A quantitative definition of engineering professional profiles

Transcription

1 Igeiería e Ivestigació vol. 35.º 2, august (89-95) DOI: ABSTRACT A quatitative defiitio of egieerig professioal profiles Defiició cuatitativa de perfiles profesioales e igeiería M. C. Barrera 1, O. G. Duarte 2, C. Sarmieto 3, ad R. A. Soto 4 A professioal profile is a set of kowledge ad skills. I this paper we propose a methodology to defie professioal profiles givig a quatitative assessmet of skills ad kowledge associated with a egieerig curriculum. This approach ca be used to evaluate the curriculum flexibility, i.e., if the curriculum offers the studets diverse ad flexible approaches ad routes to learig. We describe a mathematical model that allows us to calculate the compliace level accomplished by a studet with regard to oe or more differet profiles. Our proposal has bee applied i the Udergraduate Program of Electrical Egieerig from Uiversidad Nacioal de Colombia Keywords: Profile, professioal profile, idividual profile, ideal profile, electrical egieerig, curriculum, kowledge, skills, fuzzy implicatios, aggregatio operators. RESUMEN U perfil profesioal es u cojuto de coocimietos y habilidades. E el presete artículo se propoe ua metodología para defiir perfiles profesioales basada e ua evaluació cualitativa de habilidades y coocimietos asociados co u pla de estudios de igeiería. Esta metodología puede ser usada para evaluar la flexibilidad curricular, es decir, si el pla de estudios ofrece a los estudiates efoques y rutas de apredizaje que sea diversos y flexibles. Aquí se describe u modelo matemático que permite calcular el grado de satisfacció logrado por u estudiate co respecto a uo o varios perfiles. Esta propuesta ha sido aplicada e el programa de pregrado de Igeiería Eléctrica de la Uiversidad Nacioal de Colombia. Palabras clave: Perfil, perfil profesioal, perfil ideal, perfil idividual, igeiería eléctrica, pla de estudios, coocimietos, habilidades, implicacioes difusas, operadores de agregació. Received: October 17th 2014 Accepted: Jue 16th 2015 Itroductio A professioal profile is a set of skills ad kowledge that a professioal (i.e. a egieer) has or should have. For egieerig programs, it is difficult to defie such professioal profiles due to the iheret flexibility of those programs. Sice we require flexibility i the curricula, the questio is: how this flexibility affects the professioal profile of the studets? There is o specific methodology to defie professioal profiles i educatioal istitutios ad orgaizatios. Usually, professioal profile defiitios try to satisfy curret eeds ad expectatios from the academy, orgaizatios ad society. Educatioal istitutios propose professioal profiles accordig to what idustry, orgaizatios ad society expect from ew professioals. The way that professioal profiles are curretly established ivolves commo features (educatioal outcomes) that give us the basis to get to kow the pricipal elemets of a profile. These features ca be classified i two major groups: skills ad kowledge. I other words, a profile ca be visualized as a set of skills ad kowledge. We have developed a methodology to evaluate professioal profiles i the cotext of a egieerig curriculum. We cosider this methodology as a potetial tool i educatioal istitutios sice it allows us to kow if the curriculum fulfills the curret expectatios of the ew professioals traiig. 1 Marla Costaza Barrera Botero. Systems Egieer, Uiversidad Distrital Fracisco José de Caldas, Bogotá. Master i Systems ad Computer Egieerig studet, Uiversidad Nacioal de Colombia, Colombia. mcbarrerab@ual.edu.co 2 Oscar Germá Duarte Velasco. Electrical Egieerig, Uiversidad Nacioal de Colombia, Colombia. Master i Idustrial Automatio, Uiversidad Nacioal de Colombia, Colombia. Ph D. i iformatics, Uiversidad de Graada, España. Affiliatio: Associated professor, Uiversidad Nacioal de Colombia, Colombia. ogduartev@ual.edu.co 3 Carolia Sarmieto Gozález. Systems Egieerig, Uiversidad de Sa Bueavetura, Colombia. Master i Systems ad Computer Egieerig, Uiversidad Nacioal de Colombia, Colombia. Affiliatio: Ph D. i Systems ad Computer Egieerig studet, Uiversidad Nacioal de Colombia, Colombia. csarmietog@ual.edu.co 4 Reé Alexader Soto Pérez. Electrical Egieerig, Uiversidad Nacioal de Colombia, Colombia. Master i Idustrial Automatio, Uiversidad Nacioal de Colombia, Colombia. Affiliatio: Associated professor, Uiversidad Nacioal de Colombia, Colombia. rasotop@ual.edu.co How to cite: Barrera, M. C., Duarte, O. G., Sarmieto, C., & Soto, R. A. (2015). A quatitative defiitio of egieerig professioal profiles. Igeiería e Ivestigació, 35(2), DOI: 89

