With the rapid development and wide application of multimedia technology, the demand for the actual development of multimedia software in many industries is increasing. How to measure and improve the quality of multimedia software is an important problem to be solved urgently. In order to calculate the complicated situation and fuzziness of software quality, this paper introduced a software quality evaluation model based on the fuzzy matter element by using a method known as the fuzzy matter element analysis, combined with the TOPSIS method and the close degree. Compared with the existing typical software measurement methods, the results are basically consistent with the typical software measurement results. Then, Pearson simple correlation coefficient was used to analyse the correlation between the existing four measurement methods and the metric of practical experience, whose results show that the results of software quality measures based on fuzzy matter element are more in accordance with practical experience. Meanwhile, the results of this method are much more precise than the results of the other measurement methods.
At present, with the rise and application of multimedia technology, it is a great challenge to provide more reliable technical support and strong technical support for the development of multimedia software. At the same time, object-oriented technology has become the mainstream of current software development, which is suitable for developing multimedia software, for example, using the image processing software Adobe Photoshop developed by C++, using Action Script to develop animation processing software Flash, and using C++ for the Jedi survival and heroic alliance games.
We must point out that multimedia software is a typical complex system; therefore, how to scientifically measure the complexity of multimedia software plays a vital role in developing high-quality multimedia software. Software metrics has become the important and long-term focused research field of software engineering and also became an important and effective method in assessing and predicting software development activities. The purpose of software metrics research is to provide guidance for developing high-quality software [
Since the concept of software measurement was first proposed by Rubey R. J. and Hartwick R. D. in 1968[
In 1994, Chidamber S. and Kemerer C. proposed a CK metrics set for object-oriented software quality metrics research. The Weighted Methods per Class (WMC), Number of Children (NOC), Depth of Inheritance (DIT), Coupling Between Objects (CBO), Lack of Cohesion (LCOM), and Response for a Class (RFC) are included in set, which are the fundamental of object-oriented software quality metrics. Padhy N. et al. proposed the three metrics based on CK metrics set and combined WMC, RFC, CBO, DIT. and NOC together [
However, developers and researchers paid attention to broad software quality characteristics in the process of software quality metric research based on external attributes of software quality. These characteristics include software quality characteristics of ISO/IEC 25010 software quality model in narrow sense and other software quality characteristics associated with software development and application. Gosain A. and Sharma G. defined the dynamic software quality characteristics, including robust, unambiguous, dynamic, discriminating, and machine independent. Then they evaluated cases with Java software and found that the dynamic software quality characteristic has significant positive correlation with maintainability by Pearson correlation analysis and principal component analysis [
Class diagram, a very important software model diagram, describes the classes and their relationships among the systems. They can be scientifically constructed whether or not it has a significant impact on the complexity of software. At present, the class complexity measure method is still rare. Marchesi M. [
In this paper, the research work mentioned above is a part of existing domestic and international research work, but there is no doubt that the results of researches in the UML class diagram model are not enough. One of the important reasons is that UML standard issued by the object management group (OMG) only gives the description of the semantic conceptual level in various modelling elements, which leads to the fact that the researchers often use different weighting indicators for the class diagram model. It means that researchers do not have a uniform standard, resulting in different metrics for the same class diagram. Meanwhile, because of the comprehensiveness, fuzziness, and complexity of the software quality measurement system, the software quality measurement is a process of multiple indicator decision making; the fuzzy matter element theory is introduced in this paper. In order to overcome the limitation of weight precision of the class relationship between two classes in the literature [
Matter element analysis [
The matter element
In formula (
In the evaluation of software class diagrams, there are many evaluation indicators involved. If there are no uniform metrics among the indicators, the evaluation process will be difficult to carry out. In order to compare the different dimension indicators together for comparison, the magnitude of these evaluation indicators must be dimensionless [
In formula (
After the dimensionless treatment of formula (
In the process of software quality evaluation, the weight of an indicator reflects the relative importance of the indicator in the overall evaluation process. Therefore, the determination of weight is very important. Common weight determination methods include entropy method, expert scoring method, and analytic hierarchy process. This paper uses entropy method to calculate weights to achieve the subjective and objective unity of weights. The entropy method is based on the difference in the degree of information contained in each indicator, that is, the utility value of the information to determine the weight of the indicator. It is an objective weighting method.
