Analysis of Class Design Coupling Based on Information Entropy Di Jiang 1,2, a, Hua Zhou 1,2,b and Xingping Sun 1,2,c

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1 Advaced Materials Research Olie: IN: , Vol. 659, pp doi: / Tras Tech Publicatios, witzerlad Aalysis of Class Desig Couplig Based o Iformatio Etropy Di Jiag 1,2, a, Hua Zhou 1,2,b ad Xigpig u 1,2,c 1 chool of oftware, Yua Uiversity, Kumig, , Chia 2 Key Laboratory for oftware Egieerig of Yua Provice Republic of Chia a alexjiag.y@gmail.com, b zh6691@hotmail.com, c ysuxp@gmail.com Keywords: Iformatio etropy; Couplig; Class desig; Quatitative aalysis Abstract. I object-orieted programmig, desigig class is oe of the most importat steps of software developmet. How to aalyze ad evaluate the class desig is a importat topic i the field of software egieerig. The paper puts forward a method which is based o iformatio etropy to quatify the couplig of class desig. Compared to the covetioal methods, this method has a better operability ad accuracy. O the above basis, this paper validates the feasibility of the method by the case studies. Itroductio There are two importat idicators to measure the merits of a class desig i object-orieted software developmet. They are cohesio ad couplig. A excellet class should be desiged to meet the characteristics of high cohesio, low couplig. The couplig idicates the depedecies betwee classes which ca affect the exteral quality attributes of the system. The higher couplig meas the classes are more closely liked. I this case, if oe class is modified may result i multiple classes associated with it does ot work properly. o couplig of the system should be reduced as much as possible i the desig phase, thus esurig that the system has good extesibility. May researches about system couplig have bee doe i the past years. Ad the most represetative oe of them is the KobrA method. KobrA method is developed i KobrA project fuded by the Germa Federal Miistry of Educatio ad Research (BMBF). The method raises a set of guidig priciples for how to quatify the system couplig, but ot the cocrete methods. Ad most of the other researches just aalyze the couplig of system from a qualitative perspective, but they have ot yet doe ay quatitative aalysis about the system couplig. Therefore, the paper set the problem above as the research backgroud, proposed a quatitative aalysis method based o iformatio etropy to aalyze the couplig of class desig, ad the method is applied to the case. It has realistic value ad sigificace. The iformatio etropy mathematical model I 1948, hao has a scietific defiitio of the iformatio give i his book "Mathematical Theory of Commuicatio". Iformatio is the thig ca elimiate or reduce the ucertaity of thigs to uderstad. O this basis, hao proposed the cocept of iformatio etropy, ad poited out that the amout of iformatio ad iformatio etropy are two opposite amout. Iformatio is egative etropy. We ca use mathematical methods based o statistical to measure the amout of iformatio i quatitative metrics [1]. Assumig that the probability of occurrece of evet A is P(A), hao use Eq. 1 to calculate the amout of iformatio of evet A, called self-iformatio. I( A) = log P( A) (1) All rights reserved. No part of cotets of this paper may be reproduced or trasmitted i ay form or by ay meas without the writte permissio of Tras Tech Publicatios, (# , Pesylvaia tate Uiversity, Uiversity Park, UA-18/09/16,12:37:53)

2 Advaced Materials Research Vol Eq. 1 idicates: 1) the greater probability of occurrece of Evet A, the less iformatio it cotais; 2) the amout of iformatio ca be added. I( AB) = I( A) + I( B) (2) O the basis of Eq. 1, assumig that a radom evet has may possible results. Ad probabilities of occurrece of these results are p 1, p 2,, p. Thus the formula about the average amout of iformatio of the evet is as follow: H p l ogp i i i 1 (3) hao called the result of Eq. 3 iformatio etropy; the uit of it is bit [2]. Quatitative aalysis of class couplig From the perspective of the iformatio, the relatioship betwee classes ca essetially be uderstood as message passig betwee classes. o the couplig of class desig ca be measured by usig the iformatio etropy. I order to esure the validity ad completeess of the method, the research about couplig of class desig should be carried out from the followig aspects: The Directivity of couplig; Types of relatioships betwee classes i object-orieted desig (such as depedecy, iheritace, realizatio); Metrics of the relatioship closeess; Relatioship betwee classes withi the system. (1) The Directivity of couplig. I object-orieted desig, all relatioships are