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Assessment of Software Quality: Choquet Integral Approach
Available online at www.sciencedirect.com
Procedia Technology 6 (2012) 153 – 162
2nd International Conference on Communication, Computing & Security [ICCCS-2012]
Assessment of Software Quality: Choquet Integral Approach Vatesh Pasrija, Sanjay Kumar, Praveen Ranjan Srivastava Computer Science & Information System Department, BITS PILANI 333031 (INDIA) Email: {Er.VateshPasrija, er.sanjaykr1989, praveenrsrivastava}@gmail.com
Abstract Software measurement is a software engineering discipline which deals in quantifying the characteristics of a software product or software process. The measurement of the characteristics of software refers to the comparative study of the same and hence the quality of the software comes into picture. There are software quality models made but none of these give quantification of quality parameters. Hence this paper proposes a methodology for comparing different software solutions based on the SRS to a common problem. Software quality is highly unpredictable, it is the existence of desirable characteristics in a solution, while the desired attributes differ with different view point and are highly interdependent. Therefore Choquet Integral is used to efficiently compare the set of solutions to be implemented for software. © Ltd...Selection and/or peer-review under responsibility ofresponsibility the Department Science & © 2012 2012Elsevier Published by Elsevier Ltd. Selection and/or peer-review under ofof theComputer Department of Computer Engineering, National Institute of Technology Science & Engineering, National Institute ofRourkela Technology Rourkela Keywords: Software Quality;Quality parameters; Choquet Fuzzy Integral; Fuzzy Measure; Interactive Criteria; Multi Criteria Decision Making; Interaction Degree.
1. Introduction Software engineering is the application of a systematic, disciplined, quantifiable approach to the development, operation, and maintenance of software, and the study of these approaches (Bourque et. al., 1999). In software development process, software quality is an important and complex issue. With the advancement of the IT industry and the growing needs of software the demand for high quality software tive, methods, processes and procedures which provide various different alternatives to a common problem. Hence which alternative to choose is decided by the quality of the solution provided i.e. the degree to which the desired set of inherent characteristics fulfils the requirements. Quality is a relative term which differs with viewpoints Transcendental View, Product View, Manufacturing View, User View and Value-based View (Kitchenham et. al, 1996). Various quality models like Boehm's Model (Milicic, 2005), McCall's Model (Cote et. al., 2006), and ISO/IEC 9126 Model (ISO/IEC 9216) have been proposed to develop generic software applications.
2212-0173 © 2012 Elsevier Ltd...Selection and/or peer-review under responsibility of the Department of Computer Science & Engineering, National Institute of Technology Rourkela doi:10.1016/j.protcy.2012.10.019
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Considering the emphasis on software quality, an effort has been made to evaluate alternative solutions. The solutions proposed for a common Software Requirements Specification (SRS) are ranked on the basis of quality attributes which are highly interdependent. This paper proposes a model to rank the alternative solutions using Choquet Integral (Grabisch et. al., 2000). The ranking allows companies, customers and clients to take appropriate decisions on which alternative to work with from a quality point of view. The remainder of the paper is segregated as follows: Section 2 mentions Background work, Section 3 deals with application of Choquet Integral for quantification, Section 4 explains the proposed architecture of this paper, Section 5 Identify fuzzy measures while Section 6 demonstrates a case study followed by Section 7 which discusses the comparison of proposed methodology with existing previous techniques, Section 8 provides the conclusion and Section 9 defines the future scope of the paper. 2. Background Work The IT industry demands software for both functionality and quality, i.e. the extent to which the inherent characteristics exist fulfilling the functional requirements. This gave birth to the problem of evaluating or measuring the software quality so that two or more solutions to a common problem can be measured on the basis of functionality and can be worked upon. There were various problems related to the measurement of quality attributes existence of multiple metrics to determine quality such as cost (Slaughter et. al., 1998); quality, effort and cycle time (Agarwal et. al.,2007); maintainability (Heitlager et. al., 2007), usability (Bertoa et. al., 2006); reliability (Brown et. al., 1975), functionality (Maryoly et. al., 2003). Secondly, these metrics or criteria cannot be taken separately to quantify quality. Thirdly, these multiple criteria are dependent on each other (Takahagi, 2005). Various quality parameters have been used for quantifying software quality from the perspectives of the developer, user and project manager (Srivastava & Kumar, 2009). These quality attributes based on various perspectives or views are not independent of each other and are also fuzzy in nature. Fuzzy set theory based on ISO 9126 Quality Model has been used to calculate software quality for evaluation of user satisfaction (Lin et. al., 2007). Similarly, Yang (2007) proposed a software quality prediction model based on fuzzy neural networks and Yuen et. al. (2008) proposed a fuzzy AHP model for software quality evaluation and software vendor selection under uncertainty. Another highly related work is the paper by Hazura (2011), that discuss the problem of extracting an overall score for a web based application. Hazura (2011) used a Fuzzy Integral approach as an aggregation operator for overall assessment. However, Hazura (2011) focused on assessing the quality of only web based application and does not take into consideration the quality from various perspectives like user, value, product etc. While quantifying the parameters, it does not justify whether the fuzzy values will be entered by user or developers. In contrast the current work provides a generic framework for quantifying quality of any type of application. The techniques used till date are considering criterion to be independent, but taking dependency nature among criteria into consideration this paper uses Choquet Integral to evaluate software quality. Choquet Integral has been used and proposed in this paper to quantify the software solutions/alternatives build on the SRS of the problem. The multiple criteria are assigned rate and weights or and are integrated using Choquet Integral as they are highly interdependent. In this paper a hybrid quality model with categorization of criterion is proposed covering the major five views to the software quality, as specified by Kitchenham (1996) in Table 1. 3. Choquet Integral Choquet Integral is an aggregation operator which generalizes the weighted arithmetic mean. It uses the concept of fuzzy measure and is able to account multiple interdependent criteria. There are various aggregation methods like Weighted Arithmetic Mean, Maximum and Minimum etc. but the Choquet
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integral provides greater flexibility. The use of Choquet Integral in multi-criteria decision making has been proposed by many authors (Grabisch, 1996; Grabisch et. al., 2000). Choquet Integral is defined by two different definitions (Grabisch et. al., 2000) as ) = 0 where (a) A B X (b)
is empty set.
