Evaluating Software Quality of Vendors using Fuzzy Analytic Hierarchy Process

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1 IMECS March 2008 Hong Kong Evaluating Software Quality of Vendors using Fuzzy Analytic Hierarchy Process Kevin K.F. Yuen* Henry C.W. au Abstract This paper proposes a fuzzy Analytic Hierarchy Process odel for evaluating the software quality of vendors. The criteria of software quality adopt the international nor ISO/IEC926-:200 which includes of six criteria. The fuzzy AHP odel applies the odified fuzzy ogarithic east Squares Method (SM in this software criteria odels. The proposed odel can help the developers and testers to evaluate the vendors software applications and select the best alternative under uncertain environent. Index Ters Fuzzy AHP Fuzzy Decision Making Software Quality Assurance Software Vendor Selection I. INTRODCTION Software systes pereate the odern life. Any failure of the software systes possibly causes any inconvenience or disaster to the people. To eet the standard of software quality software quality assurance plays an essential role in software developent. IEEE [5] defined software quality as ( the degree to which a syste coponent or process eets specified requireents and (2 the degree to which a syste coponent or process eets custoer or user needs or expectations. IEEE [5] defined software quality assurance as ( a planned and systeatic pattern of all actions necessary to provide adequate confidence that an ite or product confors to established technical requireents and (2 a set of activities designed to evaluate the process by which the products are developed or anufactured. The ter software architecture refers to the global structuring of a software syste [4]. The design of the architecture should be flexible extensible portable and reusable. sually when a large scale coplex software syste is built third party software coponents or accessories usually are needed for soe functions in the systes with the purpose of reduction of cost developent tie and advantages of the expertise of the third parties. Such incoing coponents or accessories directly influence the final product. Thus evaluating the incoing coponents is the vital activity. For quantitatively and qualitatively evaluating the software quality a quality etrics odel is established. [78] reviewed the hierarchical and non-hierarchical odels of software quality attributes. This research chooses six attributes in ISO/IEC926-: 200 [6] for discussion. As the attributes of software quality are identified the next Kevin Ka Fung Yuen is with Departent of Industrial and Systes Engineering The Hong Kong Polytechnic niversity Hung Ho KN Hong Kong (e-ail:kevinkf.yuen@gail.co ise.kevinyuen@polyu.edu.hk question is the evaluation and aggregation techniques. Analytic Hierarchy Process [] and Analytic Network Process [2] are popular odels to aggregate ultiple criteria for decision aking. The liitation is that the easure scale for the value of the utility function which is basically nuerical and probabilistically judgental induces evaluation proble. This introduces the studies of fuzzy AHP [e.g ] to address the liitation. The extent analysis ethod on fuzzy AHP [2] has been used in any studies as it is regarded as less coplexity. However [5] pointed out this ethod was probleatic. [45] proposed odified fuzzy ogarithic east Squares Method (SM as the appropriate alternative on the basis of [3]. The outline of this paper is as follows. Section 2 presents the hierarchical structure using the ISO software quality odel which consists of six ajor attributes. Section 3 presents the coputational ethod using odified fuzzy SM odel. Section 4 illustrates the nuerical exaple deonstrating the proposed odel. Conclusion is in section 5. II. HIERARCHICA MODES FOR SOFTWARE QAITY There are various hierarchical odels of software quality attributes such as Factor-Criteria-Metrics Model McCall s Model Boeh s Model FRPS and Droey s Model [78]. This paper typically chooses the ISO/IEC926-: 200 [6] odel which is a well known odel as the easureent criteria to evaluate the software quality. Fig. shows the hierarchical odel consisting of six criteria which are defined as follows [60]: Functionality ( C : the capability of the software product to provide functions which eet stated or iplied needs when the software is in use under specified conditions. 2 Reliability ( C 2 : the capability of the software product to aintain a specified level of perforance when used under specified conditions. 3 sability ( C 3 : the capability of the software product to be understood learned used and attractive to the user under specified conditions. 4 Efficiency ( C 4 : the capability of the software product to provide appropriate perforance relative to the aount of resources used under stated conditions. ISBN: IMECS 2008

