A Design-Based Cohesion Metric for Object- Oriented Classes

Transcription

1 Vo:, No:0, 007 A Design-Based Cohesion Metric for Object- Oriented Casses Jehad A Daa Internationa Science Index, Computer and Information Engineering Vo:, No:0, 007 waset.org/pubication/539 Abstract Cass cohesion is an important object-oriented software quaity attribute. It indicates how much the members in a cass are reated. Assessing the cass cohesion and improving the cass quaity accordingy during the object-oriented design phase aows for cheaper management of the ater phases. In this paper, the notion of distance between pairs of methods and pairs of attribute types in a cass is introduced and used as a basis for introducing a nove cass cohesion metric. The metric considers the methodmethod, attribute-attribute, and attribute-method direct interactions. It is shown that the metric gives more sensitive vaues than other we-nown design-based cass cohesion metrics. Keywords Object-oriented software quaity, object-oriented design, cass cohesion. I. INTRODUCTION popuar goa of software engineering is to deveop A techniques and toos to deveop appications that have high quaity. Appications that have high quaity are more stabe and maintainabe. In order to assess and improve the quaity of an appication during the deveopment process, deveopers and managers use severa metrics. These metrics estimate the quaity of different software attributes, such as cohesion, couping, and compexity. The cohesion of a modue refers to the reatedness of the modue components. The modue that has high cohesion performs one basic function and cannot be spit into separate modues easiy. Highy cohesive modues are more understandabe, modifiabe, and maintainabe []. In object-oriented paradigm, casses are the basic modues. The members of a cass are the attributes and methods. Therefore, cass cohesion refers to the reatedness of the cass members. The cass which its members are highy correated has high cohesion and cannot be spit into separate casses easiy. The degree of cass cohesion gives an indication for the quaity of cass design; where a highy cohesive cass is we designed and a owy cohesive cass is poory designed. Severa cass cohesion metrics have been proposed in the iterature. These metrics can be cassified into design-based and code-based. Design-based cass cohesion metrics require inspecting high-eve design artifacts, such as method interfaces [, 3, 4] to estimate the cass cohesion. Code-based The author woud ie to acnowedge the support of this wor by Kuwait University Research Grant WI03/07. Jehad A Daa is with Department of Information Sciences, Kuwait University, P.O. Box 5969, Safat 3060, Kuwait (e-mai: jehad@cfw.univ.edu). cass cohesion metrics e.g., [, 5, 6, 7, 8, 9, 0, ], require inspecting the cass interna code to measure the cass cohesion. Code-based cohesion metrics are more accurate than design-based ones, because they use a finer-grained artifact, which is the code itsef. At the code eve, a method-method, method-attribute, and attributes-attributes interactions are precisey defined. On the other hand, design-based cass cohesion metrics predict cohesion weanesses eary at design eve. Detecting cass cohesion weanesses and correcting the cass artifacts accordingy ate during the impementation phase are much more costy than performing the same tass eary during the design phase. Improving the cass cohesion during the design phase saves deveopment time, reduces deveopment costs, and increases the overa software quaity. The proposed design-based cass cohesion metrics have severa drawbacs. The first drawbac is that some designbased metrics are based on poory studied hypotheses. For instance, in order to increase the accuracy of the measured cass cohesion, the design-based metrics attempt to predict the actua interactions that woud be impemented during the impementation phase. The method-attribute interactions are not defined at the high-eve design phase. Therefore, as in [3] and [4], to predict the method-attribute interactions, the types of method parameters are used instead of the attributes. The hypothesis is that the attributes rey on the method parameters as a basis for the wor done by the cass. However, this hypothesis is not supported with