The formula for calculating the information entropy and weight function in the comprehensive evaluation is as follows: For the software quality evaluation model in question, if there are initial data matrix
Get information entropy of the j-th evaluation indicator according to formula (
The constant k in formula (
The entropy method is used to estimate the weight of the evaluation indicator. Its essence is to use the information utility value of the evaluation indicator to measure. When the difference
Fuzzy matter element weight matrix of optimal membership degree is
In formula (
TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) [
Further determine the ideal solution vector
There are several ways to calculate the distance between ideal solutions and negative ideal solutions, such as Euclidean distance, Manhattan distance, Chebyshev distance, and so on. Among them, Euclidean distance is an easy-to-understand distance calculation method, which is derived from the distance formula between two points in Euclidean geometry. In this paper, the Euclidean distance is used, and its calculation formula is as follows [
In formula (
In this paper, the comprehensive evaluation of software quality adopts entropy method for consideration. The source has
Similarly, the binary entropy function is used to calculate the weights of the Euclidean distances of each class diagram to be evaluated and the negative ideal solution; namely,
According to the concept of close degree [
In formula (
In order to validate the measurement method proposed in this paper, we will do an experiment to estimate the metric values. With the permission of Genero M., we selected twenty-six UML class diagrams [
Twenty-six UML class diagrams evaluation indicators.
Class diagrams | NDep | NAssoc | NAgg | NGen | NM | NA | NC |
---|---|---|---|---|---|---|---|
1 | 0 | 1 | 0 | 0 | 8 | 4 | 2 |
2 | 0 | 1 | 1 | 0 | 12 | 6 | 3 |
3 | 0 | 1 | 2 | 0 | 15 | 9 | 4 |
4 | 0 | 3 | 0 | 0 | 12 | 7 | 3 |
5 | 0 | 1 | 3 | 0 | 21 | 14 | 5 |
6 | 0 | 2 | 0 | 0 | 12 | 6 | 3 |
7 | 1 | 3 | 0 | 0 | 13 | 8 | 4 |
8 | 0 | 2 | 2 | 2 | 14 | 10 | 6 |
9 | 1 | 1 | 0 | 0 | 12 | 9 | 3 |
10 | 0 | 2 | 3 | 2 | 22 | 14 | 7 |
11 | 0 | 2 | 3 | 4 | 30 | 18 | 9 |
12 | 0 | 3 | 3 | 2 | 39 | 19 | 7 |
13 | 1 | 3 | 2 | 2 | 35 | 22 | 8 |
14 | 0 | 0 | 0 | 4 | 30 | 11 | 5 |
15 | 0 | 0 | 0 | 10 | 30 | 12 | 8 |
16 | 0 | 0 | 0 | 18 | 38 | 17 | 11 |
17 | 2 | 11 | 6 | 10 | 76 | 42 | 20 |
18 | 1 | 11 | 6 | 16 | 88 | 41 | 23 |
19 | 1 | 7 | 6 | 20 | 94 | 45 | 21 |
20 | 3 | 13 | 7 | 24 | 98 | 56 | 33 |
21 | 0 | 1 | 5 | 2 | 47 | 28 | 9 |
22 | 0 | 3 | 5 | 20 | 65 | 31 | 18 |
23 | 0 | 11 | 6 | 21 | 79 | 44 | 26 |
24 | 0 | 1 | 5 | 19 | 69 | 32 | 17 |
25 | 4 | 14 | 4 | 16 | 84 | 42 | 22 |
26 | 0 | 5 | 9 | 7 | 77 | 34 | 14 |
Note: Genero metric values from Genero M.’s experiment in Table
According to the above theory and evaluation indicator system, the steps for establishing a fuzzy matter element evaluation model are as follows.