2 IMECS March 2008 Hong Kong Fig. : AHP structure for evaluating Software vendor with respect to ISO six criteria 5 Maintainability ( C 5 : the capability of the software product to be odified. Modifications ay include corrections iproveents or adaptation of the software to changes in environent and in requireents and functional specifications. 6 Portability ( C 6 : the capability of the software product to be transferred fro one environent to another. I. FZZY AHP a Triangular Fuzzy nuber and its operation A fuzzy linguistic label can be represented by a fuzzy nuber which is represented by a fuzzy set. Fuzzy sets capture the ability to handle uncertainty by approxiate ethods. A triangular fuzzy nuber (TFN is applied ostly in the fuzzy theories and application. A TFN is l u and its ebership has represented by 3-tuple ( the for: x l l x l u x A ( x µ x u u 0 otherwise where l u l and u are the fuzzy boundaries and is the odal value. and Consider two TFNs a ( l u ( a2 l2 2 u2. Soe of the operational axios are as follows: Addition: a + a2 l u + l2 2 u2 ( ( ( l l u u Subtraction: a a2 l u l2 2 u2 ( ( ( l l u u Multiplication: aia2 l u i l2 2 u2 ( ( ( lil i uiu Division: a / a2 l u / l2 2 u2 Inversion: ( ( ( l / l / u / u ( ( l u ( u l ( u l / / /. b Modified fuzzy SM There are various coputational odels for fuzzy AHP. This paper chooses the latest research the odified fuzzy ogarithic east Squares Method (SM [45] as the fuzzy AHP odel. The related coparision with Extent fuzzy AHP odel [2] can be referred to [5] and the coparison with SM odel [3] can be referred to [4]. Details of odified fuzzy SM are presented as follows: Consider a fuzzy coparison atrix expressed by ( ( l2 2 u2 ( ln n un ( l u ( ( l u n 2n 2n A ( aij nxn ( ln n un ( ln2 n2 un2 ( ( ( ( aij lij ij uij a ji u ji ji l ji and for i j n and i j. ( a if i j. ij The odified fuzzy SM developed in [45] which derives the priorities of the triangular fuzzy coparison atrix in (. ISBN: IMECS 2008

3 IMECS March 2008 Hong Kong Table : Synthesis of local fuzzy weights Alternatives Criterion w w M w Criterion j w w M w Criterion w w M w Global fuzzy weights ( ( w w M w ( j j j M ( w j w j w j ( M ( w w w ( M w w w A A A k M wk wk wk ( M wkj wkj wkj ( wk wk M w M k w w w Ak Ak A k A ( A n M ( wn wn wn ( M wnj wnj wnj ( wn wn M w M n w w w A A A n n n The local weights have following fors: ( ln i ln j ln ij n n 2 Min J w w l + i j j i M M ( ln wi ln wj ln ij + ( ln wi ln wj lnuij 2 2 triangular fuzzy weight of criterion j ( j ( w M kj w kj w kj and is the noralized triangular fuzzy weight of alternative A k with respect to the criterion j k K j. ( Subject to n wi + wj j j i n wi + wj j j i n M wi i n (2 i n ( wi + wi 2 i M wi wi wi > 0 The optiu solution to the above odel fors w i wi wi M wi noralized triangular fuzzy weights ( i n to obtain the local fuzzy weights. After the local fuzzy weights are obtained then Global fuzzy weight should be calculated with the presentation in table. Global fuzzy weights can be obtained by solving the following two linear prograing odels and an equation for each decision alternative. Ak kj j (3 w Ω w j w Min w w k K Ak kj j (4 w Ω w j w Max w w k K M M M A kj j k (5 w Ω w j w Max w w k K ( W w w where Ω w M w j w j w j w j j j is the space of weights ( w j w M j w j is the noralized I. NMERICA EXAMPE A copany designing and anufacturing Sartphone includes the software and hardware developent. Recently the copany would like to develop the new odel of Sart phone. The copany would like to add one accessory application into its product aong three candidates with respect to the ISO six criteria in Fig.. The following illustrates how odified fuzzy SM odel is adapted to software quality odel. Firstly the fuzzy rating scales are defined as: { } Scale H M I M H which their triangular fuzzy nubers are defined as follows. M H I M H ( ( ( (.... ( ( ( Secondly the fuzzy relative iportance of the six quality attributes is deterined using Eq(2. The input values and the results are shown in table 2. Thirdly the experts copare the three candidates under each of six criteria separately. Tables 3-8 show their input coparisons under each criteria and the coparison results (or local fuzzy weights which uses Eq(2. Fourthly the coparison results under each of six criteria and the fuzzy relative iportance are aggregated by Eqs. (3-(5 and the global fuzzy weights of the three candidates are deterined. These details are shown in table 9. It is clear that is the best alternative followed by and. The result is also illustrated in Fig.2. ISBN: IMECS 2008

