A Framework for Software Quality Model Selection using ... - IEEE Xplore

IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India

A Framework for Software Quality Model Selection using TOPSIS Simarpreet Kaur, Sumeet Kaur Sehra, Sukhijt Singh Sehra applying different methods on multiple criteria best alternative is selected [2]. Multi criteria decision making have number of methods to solve MCDM problems. These methods are used for special kind of problems and depend upon the type of data available [6].

Abstract - Software and its quality is the key deciding factor about success and failure of a business. To give a check to quality of software, software quality models have been introduced to identify the type of software products and to find scope of it. Multi criteria decision-making technique has been an interesting topic to compare software quality model and then to find the best one by using different parameters. Multi Criteria Decision Making is used to select particular alternative based on different criterion. In this paper, TOPSIS technique one of the method of multi criteria decision making has been used to select the best software quality model. TOPSIS method ranking process, simplicity and precise result makes it above all the other approaches already been used. This framework selects the best model according to the criterion reliability, efficiency and maintenance. The values for these models have been calculated and ranked according to maximum value as 1 rank.

III. TOPSIS TOPSIS stands for Technique of Order Preference by Similarity to Ideal Solution. TOPSIS is a multi criteria decision-making approach from a finite set of parameters, which are based upon minimum distance from an ideal solution and maximum distance from non-ideal solution. The main advantage of using TOPSIS instead of all multi attribute methods is that best attribute can be find out quickly [7]. All other multi attribute methods are primarily focused on calculating weights or combine weights with different weight and then finding best possible ideal solution. TOPSIS method assures that each criterion has a propensity of continuously increasing or decreasing utility, which easily defines the ideal and negative ideal alternative. It is a method of aggregation that compares a set of alternatives by defining weights for each criterion and normalizing scores for each criterion and then evaluating proper distance between each alternative and the solution to be selected, which is the final and best value in each criterion [5]. TOPSIS is applied to rank the effort estimation model, so that best model can be chosen. We calculate the relative closeness to value 1 by: 𝑆∗ (1) 𝐶𝑖∗ = 𝑖 (𝑆 ∗ + 𝑆 ′ ), Where 𝑖 𝑖

Keywords: MCDM; TOPSIS; Jim McCall’s Model; W. Boehm’s Model, ISO 9126 Quality Model

I. INTRODUCTION If we talk about recipe of software engineering then software quality is the key ingredient. Quality is considered as combination of many traits. Quality models are always best to consider relationship between different traits. The main aim of software engineering in making software is its good quality, feasibility and maintainability. Software quality is needed to run software smoothly in case of many demanding applications. Software quality is important for handling software importunity, software impalpability, amassing errors, which create problem in the phase of software development. As software quality models belong to same family they do have relationship between them. Several quality models have been proposed to test the software quality. The most popular software models, which have been used in this paper, are Jim McCall’s model, W. Boehm model, and ISO 9126 quality model. The aim of this paper is to select the best software quality model according to the three parameters reliability, efficiency and maintainability. TOPSIS method will rank models according to parameters.

0< 𝐶𝑖∗ < 1 We select the option with Ci closest to 1 i.e. positive ideal alternative. *

1

Where

𝑆𝑖∗

=

2 2

∗ 𝑗 𝑣𝑗

− 𝑣𝑖𝑗 𝑖 = 1, − − − − −, 𝑚

(2)

1 2

𝑆𝑖′ =

II. MULTI CRITERIA DECISION MAKING To select relative parameter among all the parameters Multi criteria decision-making method is used. The problem in which decision maker generally have uncertain and indistinct knowledge is solved by multi criteria decision-making [9]. This method of selecting best alternatives are of importance these days for complex real problems because of their ability to select alternatives based on various criteria for best alternative. Main goal is divided into difference criteria and according to those criteria multiple alternatives are defined and then after SimarpreetKaur,GNDEC, Ludhiana, India ([email protected]) SumeetKaurSehra, GNDEC, Ludhiana, India ([email protected]) Sukhijt Singh Sehra, GNDEC, Ludhiana, India ([email protected])

978-1-5090-0774-5/16/$31.00 © 2016 IEEE

736

𝑣𝑗′ − 𝑣𝑖𝑗

2

(3)

