رویکرد فرآیند تحلیل سلسله مراتبی فازی تحلیلی گروهی برای نرم افزار مدیریت تضمین کیفیت : روش حداقل مربعات لگاریتمی

This paper proposes a Fuzzy Group Analytical Hierarchy Process approach for assessing the quality of software, with judgments by a group of experts at different levels. The international standard of software quality attributes, ISO/IEC9126-1:2001 which comprises of 6 criteria with 27 subcriteria, is applied as the attributes of software quality. Regarding the prioritization method, the modified fuzzy Logarithmic Least Squares Method (LLSM) is applied to derive the importance weight vectors. The Fuzzy Prioritization Programming for Direct Rating Scales (FPP-DRS) on the basis of the modified fuzzy LLSM and the rescaling functions is proposed to design the direct rating scales in fuzzy number. The Fuzzy Synthesis Programming for Absolute Measurement (FSPAM) including Integrated Fuzzy Scores of Individual Expert (IFSIE) and Group Integrated Fuzzy Score (GIFS) is proposed to aggregate the criteria values from various experts. The proposed approach can help a group of various experts including developers, testers and purchasers, to measure the level of the software quality of the in-house development or the third party development.

A high quality software system is one of the essential attributes of high confidence computer systems. Any malfunctions of the software systems can cause great inconvenience, even a disaster to the users. A high confidence system is a system which meets the standard of software quality. Software quality assurance plays an essential role in the development of such software systems. Measurement of the software quality includes the measurement of in-house developments and a selection of vendors’ products. SQA takes the responsibility to make the “go/not go” decision in this matter. If the quality of the product released or purchased is below standard, the company will suffer a significant loss. If the product development is behind schedule, the company also loses a lot. As it is difficult to build a perfect or error free software system or to purchase highly compatible software components, SQA must apply comprehensive techniques to determine whether the systems reach the right level of quality. These techniques include the clear definition of quality attributes, measurement tools, and the integration framework. To determine software quality, quality metric models have been studied by many researchers. This research selects six attributes with 27 subcriteria in ISO/IEC 9126-1 (2001), which is the revision of 1991 version (ISO/IEC 9126, 1991), for the development of the proposed fuzzy group analytical hierarchy process. ISO/IEC 9126-1 defines terms for the software quality characteristics and how these characteristics are decomposed into subcharacteristics. The details of this are given in Section 5. ISO/IEC 9126-1, however, does not describe how any of these subcharacteristics could be measured. To address this issue, three more parts are extended: ISO/IEC 9126-2, 2003, ISO/IEC 9126-3, 2003 and ISO/IEC 9126-4, 2003. ISO/IEC 9126-2 (2003) defines external metrics which measure the behaviours of the computer-based system that includes the software. ISO/IEC 9126-3 (2003) defines internal metrics which measure the software itself. ISO/IEC 9126-4 defines quality in use metrics which measure the effects of using the software in a specific context of use. However, a drawback of the existing international standards is that they provide very general quality models and guidelines, but are very difficult to apply specific domain (Bertoa, Troya, & Vallecillo, 2006). Expert judgments using the proposed fuzzy group analytical hierarchy process (FGAHP) can be the ideal solution, especially for some subcriteria which are less computable. Regarding measurement tools and the integration framework including aggregation techniques and synthesis approaches, the analytic hierarchy process (AHP) (Saaty, 1980, Saaty, 1990 and Saaty, 2005) is the popular approach which enables the user to make decisions to address these issues. The software development of AHP can be found in various researches (e.g. Ossadnik and Lange, 1999 and Zhu et al., 2005). The limitation is that the measurement scales for the value of the utility function, which is basically numerical and probabilistically judgmental, induce difficulties when making the evaluation. This can be solved by applying linguistic labels, represented by fuzzy numbers, as the scales for the software metrics. Studies in fuzzy AHP (e.g. Boender et al., 1989, Buyukozkan et al., 2004, Chang, 1996, Chang et al., 2008, Chen et al., 2008, Laarhoven and Pedrycz, 1983, Mikehailov and Tsvetinov, 2004, Wang et al., 2006 and Wang et al., 2008) can be applied to address this limitation. The outline of this paper is as follows. Section 2 reviews the related works. Section 3 presents the foundations of fuzzy theory. Section 4 presents the generic managerial process of FGAHP. Sections 5, 6, 7, 8 and 9 illustrate the details of the generic process. Section 5 presents the (ISO/IEC 9126-1, 2001) software quality model which consists of six criteria with 27 subcriteria. Section 6 presents the rating scale schema. Section 7 presents the prioritization methods for deriving fuzzy importance and fuzzy metric scales of the hierarchical criteria using a modified fuzzy LLSM model. Section 8 illustrates the synthesis method to integrate the evaluation scores and importance of the hierarchical criteria. Section 9 shows the case study demonstrating the proposed approach and discussion of the applicability of the proposed model. The Conclusion is in Section 10. The notation summary is shown in the Appendix.

This research proposes a fuzzy group analytical hierarchy process approach for software quality evaluation under conditions of uncertainty. Six criteria with 27 subcriteria from ISO/IEC 9126:2001 are chosen for building the model. To illustrate the usability and validity of this model, a case study has been conducted. The advantages of the FGAHP approach includes following three issues. Firstly, as fuzzy importance vectors among the hierarchical criteria are perceived differently by different people, this paper applied modified fuzzy LLSM to derive the consensus fuzzy importance or fuzzy weight. The modified fuzzy Logarithmic Least Squares Method is used. This is better than other methods as was discussed in the related works. Secondly, as fuzzy intervals of the linguistic labels, and distances among any adjacent linguistic labels are perceived differently for each criteria, and differently by each expert, this paper proposes Fuzzy Prioritization Programming for Direct Rating Scales (FPP-DRS), in which three more equations are applied to the modified fuzzy LLSM and rescale the original interval values, to address this issue. Thirdly, each expert perceives the quality of the attributes of the software products differently. Thus Fuzzy Synthesis Programming for Absolute Measurement (FSPAM) including the Integrated Fuzzy Scores of Individual Expert (IFSIE) and the Group Integrated Fuzzy Score (GIFS) is proposed to address this issue and to come to an agreement. The scope of this paper does not include the methods or frameworks of how to give the direct rating scores for each criterion as these methods are different from various software applications such as web applications, window applications, distributed applications, mobile applications, and database applications. The relevant issue was discussed by ISO/IEC 9126-2, 2003, ISO/IEC 9126-3, 2003, ISO/IEC 9126-4, 2003, Xenos and Christodoulakis, 1997 and Bevan, 1999 and Losavio, Chirinos, Matteo, Levy, and Ramdane-Cherif (2004). Future research will address this issue. Future research will also compare the fuzzy group AHP approach with the fuzzy group Cognitive Network Process (CNP) (Yuen, 2009, Yuen, 2011a and Yuen, 2011b) in the areas of Software Quality Assurance management.