4 IMECS March 2008 Hong Kong Table 2: Fuzzy coparison atrix for the iportance of six criteria and their local fuzzy weights Criteria C C 2 C 3 C 4 C 5 C 6 C ( (0.5.5 ( (0.5.5 ( ( ( C 2 (0.5.5 ( (0.5.5 (0.5.5 (0.5.5 (0.5.5 ( C 3 ( (0.5.5 ( ( (0.5.5 (0.5.5 ( C 4 (0.5.5 (0.5.5 ( ( (0.5.5 (0.5.5 ( C 5 ( (0.5.5 (0.5.5 (0.5.5 ( ( ( C 6 ( (0.5.5 (0.5.5 (0.5.5 ( ( ( Table 3: Fuzzy coparison atrix of the three candidates with respect to functionality C and their local fuzzy weights Candidates ( ( ( ( ( ( ( ( ( ( ( ( Table 4: Fuzzy coparison atrix of the three candidates with respect to reliability C 2 and their local fuzzy weights Candidates ( ( ( ( ( ( (0.5.5 ( ( (0.5.5 ( ( Table 5: Fuzzy coparison atrix of the three candidates with respect to usability C 3 and their local fuzzy weights Candidates ( ( ( ( ( ( ( ( ( ( ( ( Table 6: Fuzzy coparison atrix of the three candidates with respect to efficiency C 4 and their local fuzzy weights Candidates ( ( ( ( ( ( ( ( ( ( ( ( Table 7: Fuzzy coparison atrix of the three candidates with respect to aintainability C 5 and their local fuzzy weights Candidates ( ( ( ( ( ( (0.5.5 ( ( (0.5.5 ( ( Table 8: Fuzzy coparison atrix of the three candidates with respect to portability C 6 and their local fuzzy weights Candidates ( ( ( ( ( ( (0.5.5 ( ( (0.5.5 ( ( ISBN: IMECS 2008

5 IMECS March 2008 Hong Kong Table 9: Synthesis of local fuzzy weights of three candidates and their Global Fuzzy Weight Criterion Criterion 2 Criterion 3 Criterion 4 Criterion 5 Criterion6 Global ( ( ( ( ( ( fuzzy weights ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( Fig. 2 Global Fuzzy weights of the three candidates I. DISCSSION AND CONCSION This research proposes a fuzzy AHP odel for software quality evaluation and software vendor selection under uncertainty. The odel uses odified fuzzy ogarithic east Squares Method. Six attributes of software quality are chosen fro ISO/IEC926. A nuerical exaple illustrates the usability and validity of this odel. The liitation of this ethod is the coputational efficiency and coplexity which will be discussed and iproved in the future research. ACKNOWEDGMENT The authors wish to thank the Research Office of the Hong Kong Polytechnic niversity for support in this research project. Thanks are also extended to the editors and anonyous referees for their constructive criticiss to iprove the future work. [8] K. Khosravi Y. G. Gueheneuc A quality odel for design patterns Suer 2004 [9].Mikehailov and P. Tsvetinov Evaluation of services using fuzzy analytic hierarchy process Applied Soft Coputing 5( [0] M. Pol R. Teunissen E. V. Veenendaal Software Testing: A guide to the TMap Approach Addison-Wesley 2002 [] T.. Saaty The Analytic Hierarchy Process. New York: McGraw-Hill 980 [2] T.. Saaty Theory and Applications of the Analytic Network Process: Decision Making with Benefits Opportunities Costs and Risks RWS Publications [3] P.J.M. van aarhoven W. Pedrycz A fuzzy extension of Saaty s Priority theory Fuzzy Sets and Systes ( [4] Y. M. Wang T. M.S. Elhag Z. Hua A odified fuzzy logarithic least squares ethod of fuzzy analytic hierarchy process Fuzzy Sets and Systes 57 ( [5] Y. M. Wang Y. uo Z. Hua On the extent analysis ethod for fuzzy AHP and its application European Journal of Operational Research 86 ( REFERENCES [] C.G.E. Boender J.G. de Graan F.A. ootsa Multi-criteria decision analysis with fuzzy pairwise coparisons Fuzzy Sets and Systes 29 ( [2] D.Y. Chang Applications of extend analysis ethod on fuzzy AHP European J. Oper. Res. 95 ( [3] M.F. Chen G.-H. Tzeng C.G. Ding Cobining fuzzy AHP with MDS in identifying the preference siilarity of alternatives Applied Soft Coputing 2007 In press. [4] S. Dick A. Kandel Coputational Intelligence In Software Quality Assurance Machine Perception Artificial Intelligence volue [5] IEEE (99 IEEE std IEEE Standard Glossary of Software Engineering Terinology Correct Edition Feb. 99 in IEEE Software Engineering Standards Collection the Institute of Electrical and Electronics Engineers New York. [6] ISO/IEC926-: 200 Software engineering-product quality-part: quality odel 200 [7] R.A. Khan K. Mustafa S.I Ahson Software Quality: Concepts and Practices Alpha Science Oxford.K 2006 ISBN: IMECS 2008