Construct the composite fuzzy matrix of matter elements according to Table
Calculate the degree of optimal membership. According to the compound fuzzy matter element matrix determined in the first step, the degree of optimal membership is calculated using formula (
Based on the fuzzy matter element matrix of optimal membership degree
Get
Software quality measurement values of fuzzy matter element in this paper are calculated by formula (
To verify the effectiveness and practicability of the proposed measurement method, this paper plans to compare with the method proposed by Dr. Zhou Y. [
Comparing the experiment results of measurement methods.
Class diagrams | Zhou metric | Yi15 metric | Yi18 metric | | Understandability | Analysability | Maintainability |
---|---|---|---|---|---|---|---|
1 | 0 | 0.42 | 0.41176 | 0.02089 | 1 | 1 | 1 |
2 | 0.673012 | 0.67 | 0.73657 | 0.101997 | 2 | 2 | 2 |
3 | 0.940493 | 0.97 | 1.07097 | 0.339518 | 2 | 2 | 2 |
4 | 1.386294 | 0.76 | 0.7987 | 0.205419 | 2 | 2 | 2 |
5 | 0.989909 | 1.41 | 1.50423 | 0.856791 | 2 | 2 | 2 |
6 | 0.693147 | 0.65 | 0.66949 | 0.106658 | 2 | 2 | 2 |
7 | 1.14688 | 1.33 | 1.13783 | 0.251853 | 2 | 3 | 3 |
8 | 1.206376 | 1.26 | 1.40369 | 0.510079 | 3 | 3 | 3 |
9 | 0.381909 | 2.3 | 0.9008 | 0.105591 | 2 | 2 | 2 |
10 | 1.271002 | 1.67 | 1.8433 | 1.075057 | 3 | 3 | 3 |
11 | 1.16503 | 2.16 | 2.29233 | 1.733703 | 3 | 3 | 3 |
12 | 1.553338 | 2.18 | 2.34555 | 2.00285 | 3 | 3 | 3 |
13 | 1.414547 | 2.72 | 2.48526 | 1.906329 | 3 | 3 | 3 |
14 | 0.693147 | 1.34 | 1.237 | 0.606743 | 2 | 2 | 2 |
15 | 1.303487 | 1.88 | 1.80312 | 1.143489 | 2 | 3 | 3 |
16 | 0.04308 | 2.85 | 2.7398 | 2.588069 | 4 | 4 | 4 |
17 | 1.787461 | 6.35 | 6.45495 | 8.394743 | 6 | 6 | 6 |
18 | 1.8612 | 6.45 | 6.90285 | 9.021374 | 6 | 6 | 6 |
19 | 1.949444 | 6.72 | 6.88925 | 8.872664 | 6 | 5 | 6 |
20 | 1.883662 | 9.31 | 9.29632 | 9.91465 | 6 | 6 | 7 |
21 | 1.277816 | 2.85 | 2.91541 | 3.522168 | 3 | 3 | 3 |
22 | 1.649751 | 4.79 | 5.10804 | 6.674977 | 5 | 5 | 5 |
23 | 1.794866 | 6.45 | 7.04766 | 9.271023 | 6 | 6 | 6 |
24 | 1.480208 | 4.68 | 4.88021 | 6.446144 | 5 | 5 | 5 |
25 | 2.020782 | 7.86 | 7.5702 | 8.760155 | 6 | 5 | 6 |
26 | 2.030221 | 4.53 | 5.19316 | 7.146074 | 4 | 5 | 5 |
Comparing the experimental results of the above four software quality measurement models, as shown in Figure
Comparing the experiment results.
(1) For the class diagram 4, the Zhou metric has higher values for the computational class diagram 4 complexity, the Yi15 metric and the Yi18 metric have lower values for the complexity of the class diagram 4, and the complexity of the class diagram 4 that the practical experience has obtained has lower values. The complexity of class diagram 4 calculated using the fuzzy matter element model in this paper is low, which is consistent with the actual experience.