𝑗

𝑖 = 1, − − − − −, 𝑚 IV. PROBLEM FORMULATION Software is the most important component of the all computer systems. As the technology is rising to its peak level, the need of software is also increasing. But with the increasing demand of the technology the quality of software is the main requirement of users. To give a perfect check on software quality, software quality models are taken into consideration because quality models represent the characteristics and relationships. The quality models manage the software completely but calibration of quality model criteria is difficult. Software quality models have researched by many researchers by taking into consideration different parameters, which are generally related to quality of

IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India

software. The models, which are discussed in detail, are ISO 9126 quality model, Boehm’s model, McCall’s model. V. METHODOLGY The methodology presented in this paper is a multi-criteria decision-making method, Technique for Order of Preference by Similarity to Ideal Solution. This technique uses a method in which the decision is based on the best alternative chosen among criteria that has the less distance from the positive ideal alternative but is far from the negative ideal alternative [3]. In this case output of fuzzy AHP was used as input of weights in TOPSIS method [5]. To find accuracy in infinite order metrics TOPSIS is quite useful. This section presents the steps, which are followed to calculate the final result for selecting best model. These steps are: 1: Collect project data to create a matrix of m columns and n rows:-In the very first step comparison between different models have been made which provide us with alternatives and calculations are made. The parameters used in this research are given follows: Reliability (A1): It represents the behavior of the models corresponding to different conditions. It differs from hardware reliability in that it echoes the design perfection, rather than framing perfection. Efficiency (A2): It defines the extent to which a software product can be operated using the less number of resources i.e. CPU- time, Memory, Disk space and other resources. Maintainability (A3): It is concerned with modification of a component within specified period of time in a defined environment. By the help of these parameters we will be able to create a matrix (𝓍𝒾𝒿 )𝓂×𝓃 of m rows and n columns.

Step 3: A new matrix will contain the elements by the equation: 𝓋𝒾𝒿 = 𝓌𝒿 𝓇𝒾𝒿 . (5) 4: Determine the ideal and negative ideal solutions:  Ideal Solution is the one which has the maximum benefit for all attributes considered. Ideal solution will be given by:





𝐴∗ = 𝓋1∗ , − − − − −, 𝓋𝑛∗ . (6) Where 𝓋𝑗∗ = max 𝑣𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐽 ; min⁡ ( 𝑣𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐽′}. Non-Ideal Solution is the one, which has the worst attribute value. 𝐴 ′ = 𝓋1′ , − − − − −, 𝓋𝑛′ .(7) Where 𝓋𝑗′ = min 𝑣𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐽 ; max⁡( 𝑣𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐽′}. 5: Calculate the distance measures for each alternative: Separation from ideal solution is: 1

2 2

𝑆𝑖∗ =



∗ . (2) 𝑗 𝑣𝑗 − 𝑣𝑖𝑗 𝑖 = 1, − − − − −, 𝑚 Separation from non ideal solution is: 1

𝑆𝑖′

′ 𝑗 𝑣𝑗

2 2

. (3) 𝑖 = 1, − − − − −, 𝑚 6: Evaluate the relative closeness to the ideal alternative:Relative closeness to the ideal solution is given by equation: 𝑆∗ 𝐶𝑖∗ = 𝑖 𝑆 ∗ + 𝑆 ′ .(1) 𝑖 𝑖 =

− 𝑣𝑖𝑗

, Where. 0< 𝐶𝑖∗ < 1 7: Ranking: The best solution will be selected from the given set of solution that will be closest to 1. That will be the best solution for particular problem. VI. RESULTS The technique discussed in methodology has been applied to the data taken according to decision maker. Decision maker provide the values of parameters according to they see those parameters in their development, which has been used to find best model. Weights have been used which was calculated using FUZZY AHP and then TOPSIS has been applied to calculate the final result. This technique has number of steps to read the optimal solution to select the best model. Weights are being normalized and then TOPSIS was applied to find optimal solution. A. Collect project data to create a matrix of m columns and n rows: Table 1: Matrix of m rows and n columns according to decision maker’s values.

