques and concepts.

    Table 1. Research on Software Development Effort Estimation Based On Fuzzy Logic Techniques.



    Related Work Done

    Result Reported

    Fei Z and Liu X


    Introduced the f-COCOMO model

    Since there was no comparison of


    which applied Fuzzy Logic to the COCOMO model for software effort

    results between the f-COCOMO and other effort estimation models in their


    study the estimation capability of their

    model is unknown.

    S. Kumar, B.A.


    Had applied fuzzy logic in

    The w o r k s h o w e d h o w fuzzy

    Krishna and P.S.

    Putnams manpower buildup index

    F A M s can be effectively applied to

    Satsangi [16]

    ( MBI) estimation model. MBI

    the domain of software project

    selection process was based

    management and control for the

    upon 64 different fuzzy associative

    estimation of the MBI.

    memory (FAM) rules.

    Gray and MacDonell [17]


    Compared Function Point Analysis, Regression techniques, feedforward neural network and fuzzy logic in software effort estimation.

    Their results showed that fuzzy logic model achieved good performance, being outperformed in terms of accuracy only by neural network model with considerably more input variables.

    Gray and


    Developed FULSOME (Fuzzy

    The automatically generated fuzzy

    MacDonell [18]

    Logic for Software Metrics) which is a

    model performs acceptably when

    set of tools that helps in creating fuzzy

    compared to regression-based models.


    J. Ryder [19]


    Researched on the application of fuzzy logic to COCOMO and Function Points models.

    Result showed Fuzzy Logic is good at making effort estimations.

    P. Musflek, W.


    Worked on fuzzifying basic COCOMO

    They concluded that (a) fuzzy sets help

    Pedrycz, G. Succi

    model without considering the

    articulate the estimates and their

    and M. Reformat

    adjustment factor. In their simple f-

    essence (by exploiting fuzzy numbers


    COCOMO model, the size input into the

    described by asymmetric membership

    COCOMO model is represented by a

    functions) and (b) they generate a

    fuzzy set, while a and b coefficients are

    feedback as to the given uncertainty

    crisp values. Besides the size,

    (granularity) of the results.

    augmented f- COCOMO also fuzzified

    both the coefficients related to the

    developm ent mode.Triangular memb-

    ership functions are used in this


    A.Idri, A. Abran,


    Proposed fuzzy intermediate

    Validation results showed that the

    L. Kjiri [21]

    COCOMO'81. The FLM is based upon

    fuzzy intermediate COCOMO81 can

    trapezoidal membership functions. The

    tolerate imprecision in its input (cost

    dataset is randomly generated and

    drivers) and generate more gradual

    compared with actual data of

    outputs. Thus fuzzy intermediate

    COCOMO 81. The effort multiplier for

    COCOMO81 is less sensitive to the

    each cost driver is obtained from fuzzy

    changes in the inputs as compared

    set, enabling its gradual transition from one interval to a contiguous interval such as from high to very high).

    to intermediate COCOMO81.

    A. Idri, and A.


    Proposed an approach based on

    Taking into account their results,


    fuzzy logic named Fuzzy Analogy. Its

    they suggested the following ranking of the

    dataset is that of COCOMO 81.

    four techniques in terms of accuracy and

    adequacy to deal with linguistic values: 1.

    Fuzzy Logic, 2. Fuzzy intermediate

    COCOMO81, 3.Classical intermediate

    COCOMO81, and 4. Classical Analogy.

    Huang, X.,


    Proposed a model combining fuzzy

    The results of the fuzzy logic model

    Capretz. L.F.,

    logic and neural networks. The

    were better than those of the COCOMO

    Ren, J., Ho. [23]

    dataset was obtained from the

    equations. The FLM was based

    original COCOMO (1981).

    upon triangular membership functions.

    The main benet of this model is its

    good interpretability by using the fuzzy


    M.O. Saliu, M.