C (f )
n i 1
f ( x (i)) f ( x (i 1)) (A(i))
The use of Choquet Integral can be seen in the later sections. Table 1: Views of Software Quality View User View Manufacturing View
Product View
Value Based View Transcendental View
Description User interaction point of view Product quality during the manufacturing phase i.e. the production and after delivery phase
P
qualities
Quality Parameters Reliability, Usability Architecture (Hansen et. al., 2009), Flexibility (Eden, 2006), Maintainability (Cote , 2006), Modifiability (Dromey, 1995), Testability (Ganesh, 2010), Reusability (Singh et. al., 2010) Correctness (Dromey, 1995), Efficiency (Cote et. al., 2006), Functionality (Dromey, 1995), Interoperability (Yuen et. al., 2011), Portability (Cote et. al., 2006), Security (Dromey, 1995), System (Cote et. al., 2006)
Cost and Economic aspects
Cost, Time, Schedule Pressure
States that product quality is abstract yet universally identifiable
Brand Value, Human Touch
4. The Proposed Architecture This paper proposes a technique to evaluate the prepared alternative solutions based on the SRS of a problem statement and choosing the best among them. The proposed method uses ISO/IEC 9126 as baseline model to select the criteria based on which the software quality can be calculated. The technique takes direct input for weight of each criteria considered for software quality. In general (Challa et. al., 2011), weight and rate of criteria are fuzzy in nature and cannot be accurately measured. Hence the technique known as fuzzification (Srivastava et. al., 2010) plays an important role in the assessment of software quality. The weights and rating of the criteria are purely on the basis of the judgment of the decision maker. The decision makers provide the rating to the criteria from the user, product, man authority in the organization. The ratings collected are then aggregated by recursively using Choquet Integral (Grabisch et. al., 2000) taking into consideration the interaction among the criteria. The Choquet Integral used is based on the fuzzy measure and is used for aggregation of partial values. The concept of fuzzy measure in Choquet Integral acts as indices on parameters which help to interpret the importance of each criterion. The shapely value (Winter, 2002) is used for the identification of fuzzy measurers which are used by Choquet Integral to rank the alternatives. The proposed flow graph is as shown in fig.1.
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Software quality can be seen from different viewpoints each having their own criteria which act as a metric for accessing the software quality. The assessment of software quality is done by aggregating the weight and rate of these criteria in particular views and then again aggregating the weight and rate of views using the Choquet Integral for the second time to get final software quality.
Start
Solutions to SRS
Direct Input of Weight and Rate of Criteria by Decision Maker
Apply Choquet Integral
Fuzzy Measure Identification Standard Using Shapely Value
Result
Fig. 1. Flow Graph for proposed methodology. Stop
5. Fuzzy Measures Fuzzy measure μi indicates the importance of individual criteria and group of criteria when taken together in a Set. The following interpretations (J. L. Marichal, 2000) can be made from fuzzy measures. A criteria xi is important if value of μi is high. However for the importance of xi, it may not be enough to look at only the value of μi but also we have to consider the value of μij, μijk etc. where j,k are other criteria. Now if μi and μj are high but μij do not have much difference from μi and μj then we can interpret that the importance of criteria x i and xj taken separately is same as xi and xj taken together. So we should not have much interest in considering them both. On the other hand if μ i and μj have low values but μij is very large then xi and xj are not much importance as compared to the importance when both taken together. Based on this concept importance and interaction indexes can be computed and Fuzzy Measures can be identified using Shapely value Standard. Shapley Value Standard: Shapley (Winter, 2002) proposed in 1953 a definition of a coefficient of importance, based on a set of reasonable axioms. In this standard, weights are positive values. This method (Takahagi, 2005) calculates the fuzzy measure μ such that shi (μ ) = wi, i where shi (μ ) is the Shapley Value of ith evaluation item of the fuzzy measure μ and is represented as:
shi
(S )[ S x n
(S )
] , where n (S) ( S /{i})
(n
S )!( S 1)! n!
and of X containing ith criteria, |S|= Number of subsets in S. This method is used to find fuzzy measures for each criterion, for Algorithm refer (Takahagi, 2005).Using Shapely value standard and Choquet Integral case study is mentioned in next section. 6. The Case Study An example to above procedure is solved to find the best alternative solution to common SRS based on five different view point of software quality. The ranking among the alternatives, for e.g. A1, A2, A3, is done by Choquet Integral using fuzzy measure. Before calculating the quality aspect in each alternative there is a need to define criteria on the basis of which comparison can be made. To find the quality, this paper considers three views i.e. User, Product, Manufacturing and their criteria as shown in fig.2.