2 A quatitative defiitio of egieerig professioal profiles I the sectio titled Professioal Profiles, the defiitio of professioal profile is give ad two importat cocepts derived from this are suggested. Our proposed mathematical model is illustrated i the sectio titled Mathematical Model. Our model was built usig techiques take from computatioal itelligece to propose a quatitative assessmet of profiles. The effects of varyig values of fuzzy implicatios ad aggregator operators o the profiles are preseted i the results. Our methodology was applied at the Udergraduate Program of Electrical Egieerig from Uiversidad Nacioal de Colombia. A team of domai ad huma resources experts has helped us to build, test ad evaluate the model. The applicatio process is show i the sectio titled Applicatio. Fially, we preset coclusios ad future work regardig this project. Professioal Profiles Despite professioal profiles arise from curret eeds from the academy, orgaizatios ad society, there is o specific methodology that defies or determies them. Eve though each of these has their ow defiitio of professioal profiles, the techiques used by each oe have commo objectives: to satisfy the curret ad future eeds from society ad orgaizatios; to develop persoal ad commuicatio skills, besides the kowledge ad skills withi specific domai ad to reiforce leadership ad teamwork abilities (Crosthwaite, 2006; Hor, 2003; Alles, 2009). There is o formal defiitio of professioal profile that is uiversally accepted. However, the explicit defiitio is: Previous image of features, kowledge, skills, values ad feeligs that should have bee developed for a studet i her/his traiig process (Herádez, 2004). Accordig to the above defiitio, a professioal profile is maily based o the kowledge ad skills expected by academy, society ad orgaizatios. For this reaso, i our project we have defied that: Defiitio 1. Professioal profile: the set of skills ad kowledge that a professioal (i.e., a egieer) has or should have. Idividual ad Ideal Profiles We use the word or i the previous defiitio i order to iclude two differet cocepts that have bee adopted i this project: ideal profile, a professioal profile expected; ad idividual profile, a professioal profile acquired. Formally, we propose the followig defiitios: Defiitio 2. Ideal profile: the set of skills ad kowledge that a studet must achieve accordig to his/her expected future professioal role. These expectatios are defied by educatioal istitutios, idustry, orgaizatios ad society, ad they are based o curret requiremets of each sector. Defiitio 3. Idividual profile: the actual set of skills ad kowledge acquired ad/or developed by a studet durig the professioal traiig process. Defiitio 4. Compliace Level: itis the measure that determies to what exted a idividual profile satisfies oe or more ideal profiles. It is a quatitative assessmet of skills ad kowledge associated to a curriculum. The sectio Mathematical Model describes the model that we have developed to quatify this measure. Kowledge Sources for Profile Obtaiig Accordig with the first defiitio, a professioal profile is composed by a set of skills ad a set of kowledge. We eed to relate each elemet from these sets with the curriculum, for this reaso, three sources of kowledge have bee the basis to build the sets of kowledge ad skills ad geerate the frame to get both, idividual ad ideal profiles. The three sources of kowledge are: 1. The Coceive, Desig, Implemet ad Operate (CDIO) Syllabus, 2. Techical kowledge i Electrical Egieerig, ad 3. Electrical Egieerig curriculum of Uiversidad Nacioal de Colombia. CDIO CDIO is a iitiative from the Massachusetts Istitute of Techology (MIT) ad other uiversities, whose goal is to itegrate techical kowledge with some expected characteristics that a studet should possess whe he or she graduates from uiversity. These features are based o eeds from academy, idustry ad society. They allow egieers to work i real egieerig teams to produce real products ad systems (Crawley, 2001). The CDIO iitiative has created a ew cocept for