a strong empirica study. In [3], ony C++ casses are studied to support the hypothesis. The second drawbac is that some metrics are environmentay dependent. For instance, in [] a metric is introduced for Ada-object systems. The metric may not be suitabe for other environments, such as object-oriented systems. The third drawbac is that some ey features of object-oriented programming anguages, such as inheritance, are not considered in the proposed metrics. The fourth drawbac is that, as far as we now, the Unified Modeing Language (UML), a standard anguage for modeing the object-oriented high-eve design, is not used as an artifact to support the measurement of cass cohesion in any of the proposed design-based cass-cohesion metrics. The fifth drawbac is that some proposed metrics, such as CAMC [3] and NHD [4], are not vaidated against cass cohesion metric necessary-properties. The sixth drawbac is that some metrics ignore indirect interactions and method invocation interactions. Finay, the research in the area of design-based cass cohesion measuring acs some important empirica Internationa Schoary and Scientific Research & Innovation (0) schoar.waset.org/ /539

2 Vo:, No:0, 007 Internationa Science Index, Computer and Information Engineering Vo:, No:0, 007 waset.org/pubication/539 studies to examine the affect of considering the inheritance reationships, method invocation interactions, indirect interactions, and incusion of the interactions of the specia types of methods, such as constructors, destructors, accessors, and modifiers in the metrics. In this paper, some predefined design-based cass cohesion metrics are overviewed. In addition, a new mode is introduced to represent the reationship between the parameter types and the attribute types. A nove design-based cass cohesion metric that uses the mode is introduced and caed the Distance Design-based Direct Cass Cohesion (D 3 C ) metric. The metric considers the method-method, methodattribute, and attribute-attribute direct interactions identified using the Unified Modeing Language (UML) cass diagram. The notion of distance between a pair of methods and a pair of attribute types is defined and used as a basis to measure the cass cohesion. Severa sampe cases are used to assess the sensitivity of the metric to mode changes comparing to the sensitivity of other we-nown design-based cass cohesion metrics. This paper is organized as foows. Section II overviews reated wor. Section III defines the mode used by the introduced metric. Section IV defines the metric, and Section V compares the metric with other metrics in terms of sensitivity. Finay, Section VI provides concusions and a discussion of future wor. II. RELATED WORK In this section, severa predefined design-based casscohesion metrics are overviewed and discussed. In addition, other reated wor in the area of measuring software cohesion is overviewed. Finay, the specifications of UML cass diagram and its reation to this wor is briefy iustrated. A. Design-based Cass-Cohesion Metrics Severa metrics are proposed in the iterature to measure the cass cohesion during the software high-eve design phase. These metrics use different modes and different formuas as foows:. Ratio of Cohesive Interactions Briand et a. [] define a design-based cohesion metric caed the Ratio of Cohesive Interactions (RCI) for Ada object-systems. The metric considers ony the data to data (DD) and data to subroutine (DS) interactions. In Ada, a type and variabes of that type can be defined inside a software part. Briand et a. consider each definition of a variabe of a type defined within the software part as a cohesive interaction between the variabe and the type. Interactions among variabes within subroutines are not considered, because their detais are not avaiabe during the design phase. The DS interaction occurs if a type defined within the software part matches the type of one of the subroutine parameters, or a variabe within the software part is isted in the method parameter ist. The RCI metric is defined as the ratio of the number of cohesive interactions of a modue to the tota number of possibe cohesive interactions. The RCI metric does not tae the indirect interactions into account. In addition, Briand et a. consider the