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S/w Quality
User View
Reliability
Product View
Usability
Portability
Manufacturing View
Efficiency
Flexibility
Reusability
Fig. 2. Categorization of criteria in different views Table 2. Weights of criteria Name of Criteria
Weight Assigned
Name of Criteria
Weight Assigned
Usability
2
Efficiency
6
Reliability
8
Flexibility
7
Portability
4
Reusability
5
Step1:- Input weight (on the scale of 10) of criteria selected on the basis of their importance as shown in Table 2. Step 2:- Enter the rating (on the scale of 1) of each criterion for each alternative as shown in Table 3. Step 3:- Using Table 3, find the fuzzy measures for criteria of Manufacturing view i.e. Flexibility, Reusability using Shapley Value Standard. For Instance: if X= {Flexibility, Reusability} then for i=Flexibility, power set S of X containing i, can be defined as {{Flexibility, Reusability}, {Portability}}.So, |S|= Number of subsets in S=2. Now using Shapley value standard (Takahagi, 2005) for i=Flexibility and Inter get μ (Flexibility) = 0.29591. Similarly fuzzy measure for all the criteria under each view of Alternative A1, A2 and A3 can be calculated as shown in Table 4.Since Fuzzy measure are dependent on weights of criteria, so fuzzy measures for all the alternative are same as shown in Table 4. Step 4:- Now Apply Choquet Integral to aggregate the rating values of flexibility and reusability (from Table 3) to get rating value for manufacturing view as shown in Table 5. The Table 5 shown below is the simplest calculation based on formula of Choquet Integral mentioned in section 3.Similarly rating values of the criteria in other views can be aggregated and the result is as shown in Table 6.This procedure is repeated for Alternative A2 and A3 to get the aggregated value as shown in Table 6. Step 5:- Table 6 gives the rating value for each view for Alternative A1.Similarly rating value for Alternative A2, A3 can be calculated as shown in Table 6. Step 6:- Calculate the weight of Manufacturing View, User View and Product View as follows:Weight of Manufacturing View: Average of weight of Flexibility and Reusability = (7+5)/2=6 Weight of Product View: Average of weight of Portability and Efficiency = (6+4)/2=5 Weight of User View: Average of weight of Reliability and Usability = (8+2)/2=5 Table 3. Rating for each criterion Alternatives
Flexibility
Reusability
Portability
Efficiency
Reliability
Usability
A1
0.5
0.4
0.3
0.2
0.4
0.3
A2
0.4
0.3
0.4
0.3
0.2
0.1
A3
0.6
0.4
0.3
0.5
0.6
0.1
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Table 4. Fuzzy measures for each Alternatives Fuzzy Measures
Alternative A1, A2, A3
μ (Flexibility)
Fuzzy Measure
Alternative A1, A2, A3
0.29591
μ (Usability, Reliability)
1
μ (Reusability)
0.129461
μ (Efficiency)
0.319225
μ(Flexibility, Reusability)
1
μ (Portability)
0.117609
μ (Usability)
0.0346481
μ (Efficiency, Portability)
1
μ (Reliability)
0.635216
Step 7:- Again we have rate and weights of each view as in step 3, where we have for each criterion, so similar procedure of fuzzy measures and then Choquet Integral can be used to aggregate the value of Manufacturing, User and Product View to get Final Rating of the Alternatives. Choquet Values for each Alternative is shown in Table 7, since A3 Alternative is having the highest value of Choquet Integral, so it is considered to be the best Alternative among the three Alternatives (A1, A2, and A3). Table 5: Choquet Value for Manufacturing View
Criteria
Rating Values (Decreasing Order) (From Step 2)
Difference Between Succesive Rating values(D). Take 0 as Last Value
Cumulative Capacity
Fuzzy Measure Value(F)
Choquet Value= F*D
Flexibility
0.5
0.5-0.4=0.1
μ (Flexibility)
0.29591
0.029591
Reusability
0.4
0.4-0= 0.4
μ (Flexibility, Reusability)
1
0.4 0.429591
Table 6: Rating Values of Different Views for each Alternative Alternatives
Manufacturing View
Product View
User View
A1 A2
0.429591
0.21176
0.363521
0.329591
0.311759
0.163521
A3
0.459182
0.363843
0.417608
In this case study, we used recursive application of Choquet Integral where we started from input of rate and weights of criteria of each Alternative and then used Choquet Integral to aggregate the ratings of criteria to move one level up to get the Rating value for respective views of each Alternative and then again applied Choquet Integral to aggregate the calculated Rating value of views to move one more level up to get the final Software Quality of each Alternative. 7. Comparison with Existing Approach This paper addresses the solution to problem of aggregation, which is the process of aggregating several values into single value. Previous work done on software quality uses Analytic Hierarchy Process (AHP) (Kasperczyk et. al., 1996), Weighted Arithmetic Mean (Srivastava & Jain, 2009), Empirical Approach (Sharma et. al., 2008) and other multi-criteria decision making approaches (Yang, 2007; 22] for aggregation. A.Sharma (2008), P.R.Srivastava (2009), Yang (2007) and Kanellopoulos (2010)and had tried to quantify software quality but did not consider the fuzzy nature of software quality parameters
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whereas our approach in this paper incorporates fuzzy logic to deal with unpredictable nature of quality parameters. P.R.Srivastava (2009, 2010), Challa et. al. (2011), Yang (2007), Che-Wei Chang (2007) tried to quantify software quality using fuzzy multi criteria approach without considering interaction between criteria. Our approach in this paper uses Choquet Integral with fuzzy measure to quantify the interacting software quality parameters and finds the best software among different software and also made analysis of effect of interaction among criteria in finding best alternative. P.R. Srivastava (Srivastava & Kumar, 2009; Srivastava & Jain, 2009; Srivastava et. al, 2010) categorizes the software quality in terms of manager, developer and user irrespective of the relevance of the attributes. However, the current work gives the broader categorization of software quality parameters in 5 different views i.e. User, Product, Manufacturing, Transcendental, and Value. Table 7. Choquet value for Each Alternatives Alternatives A1 A2 A3
Choquet Values 0.279042 0.223303 0.389989
