Multidimensional Fuzzy Association Rules for Developing Decision Support System at Petra Christian University

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1 Multidimensional Fuzzy ssociation Rules fo eveloping ecision Suppot System at Peta histian Univesity Yulia 1, Siget Wibisono 2, Rolly Intan 1 1,2 Peta histian Univesity, Suabaya, Indonesia 1 {yulia, intan}@peta.ac.id, 2 m @ohn.peta.ac.id bstact. cademic ecods of student candidates and students of Peta histian Univesity (PU) which have been stoed so fa have not been used to geneate infomation. PU s top-level management needs a way to geneate infomation fom the ecods. The geneated infomation is expected to suppot the decision-making pocess of top-level management. efoe stating the application development, analysis and design of the student academic ecods and the needs of top-level management ae done. The design stage poduces a numbe of modeling that will be used to ceate the application. The final esult of the development is an application that can geneate infomation using multidimensional fuzzy association ules. Keywods. pplication, ata Mining, ecision Suppot System, Multidimensional Fuzzy ssociation Rules 1 Intoduction uing this time, PU has stoed academic ecods of student candidates who enoll in PU, such as math and english gades at thei schools. In addition, afte enteing the univesity, PU will save GP of all students. cademic ecods of student candidates and students that have been kept, have not been used to poduce valuable infomation. PU s top-level management needs a way to geneate infomation fom the ecods. The geneated infomation is expected to suppot the decision-making pocess of top-level management. With academic ecods of student candidates and students, infomation can be geneated in the fom of elationship between students data using multidimensional fuzzy association ules. The students data that can be used ae schools, math, and english gade in thei schools, specialization (science, social, liteatue, etc.), GP, faculty, maos, gende, eligion, and batch. Theefoe, PU need a softwae that can geneate infomation needed by top-level management elated to academic ecods of student candidates and students. 2 ata Mining ata mining is one of the most impotant steps of the knowledge discovey in databases pocess. It is consideed as significant subfield in knowledge management. Reseach in data mining continues gowing in business and in leaning oganization

2 ove coming decades[8]. ata mining is a pocess of extaction of useful infomation and pattens fom huge data. It is also known as knowledge discovey pocess, knowledge mining fom data, knowledge extaction o data /patten analysis[9]. The development of Infomation Technology has geneated geat amount of databases and huge data in vaious aeas. The eseach in databases and infomation technology has esulted in appoach to stoe and manipulate this pecious data fo futhe decision making. The impotant eason that attacted many attentions in infomation technology and the discovey of meaningful infomation fom lage collections of data industy towads field of ata mining is due to the peception of we ae data ich but infomation poo. Thee is huge volume of data but we hadly able to geneate them in to meaningful infomation and knowledge fo decision making pocess in business[10]. ata mining deives its name fom the similaities between finding valuable business infomation in a lage database fo example, finding linked poducts in gigabytes of stoe scanne data and mining a mountain fo valuable oe. oth pocesses equie eithe sifting though a geat amount of mateial, and intelligently pobing it to find exactly whee the value esides. Given databases of sufficient size and quality, data mining technology can geneate new business advantages and oppotunities[10]. 3 Multidimensional ssociation Rules ssociation ule finds inteesting association o coelation elationship among a lage data set of items [1,2]. The discovey of inteesting association ules can suppot decision making pocess. Multidimensional association ules ae association ules that involve two o moe dimensions o pedicates. onceptually, a multidimensional association ule, consists of and as two datasets, called pemise and conclusion, espectively. Fomally, is a dataset consisting of seveal distinct data, whee each data value in is taken fom a distinct domain attibute in as given by { a a, fo some N n}, whee, fom. Similaly, whee, is a set of domain attibutes in which all data values of come b b, fo some N }, { n is a set of domain attibutes in which all data values of come fom. Fo example, database of medical tack ecod patients is analyzed fo finding association (coelation) among diseases taken fom the data of complicated seveal diseases suffeed by patients in a cetain time. dditional elated infomation egading the identity of patients, such as age, occupation, sex, addess, blood type,