(2) For the class diagram 9, the Zhou metric and the Yi18 metric have lower values for the computational class diagram 9 complexity, the Yi15 metric has higher values for the complexity of the class diagram 9, and the complexity of the class diagram 9 that the practical experience has obtained has lower values. The complexity of class diagram 9 calculated using the fuzzy matter element model in this paper is low, which is consistent with the actual experience.
(3) For the class diagram 16, the Zhou metric has lower values for the computational class diagram 16 complexity, the Yi15 metric and the Yi18 metric have higher values for the complexity of the class diagram 16, and the complexity of the class diagram 16 that the practical experience has obtained has higher values. The complexity of class diagram 16 calculated using the fuzzy matter element model in this paper is high, which is consistent with the actual experience.
(4) For the class diagram 19, the Yi18 metric for the complexity of the class diagram 19 has lower values than the class diagram 18, the Zhou metric and the Yi15 metric have higher values for the computational class diagram 19 complexity, and the complexity of the class diagram 19 that the practical experience obtained has lower values than the class diagram 18. The complexity of class diagram 19 calculated using the fuzzy matter element model in this paper is consistent with actual experience.
(5) For the class diagram 25 and the class diagram 26, the Zhou metric shows that the 26th class diagram complexity is higher than the 25th class diagram complexity and the Yi15 metric and Yi18 metric methods show the 26th class diagram complexity lower than it. The complexity of the class diagrams 25 and 26 obtained by the practical experience is opposite with the Zhou metric, which is in consistent with the complexity of the class diagram calculated by using the fuzzy matter element model in this paper.
In order to further discuss the existing correlation between the results of complexity metric and the value of understandability, the value of analysability, and the value of maintainability, we propose the Pearson simple correlation coefficient to test whether or not the complexity measure method is consistent with the practical experience. Pearson simple correlation coefficient is calculated as follows:
The correlation intensity between the two variables refers to Table
Correlation coefficient and correlation intensity.
Correlation coefficient absolute value | Correlation intensity |
---|---|
| Zero correlation |
| Weak correlation |
| Low correlation |
| Significant correlation |
| High correlation |
| Completely correlation |
Using the well-known statistical software SPSS for correlation analysis and the results of the correlation analysis are shown in Table
The correlation analysis of the complexity measurement results.
Metric methods | Understandability | Analysability | Maintainability | Average |
---|---|---|---|---|
Zhou metric | 0.741 | 0.773 | 0.775 | 0.763 |
Yi15 metric | 0.945 | 0.928 | 0.957 | 0.949667 |
Yi18 metric | 0.959 | 0.948 | 0.971 | 0.959333 |
Z | 0.959 | 0.956 | 0.962 | 0.959 |
Note:
Through the comparison and data analysis in Table
In order to compare the abovementioned four metrics methods more intuitive, the classification results of this paper are shown in Figure
Pearson simple correlation analysis.
From Figure
This paper uses the basic theory and method of matter element analysis, combined with fuzzy set theory and TOPSIS method to establish a fuzzy matter element model based on entropy weight and TOPSIS method. It is applied to the evaluation of software class diagram, and at the same time the difference between the entropy values as a weight, making full use of the information in the original data, to a certain extent reduces the subjectivity of weight determination; the evaluation results are in good agreement with the actual situation, indicating that the method is reasonable and feasible.
The data used to support the findings of this study were supplied by M. Genero under license. M. Genero at the Department of Computer Science at the University of Castilla-La Mancha, Ciduad Real, Spain, has allowed the author to quote the twenty-seven UML class diagrams related to bank information systems and the corresponding metric values. Reference: M. Genero. Defining and validating metrics for conceptual models [D], University of Castilla-La Mancha, 2002.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research has been supported by the Science and Technology Foundation of Jiangxi Provincial Department of Education (Project Name: Research on Software Complexity Measurement Based on Multiple Attribute Decision Making).