Comparison with Weighted Arithmetic Mean Method: - The Weighted Arithmetic Mean Method (WAM) can be illustrated as Choquet integral, an extension of weighted arithmetic means (WAM) (Srivastava & Kumar, 2009) which is one of the methods of multi-criteria decision making approach. The main benefit of using Choquet over the other aggregation operations is that it is an efficient approach which takes into consideration the interaction among the criteria while performing the aggregation operation (BenHassine et. al., 2010). This concept can be well understood by an illustrative example. Let us consider a problem of evaluating Students in BITS-Pilani on the basis of marks scored in following 3 subjects Statistics, Probability and Algebra. Now suppose if BITS-Pilani pay more attention towards Statistics than Algebra then considering weights of subjects as coefficient of importance can be taken as 3, 3, and 2 respectively. So using Weighted Arithmetic Mean, Student 'A' is better than Student 'B' and Student 'C', since he has highest weighted score as shown in Table 8. But if BITS-Pilani also wants the student who is well versed with all the 3 subjects then Student 'C' is better than other students as Student 'C' has scored consistent marks in all the 3 subjects. But in WAM approach Student A was considered to be better student even though he was weak in Algebra. This is due to much importance is given to Statistics and Probability, which are in sense redundant. Generally a student good at Statistics is also good at Probability (and vice versa).Hence interdependence can be seen in these two criteria. So this problem can be solved with Choquet Integral with fuzzy measure as input. Note the following points: Though BITS-Pilani is giving more importance to Statistics than Algebra then following weights of preserving the initial ratio. Table 8. Illustration of WAM using three subjects Student\Subject
Statistics
Probability
Algebra
WAM(Weighted Arithmetic Mean)
Student A
18
16
10
15.25
Student B
10
12
18
12.75
Student C
14
14
15
14.625
159
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Table 9. Illustration of Choquet Value using three subject Student
Statistics
Probability
Algebra
Choquet Value
Student A
18
16
10
13.9
Student B
10
12
18
13.6
Student C
14
14
15
14.6
As Statistics and Probability are overlapping Subjects, the weights used for the pair Statistics and Probability should be less than sum of weights of Statistics and Algebra and sum of weights of Probability and Algebra, As student equally good at Statistics subject and Algebra must be favored so that the weights for the pair of Statistics and Algebra must be greater than sum of individual weights of Statistics and Algebra. , So according to Choquet Integral Student 'C' is better than Student 'A' and 'B' as he has highest Choquet Integral value shown in Table 9. In contrast to Weighted Arithmetic Mean Score Student A was better than B and C. Hence it can be depicted that Choquet Integral takes into consideration interaction and importance of each criterion. Therefore Choquet Integral is a better methodology than Weighted Average Method. Srivastava (Srivastava & Kumar, 2009; Srivastava & Jain, 2009; Srivastava et. al, 2010), Kanellopoulos (2010), Fitzpatrick (1998) and Senior (2007) did not consider the interaction degree among criteria. But the current work shows the effect of interaction among criteria in finding the best Alternative which provide highest Software Quality among the different Alternative. In order to show the variation of result with change in interaction degree, consider an example that there are two alternative solutions to common SRS and that need to be compared on the basis of any 3 criteria. Weights of the three criteria selected are considered as w1=2, w2=4, w3=6 and rating taken are shown in Table 10. Now, the Choquet integral is calculated using fuzzy measures where the interaction degree ( ) is varied from 0 to 1. Results are depicted in Table 11 as shown below. From Table 11, it can be depicted that value of Choquet integral for both the software keeps on increasing with increase in interaction conside idered better Alternative. Fig.3. shows variation of Choquet integral value of Alternative 1 and Alternative 2 with Interaction Degree and also importance of interaction between the criteria can be analyzed. Table 10. Weights of Criteria for two Software Criteria 1
Criteria 2
Criteria 3
Alternative 1
0.4
0.5
0.3
Alternative 2
0.1
0.6
0.3
8. Conclusion This paper proposes a quality model that supports five different views of software quality and application of fuzzy theory to measure software product quality by quantifying its quality parameters which can reduce the ambiguity and uncertainty of software quality attributes. Based on the results in this study decision makers can not only understand the merits and limitations of software products before developing but can also ultimately enhance product overall quality. The proposed approach uses Choquet Integral with fuzzy measures taking into consideration the important concept of interaction between criteria. This paper shows the effect of interaction among criteria on the result. Hence results can vary
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with interaction degree whereas in other techniques like Weighted Arithmetic Mean etc. where criteria are considered independent so decision remains constant once determined. Table 11. Variation of Choquet Value with Interaction Degree for the two software Choquet value for Alternative 1
Choquet Value for Alternative 2
0
0.3
0.2
0.2
0.326931
0.257229
0.4
0.364502
0.329621
0.6
0.402266
0.404862
0.8
0.439832
0.481037
1
0.466827
0.535697
0.6
X-axis - Interaction Degr Y-axis - Choquet Value
0.5 0.4 0.3
Alternative 1
0.2
Alternative 2
0.1 0 0
0.2
0.4
0.6
0.8
1
1.2
Fig. 3. Variation of Choquet Integral Value with Interaction Degree
9. Future Scope The interaction among various software quality criteria by the aid of Choquet Integral has been the main idea of this paper; however software quality sub-criteria is found to be too insignificant to be considered for emphasis. This proves to be a setback, as sub criteria and interaction among them happens to have a significant influence on the decision to be made. Hence more work can be done taking subcriteria and their interaction into consideration. 10. References Agarwal, M., & Chari, K. (2007). Software Effort, Quality, and Cycle Time: A Study of CMM Level 5. IEEE Transactions on Software, 33, pp. 145-156. BenHassine, S., Darmont, J., & Chauchat, J. (2010). Aggregation of data quality metrics using the Choquet integral. 8th International Workshop on Quality in Databases (VLDB/QDB 10). Singapore. Bertoa, M., & Vallecillo, A. (2006). Usability metrics for software components. Proceedings of Quantitative Approaches in Object-Oriented Software Engineering (QAOOSE), (pp. 136-143). Bourque, P., Dupuis, R., Abran, A., Moore, J. W., & Tripp, L. (1999). The Guide to the Software Engineering Body of Knowledge. IEEE Software , 35-44. Brown, J., & Lipow, M. (1975). Testing for Software Reliability. Proceedings of the international conference on Reliable software, (pp. 518-527). Los Angeles, USA. Challa, J. S., Paul, A., Dada, Y., Nerella, V., & Srivastava, P. R. (2011). Quantification of Software Quality Parameters using Fuzzy Multi Criteria Approach. Process Automation Control and computing (PACC), IEEE Computer Society. Chang, C.-W., Wu, C. R., & Lin, H.-L. (2007). Integrating fuzzy theory and hierarchy concepts to evaluate software quality. Software Quality Journey, Springer Science+Business Media, 16, pp. 263-276. Côté, M.-A., Suryn, W., & Georgiadou, E. (2006). Software Quality Model Requirements for Software Quality Engineering. Dromey, R. (1995). A model for software product quality. IEEE Transactions on Software Engineering, 21, No. 2, pp. 146-162. Eden, A. H., & Mens, T. (2006). Measuring Software Flexibility. IEE Software, 153, No. 3, pp. 113 126. London, UK.