3 etc., may have a coelation to the illness of patients. onsideing each data attibute as a pedicate, it can theefoe be inteesting to mine association ules containing multiple pedicates, such as: Rule-1: ge ( X,"60") Smk( X,"yes") is( X,"Lung ance"), whee thee ae thee pedicates, namely ge, Smk (smoking) and is (disease). ssociation ules that involve two o moe dimensions o pedicates can be efeed to as multidimensional association ules. Fom Rule-1, it can be found that ={60, yes}, ={Lung ance}, ={age, smoking} and ={disease}. onsideing is an intedimension association ule, it can be poved that, and. Suppot of is then defined by: supp( ) { ti di a, a } (1) whee is the numbe of ecods o tuples (see Table 1, =12). ltenatively, in (1) may be changed to Q( ) by assuming that ecods o tuples, involved in the pocess of mining association ules ae ecods in which data values of a cetain set of domain attibutes,, ae not null data. Hence, (1) can be also defined by: { ti di a, a } supp( ) (2) ) whee Q( ), simply called qualified data of, is defined as a set of ecod numbes (t i ) in which all data values of domain attibutes in ae not null data. Fomally, Q( ) is defined as follows. Similaly, Similaly, suppot( ) is given by Q ) { t d null, } (3) ( i i { ti di b, b } supp( ) (4) ) supp( ) supp( ) { t i d i c, c ) } (5)

4 whee Q ) { t d null, } conf( ) as a ( i i measue of cetainty to assess the validity of conf( ) { t i { t d i i d i c, a is calculated by, c a } } and in the pevious discussion ae datasets in which each element of and is an atomic cisp value. To povide a genealized multidimensional association ules, instead of an atomic cisp value, we may conside each element of the datasets to be a dataset of a cetain domain attibute. Hence, and ae sets of set of data values o sets of datasets. Fo example, the ule may be epesented by Rule-2: age( X," " ) smoking( X,"yes") disease( X,"bonchitis, lung cance"), whee ={{20 60}, {yes}} and ={{bonchitis, lung cance}}. Simply, let be a genealized dataset. Fomally, is given by, fo some N }. { n oesponding to (2), suppot of is then defined by: Simila to (5), { ti di, } supp( ) (7) ) (6) supp( ) supp( ) { t i d i, ) } (8) Finally, conf( ) is defined by conf( ) { t i d { t i i d i,, } } (9) To povide a moe meaningful association ule, it is necessay to utilize fuzzy sets ove a given database attibute called fuzzy association ule as discussed in [4,5]. Fomally, given a cisp domain, any abitay fuzzy set (say, fuzzy set ) is defined by a membeship function of the fom [2,3]: : [0,1]. (10) To povide a moe genealized multidimensional association ules, we may conside and as sets of fuzzy labels[6]. Simply, and ae called fuzzy datasets.

5 Rule-2 is an example of such ules, whee ={young, yes} and ={bonchitis}. Hee young, yes and bonchitis ae consideed as fuzzy lables. fuzzy dataset is a set of fuzzy lables/ data consisting of seveal distinct fuzzy labels, whee each fuzzy label is epesented by a fuzzy set on a cetain domain attibute. Let be a fuzzy dataset. Fomally, is given by F( ), fo some N }, { n whee F( ) is a fuzzy powe set of, o in othe wods, is a fuzzy set on. oesponding to (7), suppot of is then defined by: inf { ( di )} i 1 supp( ) ) (11) Simila to (5), supp( ) supp( ) i 1 inf { ( d i ) )} (12) conf( ) is defined by inf { ( di )} i 1 conf ( ) (13) inf { ( d )} i 1 The coelation betwen two fuzzy datasets can be defined by the following definition. i 1 i inf { ( di )} i 1 co ( ) (14) inf { ( d )} inf { ( d )} k i k ik 4 Reseach Methodology 4.1 Poblems nalysis Thee ae seveal poblems faced by PU, such as:

6 1. PU s top-level management takes decisions fo the pomotion o coopeation pupose based solely on estimates and habits, has not taken advantage of the existing academic ecods. 2. PU s Faculties/Maos Pomotion Team has not equipped with infomation o facts about the academic condition of PU s students while pomoting faculties/maos to high schools. 3. Thee is no featue in the cuent academic infomation system that can show the elationship between students data. 4.2 Requiements nalysis Fom the poblems listed above, it can be concluded that the PU s top-level management equies a compute-based system to assist in geneating PU s students academic ecods, that is a data mining-based infomation systems that can poduce association ules of students attibutes. This system obtains data fom the ETL pocess and has a multidimensional concept that shows the elationships between students attibutes. The dimensions used ae schools, math and english gade in thei schools, specialization (science, social, liteatue, etc.), GP, faculty, maos, gende, eligion, and batch. 4.3 Extact, Tansfom, and Load Extact, Tansfom, and Load (ETL) is a function that integates data and involves extacting data fom souces, tansfoming it to be moe valid, and loading it into a data waehouse[7]. This pocess begins by impoting the data fom the database. The impoted data is eligions, maos, schools, specializations, student candidates, students, and student admissions. Next, the impoted data is tansfomed into moe valid data and loaded into data waehouse. 4.4 etemination of Fuzzy Values etemination of fuzzy values is done by establishing a goup fuzzy set. Fist, use must input the name and choose the attibute, such as eligions, maos, schools, GP, math gade, etc. Next, use can make as many fuzzy sets as he/she wants inside the goup fuzzy set made. Use need to fill the name and the desciption of the fuzzy set. Thee ae two types of fuzzy set based on the attibute of the goup fuzzy set, numeical and non-numeical. Fo numeical, use can input as many points as he/she wants to fom fuzzy membeship function. point includes cisp value and the membeship degee of the cisp value to the fuzzy set. Fo non-numeical, use must input membeship degee fo evey membes of the attibute. Flowchat fo detemination of fuzzy values can be seen on Figue 1.