    They fuzzyfied the two different

    This approach is able to deal with

    Ahmed and J.

    portions of the intermediate COCOMO

    uncertainty, provides transparency on

    AlGhamdi. [24]

    model i.e. nominal effort estimation

    prediction rationale through rules,

    and the adjustment fac tor . They

    incorporate experts knowledge in the

    p rop os ed a fu z z y logic framework

    definition of membership functions and

    for effort prediction by integrating the

    rules, as well as adaptable to new data

    fuzzified nominal effort and th

    by changing the parameters of

    fuzzified effort multipliers of

    membership functions.

    theintermediate COCOMO model.

    Ahmed, M.A.,


    Presented a FLM based upon

    Results showed that the FLM was

    Saliu, M.O. and

    triangular membership functions.

    slightly better than COCOMO equations.

    AlGhamdi, J. [25]

    The dataset for validating the

    In addition, they reported promising

    FLM was (a) generated randomly

    experimental summary results in

    and (b) that of COCOMO 81 was

    spite of the little background knowledge


    of the rule base and training data.

    Crespo, F.J.,


    Explored fuzzy regression techniques

    Fuzzy regression is able to obtain

    Sicicila, M.A.,

    based upon fuzzication of input

    estimation models with similar predictive

    Cuadrado, J.J.

    values. Project database of COCOMO-

    properties than existing basic estimation


    81 are used.


    M.R. Braz, S.R.


    Applied Fuzzy Logic for effort

    Results showed that FUSP fares

    Vergilio. [27]

    estimation of object-oriented software.

    better than USP.

    FUSP (Fuzzy use case size

    points) metric allows gradual

    classifications of use case size

    points in the effort estimation by using

    fuzzy numbers.

    Xu and


    Presented a fuzzy identication cost estimation modelling technique to deal with linguistic data, and

    It was observed that the fuzzy identication model provided signicantly better cost estimations than the three

    Khoshgoftaar [28]

    automatically generate fuzzy membership functions and rules. A case of study based on the COCOMO81 database compared the proposed model with all three COCOMO81 models (basic, intermediate and detailed).

    COCOMO81 models.


    Y.M. Cornelio and G.T.Agustin.



    Carried out a study to compare personal Fuzzy Logic Systems (FLS) with linear regression using evaluation criteria which is based upon ANOVA of MRE and MER, as well as MMRE, MMER and pred(25)

    Results show that a FLS can be used as an alternative for estimating the development effort at personal level.

    Moon Ting Su,


    Proposed an enhanced fuzzy logic

    The analysis of the results shows that

    Teck Chaw Ling,

    model for the estimation of software

    FLECE is able to obtain more accurate

    Keat Keong

    development effort. The model Fuzzy

    results in the estimation of software

    Phang, Chee

    Logic Model for Software

    development effort when compared

    Sun Liew and

    Development Effort and Cost

    to the previous fuzzy logic model.

    Peck Yen Man

    Estimation (FLECE) possesses

    Hence, the enhancements to FLECE


    similar capabilities as the previous

    are truly useful and had given better

    fuzzy logic model. In addition to that,

    performance to the model.

    the enhancements done in FLECE

    improved the empirical accuracy of

    the previous model in terms of MMRE

    (Mean Magnitude of Relative Error)

    and threshold- oriented prediction

    measure or prediction quality (pred).

    Venus Marza,


    Hybrid neuro-fuzzy technique is used

    The results showed that neuro-fuzzy

    Amin Seyyedi,

    for development time and is validated

    system is much better than two other

    and Luiz

    with gathered data.

    mentioned methods (fuzzy logic and


    neural network separately).Hence, In


    order to achieve more accurate

    estimation, several techniques maybe


    Parvinder S.


    Neuro-Fuzzy technique is used for

    The performance of the Neuro-fuzzy

    Sandhu, Porush

    software estimation of NASA software

    based effort estimation Model and the

    Bassi, and

    project data and performance of the

    other existing Halstead Model, Walston-

    Amanpreet Singh

    developed models are compared with the

    Felix Model, Bailey-Basili Model and Doty


    Halstead, Walston-Felix, Bailey-Basili

    Model models is compared for effort

    and Doty Models

    dataset .The results show that the Neuro-

    fuzzy system has the lowest MMRE and

    RMSSE values.