udergraduate educatio based i the skills eeded by the cotemporary egieers ad the appliace of a egieerig problem solvig paradigm. I this, two major tasks are ivolved: developig ad codifyig a comprehesive uderstadig of the skills eeded by the cotemporary egieer ad developig ew approaches to eable ad ehace the learig of these skills. A first outcome from this iitiative was the CDIO Syllabus, a compedium of cotemporary egieerig kowledge, skills ad attitudes that alumi, idustry ad academia desire i a future geeratio of youg egieers. It cosists of a template ad a associate process, which ca be used to capture the opiios of idustry, alumi ad faculty, ad customize the Syllabus to a set of learig objectives appropriate for ay specific udergraduate egieerig program (Crawley, 2002). The Departmet of Electrical ad Electroic Egieerig from Uiversidad Nacioal de Colombia has adopted the CDIO methodology i their curricula sice 2008, obtaiig two outcomes: The CDIO Syllabus of the Electrical Egieerig Curriculum (Departameto, 2008), a set of 704 skills orgaized i four levels as suggested i the CDIO methodology. The selectio of 11 major learig objectives, each oe associated to oe or more evaluatio criteria for 90 Igeiería e Ivestigació vol. 35.º 2, august (89-95)

3 BARRERA, DUARTE, SARMIENTO, AND SOTO egieerig programs accordig to ABET (Accreditatio Board of Egieerig ad Techology). Curriculum Resolutio 181 of 2009 presets a complete structure of Electrical Egieerig curriculum. I this structure, the curriculum is divided ito three compoets, which are: Fudametal compoet, Discipliary Traiig or Professioal compoet ad Free Choice compoet, each compoet is divided i groups ad each group has oe or several courses (Cosejo, 2009). A summary about structure of Electrical Egieerig curriculum give i Resolutio 181 of 2009 is preseted i the Table 1. Techical Kowledge I the techical kowledge source was takig ito accout oly the Discipliary Traiig or Professioal compoet, sice this compoet cotais the groups ad courses that specify the traiig of the future Electrical Egieers. Table 1. Electrical Egieerig Structure Compoet # of Groups # of Courses # of Credits Fudametal Discipliary Traiig or Professioal Free Choice Total I this cotext, the techical kowledge was acquired through cosults i bibliographic sources ad electrical egieerig domai experts. Represetatio of these three kowledge sources has bee realized through otologies, due that a otology is a way to formally represet ay kid of kowledge. (Sarmieto, 2010) describes the geeral structure i order to represet a curriculum through otologies ad (Soto, 2012, Ghisays, 2013) explai the represetatio of a part of techical kowledge where the courses were orgaized ito thematic cotets. These, i tur, divide each course by topics orgaized i differet levels. Mathematical Model I the followig sectios, we describe our proposal of model i order to represet a professioal profile ad to calculate compliace levels. We use fuzzy implicatios ad aggregatio operators such as OWA, to fid a level of compliace of a idividual profile i regard to ideal profiles. Profile Structure I the sectio Professioal Profiles, we have defied that a profile is composed of a set of skills ad a set of kowledge. Sice these skills ad kowledge ca be ested, they ca be represeted by a tree. The depth ad umber of ode maybe differet for each tree. Defiitio 1. Let S a set of ested Skills. S = { s1, s2, s3,, s } S Is the set of all odes of tree show i Figure 1. Figure 1. Skills Tree Structure. Defiitio 2. Let K a set of ested Kowledge. K = { k1, k2, k3,, k m } The structure of set K is a tree ad it is same at the structure of set S (see Figure 1). Accordig with profile defiitio ad structure from skills ad kowledge trees, we ca represet a profile as a tree where the mai odes are skills ad kowledge. Defiitio 3. There is a fuctio that assigs a umeric value to each elemet of the skills ad kowledge trees called Competece Fuctio. µ ( h ): S [ 01, ]; σ ( c ): K [ 01, ] i i i i Fuzzy Implicatios I order to fid the compliace level, it is ecessary to establish a kid of relatioship betwee a idividual profile ad a ideal profile. Suppose that a value µ i has bee assiged to a skill i a ideal profile ad a studet e, i.e. a idividual profile, has obtaied a value µ i i the same skill, the questio is, how is it possible to determie