directioal, e.g. associatio (uidirectioal associatio ad bidirectioal associatios), depedecies (oe-way), ad iheritace relatioships (oe-way), implemetatio (oe-way) ad so o. Depedecies, iheritace ad implemetatio are the relatioships most commoly used. Therefore, the Directivity of couplig should be take ito accout whe calculatig the couplig of the class desig. The cocept of the iput couplig ad output couplig eed to be itroduced here. Iput couplig aalyses the etities which play a role as the properties, methods, or the cliet (cosumer) of other etities. Output couplig aalyses the etities which play a role as the properties, methods, or the server (provider) of other etities. Iput couplig is related with the followig exteral attributes [3]: Comprehesibility: I order to uderstad the class, we must kow the service provided by it. Error tedecies: If a exteral service is used icorrectly because of the misuderstadig of the class, it may itroduce errors. Maitaiability: lower uderstadability ad higher error tedecy will lead to lower maitaiability. Output couplig is related with the followig exteral attributes: Dager level:ay errors i the class with a high-output couplig may be passed to other parts of the system. Testability: class with a high output couplig is relatively difficult to be tested. Assumig exist the followig sceario: There are two classes ad the relatioship betwee them is depedecy. o judgig from the above discussio about the iput ad output couplig, because the two classes ifluece each other, the depedecy betwee two classes should be a two-way relatioship. It is differet from the defiitio of depedecies directio i UML.

3 198 Advaced Materials ad Computer ciece II Therefore, i the calculatio of the class couplig, iput couplig ad output couplig of a class should be calculated respectively. iput(i) represets the iput couplig of Class C i, output(i) represets the output couplig of Class C i, the the couplig of classes C i with other classes ca be expressed as follow: i i put ( i ) out put ( i ) (4) (2) The process of differet types of relatioship. I the discussio above, a importat issue, the type of class is igored. I the actual system desig, there are may types of class, such as: abstract class, iterface class etc. Relatioships betwee differet types of classes are o loger the simple depedecy, it may also iclude iheritace (geeralizatio), implemetatio etc. o whe calculatig the couplig of classes the directioality of the couplig eed to be take ito accout. Here takig iheritace ad implemetatio for example. ee by the characteristics of object-orieted programmig, the subclass iherits all the attributes ad operatios of the paret class due to the iheritace relatioship. I aother words, the subclass kows (uderstads) the paret class. ubclass ca use the properties ad methods of the paret class, but the paret class caot use the subclass. o i iheritace relatioship, the paret class does ot have the iput couplig. Just the same as the iheritace relatioship, iterface class does ot have iput couplig. Whe calculatig the couplig betwee classes, iput couplig of the paret class (or iterface class) will ot be calculated. upposig that Class C i is the paret class or iterface class of other classes, the the couplig of class C i with other classes is show below: i out put ( i ) (5) (3)Calculatio formula of class couplig. I order to measure the relatioship betwee the classes, the cocept of iformatio etropy will be itroduced. Uder the premise of ot cosiderig the closeess of relatioships betwee classes (i.e. all depedecies are equivalet), the directioality of the relatioship should be take ito accout at the same time. That meas whe aalyzig the couplig of classes, iput couplig ad output couplig of each class are couted respectively ad based o the above discussio a specific type of relatioship eeds for special treatmet. Accordig to the iformatio etropy that the calculatio formula of the couplig betwee classes is defied as follow: Assumig that a system with may classes C 1,C 2,..,C, if there is a relatioship betwee C i ad C j, the g ij =1, or else g ij =0, R(i ) represets the total amout of the relatioship betwee the class C i ad R( i ) gij Z j 1 other classes,, the total amout of the relatioship of the system is i 1 associative stregth of classes C i i the system is ( i ) R( i ) / Z ( i ) 1, ad i 1. Accordig to iformatio etropy, the couplig betwee classes C i ad class C j is ij. R( i ), The ij 1 1 l og( ) Z Z (6) The couplig betwee the classes C i ad other classes is i. i j 1 i j (7) As ca be see from the above equatio, if the relatioship amog classes is closer i the system, the couplig of system is higher.