Fig.1:Alternatives and Criterion 2: Construct normalized decision matrix: This step transforms various matrix values dimensions into nondimensional values, which grant comparisons across criteria. Step1 Square of the each component of matrix. (𝓍𝒾𝒿 )2𝓂×𝓃 . where m is the number of rows, n is the number of column, i varies from 1,--------,m and j varies from 1,---------,n. Step 2 Make summations of the all the columns in the matrix. (𝓍𝒾𝒿 )2𝓂×𝓃 . Step3 Make the normalized matrix by dividing the given matrix with the result obtained after summation of the given matrix. 𝓇𝒾𝒿 =

(𝓍𝒾𝒿 )𝓂×𝓃 (𝓍𝒾𝒿 )2𝓂×𝓃

.

(4)

3: Construct the weighted normalized decision matrix: Step 1: Suppose that we have a set of weights 𝓌𝒿 for each criterion for j = 1,-----n. Step 2: Multiply each column of the normalized decision matrix by its associated weight that is the values of 𝓌𝒿 .

A1

A2

A3

C1

7

9

8

C2

6

7

5

C3

8

5

9

B. Construct normalized decision matrix: Step 1: In this step square of each component is taken.

737

IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India Table 7: Multiplication with weights. Table 2: Square of each component A1

A2

A3

C1

49

81

64

C2

36

49

25

C3

64

25

81

A2

A3

C1

49

81

64

C2

36

49

25

C3

64

25

81

149

155

170

A2

A3

C1

49

81

64

C2

36

49

25

C3

64

25

81

12.2066

12.4499

13.038

A3

C1

0.5737*0.32

0.7234*0.38

0.6139*0.29

C2

0.4918*0.32

0.5627*0.38

0.3837*0.29

C3

0.655*0.32

0.4019*0.38

0.6907*0.29

A1

A2

A3

C1

0.183584

0.274892

0.178031

C2

0.157376

0.213826

0.111273

C3

0.209696

0.152722

0.200303

D. Determine the ideal and negative ideal solutions: Step 1: Ideal solution Table 9: A*

Table 4:Square root of summation. A1

A2

Step 3: In this step the weighted normalizing matrix is obtained which is shown in the below table. Table 8: Weighted Normalized Matrix.

Step 2:In this step summation value has been calculated of each column. After summation square root of that summation has been calculated. Table 3:Summation of columns. A1

A1

A1

A2

A3

C1

0.1835

0.2748

0.178

C2

0.1573

0.2138

0.1112

C3

0.2096

0.1527

0.200303

Ideal solution

0.2096

0.2748

0.200303

Step 3: In this step final normalized matrix has been obtained by dividing the values of each column with the table values of table 4. Table 5: Normalized matrix. A1

A2

A3

C1

0.5737

0.7234

0.6139

C2

0.4918

0.5627

0.3837

C3

0.655

0.4019

Step 2: Non- ideal solution: Non-ideal solution has been calculated by selecting all the minimum values. Table 10: A’ A1

A2

A3

C1

0.183584

0.274892

0.178031

C2

0.157376

0.213826

0.111273

C3

0.209696

0.152722

0.200303

Non-ideal solution

0.57376

0.152722

0.111273

0.6907

C. Construct the weighted normalized decision matrix: Step 1: Table 6: Weighted Matrix. A1

A2

A3

Weights

C1

0.43

0.55

0.013

0.32

C2

0.23

0.19

0.56

0.38

C3

0.30

0.39

0.30

0.29

E. Calculate the distance measures for each alternative: In this step distance from ideal solution is calculated that is the solution, which will be close to 1 will be calculated by the equation defined in step 5 of the methodology. Step 1: Separation from ideal solution

Step 2: In this step each component is multiplied with weights in table 6. This step is calculated as follows:

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IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India Table 11: Separation S* 𝑣𝑗∗ − 𝑣𝑖𝑗

When Comparison of FAHP and TOPSIS is done then it can be seen with the same parameters results have been different. This is because when TOPSIS technique has been used with simple numerical values rather than fuzzy numbers and uncertainty is considered results have been precise and shows McCall’s model as 1st rank model.

S*

2

C1

0.0011

0.03432

C2

0.0143

0.1199

C3

0.0149

0.1221

VIII.