incusion of method invocation interactions and inheritance reations as subjects for future wor. Briand et a. [] define three properties for cohesion metrics. The first property, caed normaization, is that the cohesion measure beongs to a specific interva [0, Max]. The second property, caed monotonicity, is that adding cohesive interactions to the modue cannot decrease its cohesion. The third property, caed cohesive modues, is that merging two unreated modues into one modue does not increase the modue's cohesion. The tota cohesion of spit casses is the weighted summation of the cohesion of the individua casses.. Cohesion among Methods in a Cass Bansiya et a. [3] propose a design-based cass cohesion metric caed Cohesion Among Methods in a Cass (CAM. In this metric, ony the method-method interactions are considered. The CAMC metric uses a parameter occurrence matrix that has a row for each method and a coumn for each data type that appears at east once as the type of a parameter in at east one method in the cass. The vaue in row i and coumn j in the matrix equas when ith method has a parameter of jth data type, and equas 0 In the matrix, the type of the cass is aways incuded in the parameter type ist, and every method has an interaction with this data type, because every method impicity has a sef parameter. This means that one of the coumns is fied entirey with s. The CAMC metric is defined as the ratio of the tota number of s in the matrix to the tota size of the matrix. Counse et a. [4] suggest omitting the type of the cass from the parameter occurrence matrix and cacuating CAMC using the modified matrix. We refer to this metric as CAMCc. 3. Normaized Hamming Distance (NHD) Metric Counse et a. [4] propose design-based cass cohesion metric caed the Normaized Hamming Distance (NHD). In this metric, ony the method-method interactions are considered. The metric uses the same parameter occurrence matrix used by CAMC metric (the type of the cass is not considered). The metric cacuates the average of the parameter agreement between each pair of methods. The parameter agreement between a pair of methods is defined as the number of paces in which the parameter occurrence vectors of the two methods are equa. Formay, the metric is defined as foows: NHD= cij = xj ( xj ) j= i= j+ j= () where is the number of coumns, is the number of rows, a ij is the number of entries in rows i and j in which both are equa to, and x j is the number of s in the jth coumn of the parameter occurrence matrix. Internationa Schoary and Scientific Research & Innovation (0) schoar.waset.org/ /539

3 Vo:, No:0, 007 Internationa Science Index, Computer and Information Engineering Vo:, No:0, 007 waset.org/pubication/539 B. Other Cohesion Measuring Reated Wor In 979, Yourdon et a. [] proposed seven eves of cohesion, which incuded coincidenta, ogica, tempora, procedura, communicationa, sequentia, and functiona. The cohesion eves are isted in ascending order according to their desirabiity. Since then, severa cohesion metrics have been proposed for procedura and object-oriented programming anguages. Different modes are used to measure the cohesion of procedura programs, such as contro fow graph [3], variabe dependence graph [4], sicing metrics [5], and program data sices [6] [7]. In [8] and [9], cohesion is measured indirecty by examining the quaity of the structured designs. Severa code-based cass cohesion metrics are proposed in the iterature. These metrics are based on the use or share of the cass instance variabes. In [5], the LCOM metric counts the number of pairs of methods that do not share instance variabes. Chidamber [6] proposes another version for the LCOM metric that cacuates the difference between the number of method pairs that do and do not share instance variabes. Li and Henry [0] use an undirected graph that represents each method as a node and the sharing of at east an instance variabe as an edge. The cass cohesion is measured as the number of connected components in the graph. This cass cohesion is extended in [7] by adding an edge between a pair of methods, if one of them invoes the other. Bieman and Kang [8] propose two cass cohesion metrics, TCC and LCC, to measure the reative number of directy connected pairs of methods