7 Goup Fuzzy Set Establishment Input Goup Fuzzy Set Name hoose ttibute Input cisp value tue Input Membeship egee Save Goup Fuzzy Set in database false dd point? Save Fuzzy Set in database tue dd Fuzzy Set? tue Input Fuzzy Set Name Fuzzy Set with numeic attibute? false Input Membeship egee fo evey membes of the attibute false RETURN Fig. 1. Flowchat fo etemination of Fuzzy Values 4.5 ustomization of Fuzzy ssociation Rules ustomization of fuzzy association ules is done to geneate fuzzy association ules epot to suppot the decision-making pocess of top-level management. Fist, use must input the name and choose the attibutes that will be used to geneate the ules. fte choosing the attibutes, use must choose the goup fuzzy set(s) of the attibutes. Next, the application will geneate the ules and save them in database. The use can see the whole epot and filte the ules based on the suppot, confidence, and coelation value of the ules. Flowchat fo customization of fuzzy association ules can be seen on Figue 2. Geneate Fuzzy ssociation Rules epot Input name of the epot Input filte fo student ecods dd attibute? tue hoose ttibute hoose Goup Fuzzy Set of the attibute chosen false Geneate and save Fuzzy ssociation Rules in database Show the whole epot Filte? false RETURN tue Show the filteed epot Input filte Fig. 2. Flowchat fo Fuzzy ssociation Rules

8 5 Results test is conducted to pove the accuacy of the developed application to calculate suppot, confidence, and coelation of the multidimensional fuzzy association ules geneated. The test is stated fom a given simple academic ecods of students with thee attibutes, such as mao, math gade, Gade Point veage (GP) as shown in Table 1. Table 1. cademic Recods of Students Student Mao Math gade GP 1 English Liteatue ivil Engineeing ivil Engineeing Inteio esign Inteio esign usiness Management usiness Management usiness Management Infomatics Engineeing Infomatics Engineeing Science ommunication Science ommunication The test is conducted using thee attibutes, such as mao, math gade, and GP. Fist, we must detemine how to convet each cisp value into fuzzy value fo evey attibutes. Mao is a non-numeical attibute, so we must detemine the fuzzy value fo each mao. Fo example, we make a goup fuzzy set fo mao named 2014 which has a fuzzy set named Engineeing. Inside this fuzzy set, we detemine business management has a membeship degee of 0.2, civil engineeing has a membeship degee of 1, and so on as shown on Figue 3. Fig. 3. Input fo Mao Fuzzy Values

9 Math gade is a numeical attibute, so that the fuzzy value of math gade will be calculated though a fuzzy membeship function which is fomed fom the points stoed in the fuzzy set. Fo example, we make a goup fuzzy set fo math gade named 2014 which has a fuzzy set named High. Inside this fuzzy set, we detemine math gade of 0 has a membeship degee of 0, math gade of 75 has a membeship degee of 0, math gade of 95 has a membeship degee of 1, and math gade of 100 has a membeship degee of 1 as shown on Figue 4. Fig. 4. Input fo Math Gade Fuzzy Membeship Function These fou points will fom fuzzy membeship function as shown on Figue 5. Fig. 5. Visualization of Math Gade Fuzzy Membeship Function Fo example, if a student has math gade of 90, then the application will look fo its membeship degee though the equation of the line that fomed the point (75, 0) and (95, 1), as given by y = { x 0.05x , fo 75 x 95}. Thus, membeship degee of 90 is 0.05 * = GP is a numeical attibute like the math gade, so that the fuzzy value of GP will also be calculated though a fuzzy membeship function. Fo example, we make a goup fuzzy set fo GP named 2014 which has a fuzzy set named High. Inside this fuzzy set, we detemine points, such as (0, 0), (3.2, 0), (3.4, 0.6), (3.7, 1), and (4, 1) as shown on Figue 6. Fig. 6. Input fo GP Fuzzy Membeship Function