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Procedia Technology 6 (2012) 153 – 162
2nd International Conference on Communication, Computing & Security [ICCCS-2012]
Assessment of Software Quality: Choquet Integral Approach Vatesh Pasrija, Sanjay Kumar, Praveen Ranjan Srivastava Computer Science & Information System Department, BITS PILANI 333031 (INDIA) Email: {Er.VateshPasrija, er.sanjaykr1989, praveenrsrivastava}@gmail.com
Abstract Software measurement is a software engineering discipline which deals in quantifying the characteristics of a software product or software process. The measurement of the characteristics of software refers to the comparative study of the same and hence the quality of the software comes into picture. There are software quality models made but none of these give quantification of quality parameters. Hence this paper proposes a methodology for comparing different software solutions based on the SRS to a common problem. Software quality is highly unpredictable, it is the existence of desirable characteristics in a solution, while the desired attributes differ with different view point and are highly interdependent. Therefore Choquet Integral is used to efficiently compare the set of solutions to be implemented for software. © Ltd...Selection and/or peer-review under responsibility ofresponsibility the Department Science & © 2012 2012Elsevier Published by Elsevier Ltd. Selection and/or peer-review under ofof theComputer Department of Computer Engineering, National Institute of Technology Science & Engineering, National Institute ofRourkela Technology Rourkela Keywords: Software Quality;Quality parameters; Choquet Fuzzy Integral; Fuzzy Measure; Interactive Criteria; Multi Criteria Decision Making; Interaction Degree.
1. Introduction Software engineering is the application of a systematic, disciplined, quantifiable approach to the development, operation, and maintenance of software, and the study of these approaches (Bourque et. al., 1999). In software development process, software quality is an important and complex issue. With the advancement of the IT industry and the growing needs of software the demand for high quality software tive, methods, processes and procedures which provide various different alternatives to a common problem. Hence which alternative to choose is decided by the quality of the solution provided i.e. the degree to which the desired set of inherent characteristics fulfils the requirements. Quality is a relative term which differs with viewpoints Transcendental View, Product View, Manufacturing View, User View and Value-based View (Kitchenham et. al, 1996). Various quality models like Boehm's Model (Milicic, 2005), McCall's Model (Cote et. al., 2006), and ISO/IEC 9126 Model (ISO/IEC 9216) have been proposed to develop generic software applications.
2212-0173 © 2012 Elsevier Ltd...Selection and/or peer-review under responsibility of the Department of Computer Science & Engineering, National Institute of Technology Rourkela doi:10.1016/j.protcy.2012.10.019
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Considering the emphasis on software quality, an effort has been made to evaluate alternative solutions. The solutions proposed for a common Software Requirements Specification (SRS) are ranked on the basis of quality attributes which are highly interdependent. This paper proposes a model to rank the alternative solutions using Choquet Integral (Grabisch et. al., 2000). The ranking allows companies, customers and clients to take appropriate decisions on which alternative to work with from a quality point of view. The remainder of the paper is segregated as follows: Section 2 mentions Background work, Section 3 deals with application of Choquet Integral for quantification, Section 4 explains the proposed architecture of this paper, Section 5 Identify fuzzy measures while Section 6 demonstrates a case study followed by Section 7 which discusses the comparison of proposed methodology with existing previous techniques, Section 8 provides the conclusion and Section 9 defines the future scope of the paper. 2. Background Work The IT industry demands software for both functionality and quality, i.e. the extent to which the inherent characteristics exist fulfilling the functional requirements. This gave birth to the problem of evaluating or measuring the software quality so that two or more solutions to a common problem can be measured on the basis of functionality and can be worked upon. There were various problems related to the measurement of quality attributes existence of multiple metrics to determine quality such as cost (Slaughter et. al., 1998); quality, effort and cycle time (Agarwal et. al.,2007); maintainability (Heitlager et. al., 2007), usability (Bertoa et. al., 2006); reliability (Brown et. al., 1975), functionality (Maryoly et. al., 2003). Secondly, these metrics or criteria cannot be taken separately to quantify quality. Thirdly, these multiple criteria are dependent on each other (Takahagi, 2005). Various quality parameters have been used for quantifying software quality from the perspectives of the developer, user and project manager (Srivastava & Kumar, 2009). These quality attributes based on various perspectives or views are not independent of each other and are also fuzzy in nature. Fuzzy set theory based on ISO 9126 Quality Model has been used to calculate software quality for evaluation of user satisfaction (Lin et. al., 2007). Similarly, Yang (2007) proposed a software quality prediction model based on fuzzy neural networks and Yuen et. al. (2008) proposed a fuzzy AHP model for software quality evaluation and software vendor selection under uncertainty. Another highly related work is the paper by Hazura (2011), that discuss the problem of extracting an overall score for a web based application. Hazura (2011) used a Fuzzy Integral approach as an aggregation operator for overall assessment. However, Hazura (2011) focused on assessing the quality of only web based application and does not take into consideration the quality from various perspectives like user, value, product etc. While quantifying the parameters, it does not justify whether the fuzzy values will be entered by user or developers. In contrast the current work provides a generic framework for quantifying quality of any type of application. The techniques used till date are considering criterion to be independent, but taking dependency nature among criteria into consideration this paper uses Choquet Integral to evaluate software quality. Choquet Integral has been used and proposed in this paper to quantify the software solutions/alternatives build on the SRS of the problem. The multiple criteria are assigned rate and weights or and are integrated using Choquet Integral as they are highly interdependent. In this paper a hybrid quality model with categorization of criterion is proposed covering the major five views to the software quality, as specified by Kitchenham (1996) in Table 1. 3. Choquet Integral Choquet Integral is an aggregation operator which generalizes the weighted arithmetic mean. It uses the concept of fuzzy measure and is able to account multiple interdependent criteria. There are various aggregation methods like Weighted Arithmetic Mean, Maximum and Minimum etc. but the Choquet
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integral provides greater flexibility. The use of Choquet Integral in multi-criteria decision making has been proposed by many authors (Grabisch, 1996; Grabisch et. al., 2000). Choquet Integral is defined by two different definitions (Grabisch et. al., 2000) as ) = 0 where (a) A B X (b)
is empty set.