the compliace level betwee the value obtaied by the studet ad the value established i the ideal profile? For this, we propose to fid this compliace level through fuzzy implicatios. Whe applyig fuzzy implicatios we ca obtai the grade of membership of a set i regard to aother set; i our case, the grade of membership of a idividual profile with respect to a idividual profile. We assimilate those grades as truth-values that are i the iterval [0,1]. Relatioships are represeted through rules if the ; thus, truth values ca be calculated with some T-orms or S-orms, as these kid of relatioships ca be represeted i terms of or, respectively (Driakov, et al., 1993). I this work, we use some fuzzy implicatios i order to fid the values of the compliace level of a commo ode from both trees, idividual ad ideal profile. These trees must have the same structure (i.e. same umber of odes ad depth). This process is made from leaf odes to sigle Igeiería e Ivestigació vol. 35.º 2, august (89-95) 91

4 A quatitative defiitio of egieerig professioal profiles root ode, obtaiig a ew tree called Compliace Level Tree, as show i Figure 2. Figure 2. Relatioship betwee Tree Profiles. Aggregatio Operators. The aggregatio problem cosists i aggregatig tuples of objects, all belogig to a give set, ito a sigle object of the same set. A aggregatio operator is a fuctio, which assigs a sigle umber y to ay tuple of umbers (x 1, x 2,... x, such that: y = Aggreg ( x1, x2,, x ) Defiitio 4. A aggregatio operator is a fuctio, That satisfies: Aggreg : [ 01, ] [ 01, ] N Idetity: Aggreg(x) = x Boudary coditios: Aggreg(0,...,0) = 0 ad Aggreg(1,...,1) = 1 Mootoicity: Aggreg ( x1, x2,, x) Aggreg ( y1, y2,, y), ( x1, x2,, x ) ( y1, y2,, y ) ( a1, a2,, a 1 )= ( a ) i = 1 i (Detyiecki, 2001). I our cotext, we use aggregatio operators i the followig cases: I order to fid a value to each paret ode ad root from skills ad kowledge trees. I order to assig a sigle umeric value to a skill or kowledge, each oe has iitially a value associated with each course from curriculum. Through aggregatio operators we ca fid a sigle umeric value that allows us to kow the compliace level that a studet has with respect to oe or some ideal profiles. This value shows the compliace level of a idividual profile regardig a ideal profile. We have chose a specific kid of aggregatio operators called ordered weighted average (OWA) operators. Defiitio 5. A OWA operator of dimesios is a mappig :, such that: F( a, a,, a )= wb 1 2 j= 1 where b j is the jth largest of the α i, ad the w j are the weights, satisfyig: w j [1] ad j= 1= 1 (Yager, 2004, Merigó, 2011). OWA operator provides a class of averagig operators parameterized by the weightig vector. This property gives us some of the basic aggregatio operators such as: 1. Maximum. Where w 1 = 0 ad w j = 0 for j 1here F(a 1, a 2,...a ) = Max i [a i ]. 2. Miimum. Where w = 0 ad w j = 0 for j here F(a 1, a 2,...a ) = Max i [a i ]. 3. Simple Average. Where w = 1/ here F(a, a,...a ) = (1/ a 1 2 i (Yager, 1988). = 1 i Additioally, it is possible defie the weights values through various methods, too. Some of these methods imply: Usig learig algorithms with a set of traiig data, associatig values ad tryig to assig the weights accordig to values from traiig data. A expoetial class of OWA operators. This is see as a simple relatioship betwee oress degree ad a parameter that determies the OWA weights (Filev,, 1998). The oress degree determies how flexible (or strict) is the result o OWA operator ad it is represeted as α. Whe α 1, OWA operator treds to maximum (or), ad whe α 0 OWA operator treds to miimum (ad). Figure 3 shows the aggregatio iformatio process over the compliace level tree, which obtais the compliace level value from a idividual profile with respect to a ideal profile. Figure 3. Aggregatio Iformatio Process. Choosig Fuzzy Implicatios ad Aggregatio Operators I the sectio Fuzzy Implicatios, we were referrig to the use of fuzzy implicatios i order to fid the compliace level tree. The selectio of a type of fuzzy implicatio determies the results expected for our model. There are differet fuzzy implicatio operators reported (Driakov, j j 92 Igeiería e Ivestigació vol. 35.º 2, august (89-95)