4 Advaced Materials Research Vol (4)Itroducig depedecy coefficiets to measure the relatioship closeess. I the above sectio, calculatio formula of class couplig is put forward i the cotext of ot cosiderig the closeess of the relatioship betwee classes. But i the actual object-orieted desig, the closeess of the relatioship betwee classes is differet. This is because the class has two basic characteristics--- attributes ad operates, so the relatioship betwee classes ca be cosidered as the exteral performace of the two basic properties. The depedecy betwee classes is caused by the iterdepedece betwee attribute ad operatio of classes. o the depedecy ca be divided ito two types--- data depedecy ad method depedecy. Depedecy caused by attribute called data depedecy, deoted as RDD; depedecy is caused by the operatio kow as the method depedecy, referred as the RMD [4, 5]. This paper itroduces the cocept of depedecy coefficiet to quatify the stregth of the iterdepedece betwee two classes; the quatizatio method is show as below: Assumig that i a system, class C i depeds o the class C j, the data depedecy betwee class C i ad class C j deoted as C i RDD C j, the method depedecy betwee class C i ad class C j deoted as C i RMD C j, Cout(C i RDD C j ) represets the umber of attributes of C j which called by C i, Cout(C i RDD C j ) represets the umber of methods of C j which Called by C i, R ij deotes as the depedecy coefficiet betwee classes C i ad C j. R Cout ( C R C ) Cout ( C R C ) i j i DD j i MD j R ij represets the closeess of the relatioship betwee classes. The greater R ij is, the higher the closeess of the relatioship is, o the cotrary the smaller R ij is, the lower the closeess of the relatioship is. Assumig that there are three classes A, B, C, the relatioships of three classes are show below: (8) Class A +IvokeOperatioB1() : void +IvokeOperatioC() : void +IvokeAttributeB1() : void Class B -AttributeB1 : it +OperatioB1() : void +OperatioB2() : strig Class C +OperatioC() : strig Fig. 1 Examples of depedecy Class A deped o class B ad class C, class A calls the attribute Attribute1 ad method OperatioB2 of class B, class A also calls the method OperatioC of class C. O the basis of Eq. 8, the depedecy coefficiet of class A ad class B i Fig. 1 ca be calculated, ad the do the same operatio o the class A ad class C, it ca be fouded that: Depedecy coefficiet of class A ad class B: R AB =2 Depedecy coefficiet of class A ad class C: R Ac =1 o the relatioship betwee class A ad class B is closer, the relatioship betwee the class A ad class C is i the secod place. Now, the Eq. 6 ca be modified by itroducig the depedecy coefficiets, the ew computatioal formula of class desig couplig is show as follow: 1 1 l og( ) R i j i j Z Z (9) The couplig of whole system ca be calculated by usig the computatioal formula show below: i If the value of is greater, the couplig of the system is higher. Coversely, if is smaller, the couplig of the system is lower. i 1 (10)

5 200 Advaced Materials ad Computer ciece II Case tudies I actual software developmet, so as to achieve the purpose of reducig the couplig of system, class desig of the system is ofte based o certai desig patter. imple factory patter is oe of the most commoly used desig patters. It is usually used for object creatio operatio. Here takig the class desig before ad after the applicatio of a simple factory patter as the example to measure ad compare the couplig of a system. Assumig that there is a task to desig ad implemet a simple calculator which ca do the operatio, such as additio, subtractio, multiplicatio ad divisio of two itegers. Fig. 2 (A) shows