C (f )
n i 1
f ( x (i)) f ( x (i 1)) (A(i))
The use of Choquet Integral can be seen in the later sections. Table 1: Views of Software Quality View User View Manufacturing View
Product View
Value Based View Transcendental View
Description User interaction point of view Product quality during the manufacturing phase i.e. the production and after delivery phase
P
qualities
Quality Parameters Reliability, Usability Architecture (Hansen et. al., 2009), Flexibility (Eden, 2006), Maintainability (Cote , 2006), Modifiability (Dromey, 1995), Testability (Ganesh, 2010), Reusability (Singh et. al., 2010) Correctness (Dromey, 1995), Efficiency (Cote et. al., 2006), Functionality (Dromey, 1995), Interoperability (Yuen et. al., 2011), Portability (Cote et. al., 2006), Security (Dromey, 1995), System (Cote et. al., 2006)
Cost and Economic aspects
Cost, Time, Schedule Pressure
States that product quality is abstract yet universally identifiable
Brand Value, Human Touch
4. The Proposed Architecture This paper proposes a technique to evaluate the prepared alternative solutions based on the SRS of a problem statement and choosing the best among them. The proposed method uses ISO/IEC 9126 as baseline model to select the criteria based on which the software quality can be calculated. The technique takes direct input for weight of each criteria considered for software quality. In general (Challa et. al., 2011), weight and rate of criteria are fuzzy in nature and cannot be accurately measured. Hence the technique known as fuzzification (Srivastava et. al., 2010) plays an important role in the assessment of software quality. The weights and rating of the criteria are purely on the basis of the judgment of the decision maker. The decision makers provide the rating to the criteria from the user, product, man authority in the organization. The ratings collected are then aggregated by recursively using Choquet Integral (Grabisch et. al., 2000) taking into consideration the interaction among the criteria. The Choquet Integral used is based on the fuzzy measure and is used for aggregation of partial values. The concept of fuzzy measure in Choquet Integral acts as indices on parameters which help to interpret the importance of each criterion. The shapely value (Winter, 2002) is used for the identification of fuzzy measurers which are used by Choquet Integral to rank the alternatives. The proposed flow graph is as shown in fig.1.
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Software quality can be seen from different viewpoints each having their own criteria which act as a metric for accessing the software quality. The assessment of software quality is done by aggregating the weight and rate of these criteria in particular views and then again aggregating the weight and rate of views using the Choquet Integral for the second time to get final software quality.
Start
Solutions to SRS
Direct Input of Weight and Rate of Criteria by Decision Maker
Apply Choquet Integral
Fuzzy Measure Identification Standard Using Shapely Value
Result
Fig. 1. Flow Graph for proposed methodology. Stop
5. Fuzzy Measures Fuzzy measure μi indicates the importance of individual criteria and group of criteria when taken together in a Set. The following interpretations (J. L. Marichal, 2000) can be made from fuzzy measures. A criteria xi is important if value of μi is high. However for the importance of xi, it may not be enough to look at only the value of μi but also we have to consider the value of μij, μijk etc. where j,k are other criteria. Now if μi and μj are high but μij do not have much difference from μi and μj then we can interpret that the importance of criteria x i and xj taken separately is same as xi and xj taken together. So we should not have much interest in considering them both. On the other hand if μ i and μj have low values but μij is very large then xi and xj are not much importance as compared to the importance when both taken together. Based on this concept importance and interaction indexes can be computed and Fuzzy Measures can be identified using Shapely value Standard. Shapley Value Standard: Shapley (Winter, 2002) proposed in 1953 a definition of a coefficient of importance, based on a set of reasonable axioms. In this standard, weights are positive values. This method (Takahagi, 2005) calculates the fuzzy measure μ such that shi (μ ) = wi, i where shi (μ ) is the Shapley Value of ith evaluation item of the fuzzy measure μ and is represented as:
shi
(S )[ S x n
(S )
] , where n (S) ( S /{i})
(n
S )!( S 1)! n!
and of X containing ith criteria, |S|= Number of subsets in S. This method is used to find fuzzy measures for each criterion, for Algorithm refer (Takahagi, 2005).Using Shapely value standard and Choquet Integral case study is mentioned in next section. 6. The Case Study An example to above procedure is solved to find the best alternative solution to common SRS based on five different view point of software quality. The ranking among the alternatives, for e.g. A1, A2, A3, is done by Choquet Integral using fuzzy measure. Before calculating the quality aspect in each alternative there is a need to define criteria on the basis of which comparison can be made. To find the quality, this paper considers three views i.e. User, Product, Manufacturing and their criteria as shown in fig.2.