10 This example of engineeing fuzzy set fo mao attibute, high math gade fuzzy membeship function, and high GP fuzzy membeship function ae detemined by inteviewing one of PU s stuctual offices. Next, we choose the attibutes that ae used duing this test and each attibute s goup fuzzy set that we ust made befoe as shown on Figue 7. Fig. 7. Input ttibutes fo Fuzzy ssociation Rules This test will geneate all combinations of fuzzy association ules using evey fuzzy sets of the attibutes chosen. Fo example, one of the ules may be epesented by: Rule-3: Mao(X, Engineeing ) Math(X, high ) GP(X, high ) Rule-3 is a fuzzy ule, whee ={Engineeing, high} and ={high}. Next, each academic ecods of students shown in Table 1 will be conveted using the fuzzy sets to fuzzy values as shown in Table 2.

11 Table 2. alculation of Fuzzy Values α β ɣ X Y X*Y Z Note: α = µ engineeing (mao) β = µ high (math) ɣ = µ high (GP) X = min(α,β) Y = min(ɣ) Z = min(α,β,ɣ) Σ Theefoe, suppot of Rule-3 can be calculated by (12), supp(rule-3) = 2.45 / 12 = On the othe hand, confidence of Rule-3 can be calculated by (13), conf(rule-3) = 2.45 / 2.7 = On the othe hand, coelation of Rule-3 can be calculated by (14), co(rule-3) = 2.45 / = The manually calculated suppot, confidence, and coelation of Rule-3 ae match with the output of the fuzzy association ules geneated by this test as shown on Figue 8. Fig. 8. Example Output of Fuzzy ssociation Rules To evaluate this application, eseach on the use of this application is conducted. Samples of this eseach is five stuctual offices of PU. To collect the data, distibuted a questionnaie containing indicatos to evaluate the use of the application. The indicatos include display of application, detemination of fuzzy values, customization of fuzzy association ules, ease of use, the ability to addess the needs of uses, and oveall. Fom the data collected, the calculation of the pecentage of use satisfaction in using this application is done. ssessment of the feasibility of the application:

12 1. isplay of application is 100% good 2. etemination of fuzzy values is 80% good 3. ustomization of fuzzy association ules is 80% good 4. Ease of use is 100% good 5. The ability to addess the needs of uses is 60% good 6. Oveall is 100% good 6 onclusion The geneated fuzzy association ules have been tested and matched with the Multidimensional Fuzzy ssociation Rules algoithm and the eality of academic situation of PU s students. Fom the assessment, obtained that oveall application is 100% good. This suggests that the application developed has benefits fo PU and can be continued fo the pupose of decision-making pocess by top-level management. Refeences 1. Han, J., Kambe, M., Pei, J.: ata mining: oncepts and Techniques (3 d ed.). Mogan Kaufmann, San Fansisco (2012) 2. Kli, G. J., Yuan,.: Fuzzy Sets and Fuzzy Logic: Theoy and pplications. Pentice Hall, New Jesey (1995) 3. Zadeh, L..: Fuzzy Sets and Systems. In: Intenational Jounal of Geneal Systems, Vol. 17, pp (1990) 4. Intan, R.: Poposal of Fuzzy Multidimensional ssociation Rules, Junal Infomatika Vol. 7 No. 2 (2006) 5. Intan, R.: Poposal of an lgoithm fo Geneating Fuzzy ssociation Rule Mining in Maket asket nalysis. In: Poceeding of IRS (IEEE). Singapoe (2005) 6. Intan, R.: Hybid-Multidimensional Fuzzy ssociation Rules fom a Nomalized atabase. In: Poceedings of Intenational onfeence on onvegence and Hybid Infomation Technology. IEEE ompute Society, aeeon, Koea (2008) 7. Gou, V., Saangdevot, S. S., Tanwa, G. S., Shama,.: Impove Pefomance of Extact, Tansfom and Load (ETL) in ata Waehouse. In: Intenational Jounal on ompute Science and Engineeing, 2(3), (2010) 8. Silwattananusan, T., Tuamsuk, K.: ata Mining and Its pplications fo Knowledge Management: Liteatue Review fom 2007 to In: Intenational Jounal of ata Mining & Knowledge Management Pocess (IJKP), 2(5), (2012) 9. Ramagei,. M.: ata Mining Techniques and pplications. In: Indian Jounal of ompute Science and Engineeing, 1(4), (2010) 10. Padhy, N., Misha, P., Panigahi R.: The Suvey of ata Mining pplications and Featue Scope. In: Intenational Jounal of ompute Science, Engineeing and Infomation Technology (IJSEIT), 2(3), (2012)