and reative number of directy or indirecty connected pairs of methods, respectivey. These two metrics consider two methods to be connected, if they share at east one instance variabe. Cohesion metrics DCD and DCI [9] are simiar to TCC and LCC, respectivey, but by considering two methods connected when one of them invoes the other. Wang et a. [0] introduce a DMC cass cohesion metric based on a dependence matrix that represents the dependence degree among the instance variabes and methods in a cass. In [] a cass cohesion metric that considers the cardinaity of intersection between each pair of methods is proposed. In [] and [] cass cohesion metrics simiar to CAMC but for the method/instance variabe matrix are proposed. C. UML Cass Diagram UML is a standard anguage used for modeing objectoriented design. UML.0 [3] consists of 3 types of diagrams. In this paper, we are interested in cass diagram. The cass diagram describes the system's casses and the static reationship between them. The description of a cass incudes the names and types of the attributes and the names, return types, and parameter types of the methods. Fig shows a sampe cass diagram for the AccountDiaog cass. III. MODEL DEFINITION In [3] and [4], the parameter occurrence matrix uses the parameter types as bases for their metrics. Their argument is that it is expected that the method uses the attributes that their types are matching the types of the parameters. The main criticism for this argument is that some methods can have parameters of types not matching the types of the attributes. In this case, methods that share these types are considered cohesive despite the fact that they do not share any attributes. In addition, the parameter occurrence matrix does not inform whether a attributes are used within the methods. Therefore, in some cases, the cass is considered fuy cohesive despite the fact that some of its attributes are never used by the methods. Since the aim is to predict the share of attributes between the methods, we introduce the Direct Attribute-Type (DAT) matrix that uses the types of the attributes themseves instead of using the types of the method parameters. The matrix is a binary matrix, where is the number of methods and is the number of distinct attribute types in the cass of interest. To construct the matrix, the names and return types of the methods and the types of the parameters and the attributes are extracted from the UML cass diagram overviewed in Section.3. The DAT matrix has rows indexed by the methods and coumns indexed by the distinct attribute types, and for i, j, m ij 0 if jth data type is a type for at east one of the parametersor return of ith method, otherwise Fig. UML cass diagram for AccountDiaog The matrix expicity modes the direct attribute-method interactions. A method has a cohesive interaction with an attribute, if the attribute type matches the type of at east one parameter or return of the method. In addition, the matrix impicity modes the method-method and attribute-attribute interactions. A method has a cohesive interaction with another method, if their parameters or returns share the same attribute type. An attribute has a cohesive interaction with another attribute, if their types are shared in a method. This indicates that the method defines an interaction between the two attributes. A binary vaue in the DAT matrix indicates a cohesive attribute-method interaction. A cohesive methodmethod interaction is represented in the DAT by two rows sharing binary vaues in a coumn. Simiary, a cohesive attribute-attribute interaction is represented in the DAT by two coumns sharing binary vaues in a row. In this matrix, the return type of the method is considered. The reason is that it is Internationa Schoary and Scientific Research & Innovation (0) schoar.waset.org/ /539