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S/w Quality
User View
Reliability
Product View
Usability
Portability
Manufacturing View
Efficiency
Flexibility
Reusability
Fig. 2. Categorization of criteria in different views Table 2. Weights of criteria Name of Criteria
Weight Assigned
Name of Criteria
Weight Assigned
Usability
2
Efficiency
6
Reliability
8
Flexibility
7
Portability
4
Reusability
5
Step1:- Input weight (on the scale of 10) of criteria selected on the basis of their importance as shown in Table 2. Step 2:- Enter the rating (on the scale of 1) of each criterion for each alternative as shown in Table 3. Step 3:- Using Table 3, find the fuzzy measures for criteria of Manufacturing view i.e. Flexibility, Reusability using Shapley Value Standard. For Instance: if X= {Flexibility, Reusability} then for i=Flexibility, power set S of X containing i, can be defined as {{Flexibility, Reusability}, {Portability}}.So, |S|= Number of subsets in S=2. Now using Shapley value standard (Takahagi, 2005) for i=Flexibility and Inter get μ (Flexibility) = 0.29591. Similarly fuzzy measure for all the criteria under each view of Alternative A1, A2 and A3 can be calculated as shown in Table 4.Since Fuzzy measure are dependent on weights of criteria, so fuzzy measures for all the alternative are same as shown in Table 4. Step 4:- Now Apply Choquet Integral to aggregate the rating values of flexibility and reusability (from Table 3) to get rating value for manufacturing view as shown in Table 5. The Table 5 shown below is the simplest calculation based on formula of Choquet Integral mentioned in section 3.Similarly rating values of the criteria in other views can be aggregated and the result is as shown in Table 6.This procedure is repeated for Alternative A2 and A3 to get the aggregated value as shown in Table 6. Step 5:- Table 6 gives the rating value for each view for Alternative A1.Similarly rating value for Alternative A2, A3 can be calculated as shown in Table 6. Step 6:- Calculate the weight of Manufacturing View, User View and Product View as follows:Weight of Manufacturing View: Average of weight of Flexibility and Reusability = (7+5)/2=6 Weight of Product View: Average of weight of Portability and Efficiency = (6+4)/2=5 Weight of User View: Average of weight of Reliability and Usability = (8+2)/2=5 Table 3. Rating for each criterion Alternatives
Flexibility
Reusability
Portability
Efficiency
Reliability
Usability
A1
0.5
0.4
0.3
0.2
0.4
0.3
A2
0.4
0.3
0.4
0.3
0.2
0.1
A3
0.6
0.4
0.3
0.5
0.6
0.1
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Table 4. Fuzzy measures for each Alternatives Fuzzy Measures
Alternative A1, A2, A3
μ (Flexibility)
Fuzzy Measure
Alternative A1, A2, A3
0.29591
μ (Usability, Reliability)
1
μ (Reusability)
0.129461
μ (Efficiency)
0.319225
μ(Flexibility, Reusability)
1
μ (Portability)
0.117609
μ (Usability)
0.0346481
μ (Efficiency, Portability)
1
μ (Reliability)
0.635216
Step 7:- Again we have rate and weights of each view as in step 3, where we have for each criterion, so similar procedure of fuzzy measures and then Choquet Integral can be used to aggregate the value of Manufacturing, User and Product View to get Final Rating of the Alternatives. Choquet Values for each Alternative is shown in Table 7, since A3 Alternative is having the highest value of Choquet Integral, so it is considered to be the best Alternative among the three Alternatives (A1, A2, and A3). Table 5: Choquet Value for Manufacturing View
Criteria
Rating Values (Decreasing Order) (From Step 2)
Difference Between Succesive Rating values(D). Take 0 as Last Value
Cumulative Capacity
Fuzzy Measure Value(F)
Choquet Value= F*D
Flexibility
0.5
0.5-0.4=0.1
μ (Flexibility)
0.29591
0.029591
Reusability
0.4
0.4-0= 0.4
μ (Flexibility, Reusability)
1
0.4 0.429591
Table 6: Rating Values of Different Views for each Alternative Alternatives
Manufacturing View
Product View
User View
A1 A2
0.429591
0.21176
0.363521
0.329591
0.311759
0.163521
A3
0.459182
0.363843
0.417608
In this case study, we used recursive application of Choquet Integral where we started from input of rate and weights of criteria of each Alternative and then used Choquet Integral to aggregate the ratings of criteria to move one level up to get the Rating value for respective views of each Alternative and then again applied Choquet Integral to aggregate the calculated Rating value of views to move one more level up to get the final Software Quality of each Alternative. 7. Comparison with Existing Approach This paper addresses the solution to problem of aggregation, which is the process of aggregating several values into single value. Previous work done on software quality uses Analytic Hierarchy Process (AHP) (Kasperczyk et. al., 1996), Weighted Arithmetic Mean (Srivastava & Jain, 2009), Empirical Approach (Sharma et. al., 2008) and other multi-criteria decision making approaches (Yang, 2007; 22] for aggregation. A.Sharma (2008), P.R.Srivastava (2009), Yang (2007) and Kanellopoulos (2010)and had tried to quantify software quality but did not consider the fuzzy nature of software quality parameters
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whereas our approach in this paper incorporates fuzzy logic to deal with unpredictable nature of quality parameters. P.R.Srivastava (2009, 2010), Challa et. al. (2011), Yang (2007), Che-Wei Chang (2007) tried to quantify software quality using fuzzy multi criteria approach without considering interaction between criteria. Our approach in this paper uses Choquet Integral with fuzzy measure to quantify the interacting software quality parameters and finds the best software among different software and also made analysis of effect of interaction among criteria in finding best alternative. P.R. Srivastava (Srivastava & Kumar, 2009; Srivastava & Jain, 2009; Srivastava et. al, 2010) categorizes the software quality in terms of manager, developer and user irrespective of the relevance of the attributes. However, the current work gives the broader categorization of software quality parameters in 5 different views i.e. User, Product, Manufacturing, Transcendental, and Value. Table 7. Choquet value for Each Alternatives Alternatives A1 A2 A3
Choquet Values 0.279042 0.223303 0.389989