    Iman Attarzadeh and Siew


    Proposed an enhanced Fuzzy Logic approach for the estimation of software development effort.

    Results s h o w e d t h a t t h e v a l u e of M M R E applying their Fuzzy Logic model was substantially lower than MMRE values

    Hock Ow [33]

    as calculated by applying other Fuzzy Logic models.

    Ch. Satyananda Ready, KVSVN Raju[34]


    The proposed work is based on COCOMO dataset and the experimental part of the study illustrates the approach using Gaussian membership function

    Result showed the proposed model gives more precise result than that of using the TMF. Thus by using GMF, the accuracy of effort estimation can be improved and the estimated effort can be very close to the actual effort.


    Proposed an approach combining the neuro-fuzzy technique and the SEER-

    Results shows that that combining the neuro-fuzzy model with the SEER-SEM

    Wei Lin Du, Danny Ho, Luiz Fernando Capretz[35]

    SEM effort estimation algorithm and evaluate the prediction performance of the proposed neuro-fuzzy model with SEER-SEM in software estimation practices.

    effort estimation model produces unique characteristics and performance improvements. Results also proves that the proposed neuro-fuzzy structure can be used with other algorithmic models besides the

    COCOMO model.

    Abou Bakar Nauman, Romana Aziz[36]


    This paper proposes a simple Bayesian Network (BN), based on classification approach. The classes of ranges of size value are distributed with help of fuzzification to distribute the probability of crisp value.

    The proposed model shows two specific achievements. 1). Model shows that a smaller Bayesian network can be developed to achieve intelligent effort estimates. 2). The classifications of sizes can be managed with the help of fuzzy logic.

    Prasad Reddy P.V.G.D, Sudha

    K. R, Rama Sree [37]


    Software development effort predicted using Fuzzy Triangular Membership Function and GBell Membership Function is implemented and compared with COCOMO using NASA93 dataset.

    Results shows that software effort estimation using Fuzzy method with TMF (triangular membership function) is

    better than Fuzzy method using GBellMF or Intermediate COCOMO. It is not possible to evolve a method, which can give 100 % VAF. By suitably adjusting the values of the parameters in FIS we can optimize the estimated effort.

    A.BalaKrishna, T.K.Rama Krishna[38]


    The propsed work is to employ Particle Swarm Optimization for tuning the effort parameters, fuzzy logic for reducing uncertainty in input and test its

    Results shows that the proposed model reduce the uncertainty in the input sizes by using fuzzy logic and by lining the parameters of the cost model using PSO

    suitability for software effort estimation.

    with inertia weight in order to generate an

    This methodology is then tested using

    optimal result. The model was proved to be

    NASA dataset provided by Boehm. The

    efficient on the basis of VARE, MARE and

    results are then compared with the models such as Baily-Basili, Alaa F.

    VAF after comparing with the models such as Baily-Basili, Alaa F. Sheta, and Harish

    Sheta, and Harish models.


  3. Conclusion

    Although many researchers contributed on cost/effort estimation, still many issues on cost/effort estimation remain unresolved. In this paper we presented a review on the Fuzzy Logic applications in Software development effort estimation models development. We also discussed the various advantages of Fuzzy Logic for developing prediction models. In order to achieve more accurate estimation, voting the estimated values of several techniques and combine their results maybe be useful. Further results can explore using four fuzzy logic membership functions Fuzzy Triangular Membership Function, GBell Membership Function, Gauss Membership Function and Trapezoidal Membership Function and their results will be compared with other estimation models and actual data set of the project. The fuzzy logic models for effort estimation can be deployed on COCOMO II environment for creating an appropriate expert system for providing required information for developing fuzzy sets and an appropriate rule base.

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