4 Vo:, No:0, 007 Internationa Science Index, Computer and Information Engineering Vo:, No:0, 007 waset.org/pubication/539 occasionay noticeabe that some methods access some attributes not passed as parameters and return resuts that match the types of the accessed attributes. Consequenty, the return type gives an indication for the accessed attributes within methods, and therefore, it shoud be considered in the cass cohesion measurement. Fig. shows the DAT matrix of the AccountDiaog cass. The matrix is constructed using the information provided by the UML cass diagram given in Fig. The matrix shows that three of the attribute types are used by showinfo method, one of the attribute types is used by showaddress method, and one of the attributes is used by readname method (as a return type). String int Date Address showinfo 0 showaddress showextrainfo readname Fig. The DAT matrix for the AccountDiaog cass IV. THE DISTANCE DESIGN-BASED DIRECT CLASS COHESION (D 3 C ) METRIC DEFINITION The D 3 C metric uses the DAT matrix to measure the method-method interactions caused by sharing attribute types, the attribute-attribute interactions caused by the expected use of attribute within the methods, and the attribute-method interactions. The different types of cohesion caused by the three types of interactions are referred to as Method-Method through Attributes Cohesion (MMA, Attribute-Attribute Cohesion (AA, and Attribute-Method Cohesion (AM, respectivey. A. MMAC and AAC Metrics The simiarity between two items is the coection of their shared properties, and the distance is the opposite [4]. In the context of the DAT matrix introduced in Section 3, the distance between two rows and two coumns quantifies the ac of cohesion between a pair of methods and a pair of attributes, respectivey. The distance between a pair of rows or coumns is defined as the number of entries in a row or coumn that have different binary vaues than the corresponding ones in the other row or coumn. The normaized distance, denoted as ndist(i,j), between a pair of rows or coumns i and j is defined as the ratio of the distance between the two rows or coumns to the number of entities Y in the row or coumn of the matrix, and it is defined formay as foows: MMAC ( = ndist( i, j) () i = j = i + where is the ogica excusive-or reation (i.e., equas if the two operands have different vaues). A distance measure has to satisfy three properties: () the distance is aways greater than or equa to zero, () the distance reation is symmetric, and (3) the distance between an eement and itsef is equa to zero [4]. For a pair of rows or coumns, the minimum number of corresponding entries that have different binary vaues is zero; that is it when both rows or coumns are identica. On the other hand, the maximum number of corresponding entities that have different binary vaues is equa to the tota number of ces in the row or coumn. This occurs when each corresponding entries have different binary vaues. As a resut, the normaized distance ranges in the interva [0, ]. Since reation is symmetric, the normaized distance between any pair of rows or coumns is symmetric. Finay, the excusive-or of an entry and itsef is equa to zero. Therefore, the distance between a row or coumn and itsef is equa to zero. As a resut, the metric given in Formua is a distance measure. Generay, cohesion refers to the degree of simiarity between modue components. Simiarity and distance are compementary measures. As a resut, cohesion and distance are compementary measures [4]. Formay, we define cohesion of a pair of methods or attributes as the degree of simiarity between them, and it is cacuated as foows: C(i,j) = - ndist(i,j) (3) The MMAC is the average cohesion of a pairs of methods, and the AAC is the average cohesion of a pairs of attributes. Formay, using the DAT matrix, the MMAC of a cass C consists of methods and distinct attribute types is defined formay as foows: if = 0or = 0, if =, MMAC ( (4) C( i, j) i= j= i+ Given the fact that the normaized distance between any pair of methods is symmetric and by substituting Formua 3 into Formua 4, the MMAC of cass C is cacuated in the case of having more than one method in the cass as foows: MMAC ( = ndist( i, j) (5) i= j= i+ By substituting Formua into Formua 5, the MMAC of cass C is cacuated in the case of having more than one method in the cass as foows: MMAC ( = ( m iw m jw ) (6) i= j= i+ w= The foowing metric is an aternative form of the MMAC metric, which faciitates the anaysis of the metric and speeds up its computation: Internationa Schoary and Scientific Research & Innovation (0) schoar.waset.org/ /539