Comparison with Weighted Arithmetic Mean Method: - The Weighted Arithmetic Mean Method (WAM) can be illustrated as Choquet integral, an extension of weighted arithmetic means (WAM) (Srivastava & Kumar, 2009) which is one of the methods of multi-criteria decision making approach. The main benefit of using Choquet over the other aggregation operations is that it is an efficient approach which takes into consideration the interaction among the criteria while performing the aggregation operation (BenHassine et. al., 2010). This concept can be well understood by an illustrative example. Let us consider a problem of evaluating Students in BITS-Pilani on the basis of marks scored in following 3 subjects Statistics, Probability and Algebra. Now suppose if BITS-Pilani pay more attention towards Statistics than Algebra then considering weights of subjects as coefficient of importance can be taken as 3, 3, and 2 respectively. So using Weighted Arithmetic Mean, Student 'A' is better than Student 'B' and Student 'C', since he has highest weighted score as shown in Table 8. But if BITS-Pilani also wants the student who is well versed with all the 3 subjects then Student 'C' is better than other students as Student 'C' has scored consistent marks in all the 3 subjects. But in WAM approach Student A was considered to be better student even though he was weak in Algebra. This is due to much importance is given to Statistics and Probability, which are in sense redundant. Generally a student good at Statistics is also good at Probability (and vice versa).Hence interdependence can be seen in these two criteria. So this problem can be solved with Choquet Integral with fuzzy measure as input. Note the following points: Though BITS-Pilani is giving more importance to Statistics than Algebra then following weights of preserving the initial ratio. Table 8. Illustration of WAM using three subjects Student\Subject
Statistics
Probability
Algebra
WAM(Weighted Arithmetic Mean)
Student A
18
16
10
15.25
Student B
10
12
18
12.75
Student C
14
14
15
14.625
159
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Table 9. Illustration of Choquet Value using three subject Student
Statistics
Probability
Algebra
Choquet Value
Student A
18
16
10
13.9
Student B
10
12
18
13.6
Student C
14
14
15
14.6
As Statistics and Probability are overlapping Subjects, the weights used for the pair Statistics and Probability should be less than sum of weights of Statistics and Algebra and sum of weights of Probability and Algebra, As student equally good at Statistics subject and Algebra must be favored so that the weights for the pair of Statistics and Algebra must be greater than sum of individual weights of Statistics and Algebra. , So according to Choquet Integral Student 'C' is better than Student 'A' and 'B' as he has highest Choquet Integral value shown in Table 9. In contrast to Weighted Arithmetic Mean Score Student A was better than B and C. Hence it can be depicted that Choquet Integral takes into consideration interaction and importance of each criterion. Therefore Choquet Integral is a better methodology than Weighted Average Method. Srivastava (Srivastava & Kumar, 2009; Srivastava & Jain, 2009; Srivastava et. al, 2010), Kanellopoulos (2010), Fitzpatrick (1998) and Senior (2007) did not consider the interaction degree among criteria. But the current work shows the effect of interaction among criteria in finding the best Alternative which provide highest Software Quality among the different Alternative. In order to show the variation of result with change in interaction degree, consider an example that there are two alternative solutions to common SRS and that need to be compared on the basis of any 3 criteria. Weights of the three criteria selected are considered as w1=2, w2=4, w3=6 and rating taken are shown in Table 10. Now, the Choquet integral is calculated using fuzzy measures where the interaction degree ( ) is varied from 0 to 1. Results are depicted in Table 11 as shown below. From Table 11, it can be depicted that value of Choquet integral for both the software keeps on increasing with increase in interaction conside idered better Alternative. Fig.3. shows variation of Choquet integral value of Alternative 1 and Alternative 2 with Interaction Degree and also importance of interaction between the criteria can be analyzed. Table 10. Weights of Criteria for two Software Criteria 1
Criteria 2
Criteria 3
Alternative 1
0.4
0.5
0.3
Alternative 2
0.1
0.6
0.3
8. Conclusion This paper proposes a quality model that supports five different views of software quality and application of fuzzy theory to measure software product quality by quantifying its quality parameters which can reduce the ambiguity and uncertainty of software quality attributes. Based on the results in this study decision makers can not only understand the merits and limitations of software products before developing but can also ultimately enhance product overall quality. The proposed approach uses Choquet Integral with fuzzy measures taking into consideration the important concept of interaction between criteria. This paper shows the effect of interaction among criteria on the result. Hence results can vary
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with interaction degree whereas in other techniques like Weighted Arithmetic Mean etc. where criteria are considered independent so decision remains constant once determined. Table 11. Variation of Choquet Value with Interaction Degree for the two software Choquet value for Alternative 1
Choquet Value for Alternative 2
0
0.3
0.2
0.2
0.326931
0.257229
0.4
0.364502
0.329621
0.6
0.402266
0.404862
0.8
0.439832
0.481037
1
0.466827
0.535697
0.6
X-axis - Interaction Degr Y-axis - Choquet Value
0.5 0.4 0.3
Alternative 1
0.2
Alternative 2
0.1 0 0
0.2
0.4
0.6
0.8
1
1.2
Fig. 3. Variation of Choquet Integral Value with Interaction Degree
9. Future Scope The interaction among various software quality criteria by the aid of Choquet Integral has been the main idea of this paper; however software quality sub-criteria is found to be too insignificant to be considered for emphasis. This proves to be a setback, as sub criteria and interaction among them happens to have a significant influence on the decision to be made. Hence more work can be done taking subcriteria and their interaction into consideration. 10. References Agarwal, M., & Chari, K. (2007). Software Effort, Quality, and Cycle Time: A Study of CMM Level 5. IEEE Transactions on Software, 33, pp. 145-156. BenHassine, S., Darmont, J., & Chauchat, J. (2010). Aggregation of data quality metrics using the Choquet integral. 8th International Workshop on Quality in Databases (VLDB/QDB 10). Singapore. Bertoa, M., & Vallecillo, A. (2006). Usability metrics for software components. Proceedings of Quantitative Approaches in Object-Oriented Software Engineering (QAOOSE), (pp. 136-143). Bourque, P., Dupuis, R., Abran, A., Moore, J. W., & Tripp, L. (1999). The Guide to the Software Engineering Body of Knowledge. IEEE Software , 35-44. Brown, J., & Lipow, M. (1975). Testing for Software Reliability. Proceedings of the international conference on Reliable software, (pp. 518-527). Los Angeles, USA. Challa, J. S., Paul, A., Dada, Y., Nerella, V., & Srivastava, P. R. (2011). Quantification of Software Quality Parameters using Fuzzy Multi Criteria Approach. Process Automation Control and computing (PACC), IEEE Computer Society. Chang, C.-W., Wu, C. R., & Lin, H.-L. (2007). Integrating fuzzy theory and hierarchy concepts to evaluate software quality. Software Quality Journey, Springer Science+Business Media, 16, pp. 263-276. Côté, M.-A., Suryn, W., & Georgiadou, E. (2006). Software Quality Model Requirements for Software Quality Engineering. Dromey, R. (1995). A model for software product quality. IEEE Transactions on Software Engineering, 21, No. 2, pp. 146-162. Eden, A. H., & Mens, T. (2006). Measuring Software Flexibility. IEE Software, 153, No. 3, pp. 113 126. London, UK.
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