Step 2: Separation from non-ideal solution Table 12: Separation S’ 𝑣𝑗′ − 𝑣𝑖𝑗

2

S’

C1

0.0200689

0.1416647

C2

0.0611039

0.247192

C3

0.0106636

0.103264

F. Evaluate the relative closeness to the ideal alternative: Table 13: Closeness C 𝑆𝑖∗ C1

C*

(𝑆𝑖∗ + 𝑆𝑖′ )

(0.1416647/0.17598)

VII. CONCLUSION To select the software quality model the main thing that we should keep in mind is that it should satisfy the need of the software product being developed. The main aim of this paper is to select the best software quality model using TOPSIS. The decision makers used this approach to find the ideal and non-ideal solution. The model is selected as best model, which will be close to ideal solution and far from negative ideal solution. The earlier models used crisp numbers and fuzzy numbers to select the best model in which much variation can occur. TOPSIS method selects the best model in a simple and structured manner. The final result stated that when Technique of Order Preference by Similarity to Ideal Solution method was applied satisfactory results have been obtained and provided with the selected software quality model.

0.80500 REFERENCES

C2

(0.247192/0.367092)

0.67337

C3

(0.103264/0.225364)

0.45820

[1] Abbas et al. (2015),” Sustainable and Renewable Energy: An Overview of the Application of Multiple Criteria Decision Making Techniques and Approaches”, Sustainability 2015, 7, 13947-13984, ISSN 2071-1050 [2]Ridvan et al. (2014),” A Multi-criteria neutrosophic group decision making method based TOPSIS for supplier selection”, in Researchgate.net [3]Ghosh et al. (2011),” Analytic Hierarchy Process & TOPSIS Method to Evaluate Faculty Performance in Engineering Education”, in UNIASCIT, Vol 1 (2), 2011, pp: 63-70 [4] Lourenzutti et al. (2015),” A generalized TOPSIS method for group decision making with heterogeneous information in a dynamic environment”, in Information Sciences 330 (2016) 1–18. [5] Mohammed et al. (2013),” Integrated Fuzzy (GMM) -TOPSIS Model for Best Design Concept and Material Selection Process”, in International Journal of Innovative Research in Science, Engineering and Technology, Vol. 2, Issue 11, November 2013, ISSN: 2319-8753 [6] Lakshmi et al. (2013),” A Survey on Multi Criteria Decision Making Methods and Its Applications”, in American Journal of Information Systems, 2013, Vol. 1, No. 1, 31-43 [7] Hunag et al. (2010),” Study on the Application of Fuzzy TOPSIS to the Multi-objective Decision Making”, in IEEE International Conference on Intelligent Computation Technology and Automation [8] Mehrotra et al. (2015),” Rank University Websites Using Fuzzy AHP and Fuzzy TOPSIS Approach on Usability”, I.J. Information Engineering and Electronic Business, 2015, 1, 29-36 [9] Safari et al. (2013),” A New Technique for Multi Criteria Decision Making Based on Modified Similarity Method”, in Middle-East Journal of Scientific Research 14 (5): 712-719, 2013 ISSN 1990-9233
 [10] Sehra et al. (2012),” Multi Criteria Decision Making Approach for Selecting Effort Estimation Model”, in International Journal of Computer Applications (0975 – 8887) Volume 39– No.1, January 2012 [11] Ying et al. (2010),” Application of Interval-Valued AHP and Fuzzy TOPSIS in the Quality Classification of the Heaters”, in IEEE Second International Conference on Computational Intelligence, Modelling and Simulation.

G. Ranking: Table 14: Final Result. A1

RANK

McCall’s

0.80500

1

ISO 9126

0.67337

2

Boehm’s

0.45820

3

Models

With all the parameters taken into consideration, software quality models have been prioritized. TOPSIS technique ranks these models according to the values of different criteria calculated. This consider that Boehm’s Model is at 3 rank with value far from ideal solution and McCall’s model is at rank 1 with value close to ideal solution. McCall’s model value is near to 1 so considered as best model from all the three models. Table 15: Comparison. Criterion Models McCall’s model ISO 9126 model Boehm’s model

FAHP

TOPSIS RANK

0.32

1

0.38

2

0.29

3

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