5 Vo:, No:0, 007 Internationa Science Index, Computer and Information Engineering Vo:, No:0, 007 waset.org/pubication/539 if = 0or = 0, if =, xi ( xi ) i= where x i is the number of s in the ith coumn of the DAT matrix. Proof: By definition, when = or =0 and =0, Formua 4 and 6 are equa. Otherwise, for the ith coumn, there are x i (x i -)/ simiarities between the methods, and therefore, there are - )/- x i (x i -)/ differences between the methods. By definition, xi ( xi ) = ( ) i= xi ( xi ) = i= The resut foows. Simiary, the AAC of a cass C is defined formay as foows: if = 0or = 0, if =, AAC( = (8) yi ( yi ) i= ( ) where y i is the number of s in the ith row of the DAT matrix. For exampe, using Formua 7, the MMAT for AccountDiaog cass is cacuated as foows: () + (0) + (0) + (0) MMAT( AccountDiaog) = = (4)(3) Using Formua 8, the AAC for AccountDiaog cass is cacuated as foows: 3() + (0) + 0( ) + (0) AAC( AccountDiaog) = 0.5 4(4)(3) B. AMC Metric The notion of simiarity and distance is appicabe ony when the considered pair is of the same entity. Therefore, the notion of simiarity and distance is appicabe for pairs of method-method and attribute-attribute, but it is not appicabe for pairs of attribute-method, because attributes and methods are of two different entities. In this case, the cohesion is the average number of attribute-method interactions represented in the DAT matrix. In other words, the AMC is the ratio of the number of s in the DAT matrix to the tota size of the matrix. The AMC of a cass C is defined formay as foows: (7) AMC( 0 if = 0 or = 0, m i= j= = ij (9) Using Formua 9, AMC(AccountDiaog)=5/6=0.33 C. D 3 C Metric The D 3 C metric is not defined if the cass has no methods and no attributes. The D 3 C metric is defined as the weighted summation of the MMAC, AAC, and AMC metrics. The D 3 C of a cass C is defined for > and > as foows: D C 3 MP* + AP* AAC( + * AMC( = (0) MP + AP + ( where MP is the number of method pairs, and AP is the number of distinct attribute-types pairs. By substituting MP and AP with their formuas in Formua 0 and considering a cases of and except when both are equa to 0, the D 3 C is more formay defined as foows: if = 0 and =, () if = and = 0, D3C ( + ( ) AAC( + AMC( + ( ) + Using Formua, the D 3 C for AccountDiaog cass is cacuated as foows: 4(3)(0.04) + 4(3)(0.5) + (4)(4)(0.33) D3 C( AccountDiaog) = = 0.7 3(3) + 4(3) + (4)(4) V. SENSITIVITY Tabe I shows severa patterns for the matrices used by CAMCc, NHD, and D 3 C metrics. The tabe shows that the vaue of the CAMCc metric resut is the same for casses A and B despite the fact that the intuition informs that cass A is more cohesive than cass B. The same scenario appies for casses D and C. The NHD metric vioates the intuition by giving the same resut for casses A, B, and D and by considering cass C to be more cohesive than cass D. The D 3 C metric foows the intuition for a the isted cases. The metric resuts show that cass A is more cohesive than cass B, which is expected, because none of the pairs of rows or coumns in the matrix representing cass B share any commonaity, whereas the pairs of coumns in the matrix representing cass A share some commonaities. Cass D is more cohesive than cass A, because the pairs of coumns and the pairs of rows in the matrix representing cass D share some commonaities. Cass C is more cohesive than cass D, because the matrix representing cass C has more pairs of rows sharing some commonaities. Finay, cass E is the most cohesive, because its matrix shows that it has the argest number of cohesive interactions among the other matrices. This shows that the D 3 C metric is more sensitive than the other two metrics, and it gives more meaningfu and Internationa Schoary and Scientific Research & Innovation (0) schoar.waset.org/ /539