the class desig without ay desig patter. Fig. 2 (B) shows the class desig which is based o the simple factory patter. Oly from the perspective of complexity, the class desig which uses the simple factory patter is seemigly more complex ad has a higher couplig. Now, the Eq. 10 is used to distiguish which class desig has the lower couplig. Factory +CreateObj() : Operatio Operatio ub ub (A) (B) Fig. 2 The compariso of class desig I Fig. 2 (A), the couplig of class diagram without ay desig patter is show as follow: 2 9l og (11) I Fig. 2 (B), the couplig of class diagram usig sample factory patter is show as follow: ' l og (12) The result is <. o it ca be see from the results that the couplig of the class desig which uses the simple factory patter is sigificat reduced. Next, i order to observer the chage of couplig after fuctio expasio, the requiremet eeds to make some adjustmets. The modulus operatios will be added o the basis of the existig fuctio. The class diagrams after adjustmet are show as Fig. 3. Factory +CreateObj() : Operatio Operatio ub Mod ub Mod (A) (B) Fig. 3 The compariso of class desig (after expasio)

6 Advaced Materials Research Vol I Fig. 3 (A), the couplig of class desig without ay desig patter is show as follow: ex 10 3l og (13) I Fig. 3 (B), the couplig of class desig usig sample factory patter is show as follow: 2. 6l og ' 9 ex (14) It ca be see from the above results, ex < ex. That meas whe carryig out the same fuctio expasio to both class desigs, the class desig usig the simple factory patter still has a lower couplig. Now let us compare the couplig icremet of two class desigs before ad after expasio. Fig. 3 (A) compared to Fig. 2 (A), the icremet of the couplig is show as follow: add ex 0. 3 (15) Fig. 3 (B) compared to Fig. 2 (B), the icremet of couplig is show as follow: ' ' ' add ex (16) It is sigificat that add < add. By comparig the result, it is easy to get the coclusio that whe carryig out the same expasio, class desig which uses the simple factory patter has less couplig icesemet tha the oe without ay desig patter used. It idicates that by usig the sample factory patter, the class desig has a obvious superiority i expasibility. Coclusio I the object-orieted software desig, the couplig of class desig ca reflect the pros ad cos of the class desig o some level. O the basis of iformatio etropy, this paper proposes a method of quatitative aalysis which is used to aalyze ad evaluate the class desig. I additio, this paper validates the feasibility of the method by the case studies. The research fidigs show that, I the case of achievig the same fuctio, if a desiger ca correctly apply a desig patter whe desigig class, it ca effectively reduce couplig amog classes, ad make the desig have good extesibility. Ackowledgemets This work is fuded by the Ope Foudatio of Key Laboratory of oftware Egieerig of Yua Provice uder Grat No. 2011E11, ad ciece ad egieerig uiversity-level research projects of Yua Uiversity uder Grat No. 2010YB048. Referece [1] u Dogchua, Li Fuyog, Itroductio to ystems Egieerig, Tsighua Uiversity Press, Beijig, [2] Zhag Yi, Zhou Hua, Dua Qig, Liao Yu, Liu Huhui, He Zheli, Quatitative aalysis of system couplig, Proceedigs th Iteratioal Coferece o Fuzzy ystems ad kowledge Discovery. (2011) [3] Coli Atkiso, Compoet-based product lie egieerig with UML, iso-wesley, [4] Ou Yag, Hu hure, Wag Zhihua, Measuremet Research of Depedecy Relatios amog Class Based o Object-Orieted ystem, Computer ciece. 31 (2004) [5] Yu Yog, Tag Jia hua, Li Wehog, Li Tog, Approach to measuremet of class cohesio based o structure etropy, ystems Egieerig ad Electroics. 31 (2000)