6 Vo:, No:0, 007 Internationa Science Index, Computer and Information Engineering Vo:, No:0, 007 waset.org/pubication/539 representative resuts. VI. CONCLUSION AND FUTURE WORK This paper introduces a design-based cass cohesion metric that considers three types of interactions: method-method interactions caused by sharing attribute types, attributeattribute interactions caused by the expected use of attributes within the methods, and attribute-method interactions. The metric uses a matrix constructed using a UML cass diagram avaiabe at the high-eve design phase. The metric uses the distance between pairs of methods and pairs of attributes as bases to compute their degree of simiarity. The introduced metric can be improved in severa directions, such as considering indirect interactions and method invocation interactions. In the future, we pan to compare our metric with others empiricay. In addition, we pan to introduce a simiar code-based cass metric and study it empiricay. TABLE I VALUES OF DIFFERENT COHESION METRICS ON 5 SAMPLE CLASSES Cass Matrix pattern CAMC c NHD D 3 C A B C D E REFERENCES [] Z. Chen, Y. Zhou, and B. Xu, A nove approach to measuring cass cohesion based on dependence anaysis, Proceedings of the Internationa Conference on Software Maintenance, 00, pp [] L. C. Briand, S. Morasca, and V. R. Basii, Defining and vaidating measures for object-based high-eve design, IEEE Transactions on Software Engineering, Vo. 5, No. 5, 999, pp [3] J. Bansiya, L. Etzorn, C. Davis, and W. Li, A cass cohesion metric for object-oriented designs, Journa of Object-Oriented Program, Vo., No. 8, pp [4] S. Counse, S. Swift, and J. Crampton, The interpretation and utiity of three cohesion metrics for object-oriented design, ACM Transactions on Software Engineering and Methodoogy (TOSEM), Vo. 5, No., 006, pp [5] S.R. Chidamber and C.F. Kemerer, Towards a Metrics Suite for Object- Oriented Design, Object-Oriented Programming Systems, Languages and Appications (OOPSLA), Specia Issue of SIGPLAN Notices, Vo. 6, No. 0, 99, pp [6] S.R. Chidamber and C.F. Kemerer, A Metrics suite for object Oriented Design, IEEE Transactions on Software Engineering, Vo. 0, No. 6, 994, pp [7] M. Hitz and B. Montazeri, Measuring couping and cohesion in object oriented systems, Proceedings of the Internationa Symposium on Appied Corporate Computing, 995, pp [8] J. M. Bieman and B. Kang, Cohesion and reuse in an object-oriented system, Proceedings of the 995 Symposium on Software reusabiity, Seatte, Washington, United States, pp. 59-6, 995. [9] L. Badri and M. Badri, A Proposa of a new cass cohesion criterion: an empirica study, Journa of Object Technoogy, Vo. 3, No. 4, 004. [0] J. Wang, Y. Zhou, L. Wen, Y. Chen, H. Lu, and B. Xu, DMC: a more precise cohesion measure for casses. Information and Software Technoogy, Vo. 47, No. 3, 005, pp [] L. Fernández, and R. Peña, A sensitive metric of cass cohesion, Internationa Journa of Information Theories and Appications, Vo. 3, No., 006, pp [] E. Yourdon and L. Constantine, Structured Design, Prentice-Ha, Engewood Ciffs, 979. [3] T. Emerson, A discriminant metrics for modue cohesion, In Proceedings of the 7th Internationa Conference on Software Engineering, 984, pp [4] A. Lahotia, Rue-based approach to computing modue cohesion, Proceedings of the 5th internationa conference on Software Engineering, Batimore, US, 993, pp [5] L. Ott and J. Thuss, Sice based metrics for estimating cohesion, Proceedings of the First Internationa Software Metrics Symposium, Batimore, 993, pp [6] J. Bieman and L. Ott, Measuring functiona cohesion, IEEE Transactions on Software Engineering, Vo. 0, No. 8, 994, pp [7] J. A Daa, Using distance measurement for software functiona cohesion, IASTED Internationa Conference on Software Engineering (SE 005), Innsbruc, Austria, 005, pp [8] D. Troy and S. Zweben, Measuring the quaity of structured designs, Journa of Systems and Software,, 98, pp [9] J. Bieman and B. Kang, Measuring design-eve cohesion, IEEE Transactions on Software Engineering, Vo. 4, No., 998, pp [0] W. Li and S.M. Henry, Maintenance metrics for the object oriented paradigm. In Proceedings of st Internationa Software Metrics Symposium, Batimore, MD, 993, pp [] B. Henderson-seers, Object-Oriented Metrics Measures of Compexity, Prentice-Ha, 996. [] L. C. Briand, J. Day, and J. Wuest, A unified framewor for cohesion measurement in object-oriented systems, Empirica Software Engineering - An Internationa Journa, Vo. 3, No., 998, pp [3] D. Pione and N. Pitman, UML.0 in a Nutshe, O'Reiy Media, Inc., nd edition, 005, pp. 34. [4] F. Simon, S. Loffer, C. Lewerentz, Distance based cohesion measuring, Proceedings of the FESMA'99, Amsterdam, Netherands, 999, pp Internationa Schoary and Scientific Research & Innovation (0) schoar.waset.org/ /539