5 BARRERA, DUARTE, SARMIENTO, AND SOTO 1993) ad some of them are parameter adjustable. All of them exted the biary implicatio to fuzzy values: they compute the same values whe the iputs are 0 or 1. However, their performace is differet for values betwee 0 ad 1. We aalysed the performace of 9 fuzzy implicatio operators as compliace level operators, ad selected Gödel ad Goguel implicatios. Similarly, the choosig of a aggregatio operator defies how flexible or strict the compliace level of a idividual profile must be i regard to ideal profiles. I this case, we foud the followig results show i the Table 2: Table 2. Comparig class of Aggregatio Operators Operator Maximum (or α = 1) OWA whe α 1 Simple Average OWA whe α = 0 Miimum (or α 0) Result Most strict Strict Middle Flexible Most flexible The ext example aims to show the impact of α parameter o flexibility level i compliace level: suppose that there is a set of argumets values v (0.8, 0.5, 0,3) ad a set of α (oress degree) values α = (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, ), we have applied the expoetial OWA i order to fid the weights accordig with oress degree ad establish the compliace level, the results obtaied ca be see i Figure 4. Applicatio I the sectio titled Kowledge Sources for Profile Obtaiig we have described that three kowledge sources are the bases i order to build the geeral frame of idividual ad ideal profiles. We have chose two profiles defied by a group of experts by the Udergraduate Program of Electrical Egieerig from Uiversidad Nacioal de Colombia. These profiles are: Power distributio systems ad Idustry applicatios ad they are the basis i order to obtai the ideal profiles. Figure 4. Behavior of Compliace Level with respect to α Parameter. We defie a impact matrix (a table) for every professioal profile. That matrix relates skills ad kowledge with courses which was extracted from the Curriculum otology (Sarmieto, 2010). I every cell of the matrix there is a umeric value i the iterval [0,1] that reflects the expected impact that a course would have o a specific studet s skill or kowledge. The values have bee estimated by the same group of experts. Notice, that every row of the matrix represets a skill or kowledge that belogs to the last level (a leaf ode i the tree). I order to fid the values of the higher levels where there are o desigated values, we apply a kid of OWA operator that has bee explaied i Aggregatio Operators. The impact matrices are the basis to create a idividual profile. We use them i cojuctio with the studet s academic record to estimate the studet s skills ad kowledge acquired. I order to do this, we multiply the values of the impact matrices for a performace factor (ad agai i the iterval [0,1]) that is proportioal to the grade that the studet obtaied i every course. It is possible desig other kid of tests (for example, a test focused oly i skills) ad ca use these. However, the desig of these tests is ot a part of this work. For this reaso, we have used the academic record i order to fid the idividual profile. Oce we have established the relatioship betwee skills or kowledge ad the level of performace of a studet, we eed to assig a sigle value for each skill or kowledge. For this reaso, we propose to use OWA operators i each row from each matrix. Ideal profiles have also bee obtaied from a group of experts. They have provided us two profile matrices that lik skills ad kowledge sets with the two ideal profiles, where each cell cotais umeric value i the iterval [0,1]. I order to fid the compliace level of a idividual profile with respect to ideal profiles, we apply fuzzy implicatios to get the compliace level tree described i Fuzzy Implicatios. This gives us the level of compliace obtaied by a studet i each oe of the skills ad kowledge. With OWA operators it is possible to calculate the compliace level of a idividual profile i regard to oe or more ideal profiles as a oly umeric value i the iterval [0,1], as it has bee described i Aggregatio Operators. I order to test ad evaluate the proposed methodology, a software prototype has bee implemeted. The mai purpose of this software prototype is to facilitate the evaluatio of the model by experts i the domai of kowledge i Electrical Egieerig, i.e., teachers, Electrical Egieers ad huma resources experts. Usig the web applicatio, a user ca select a studet, oe, several or all ideal profiles, fuzzy implicatios ad OWA operators (ad a α parameter if it is required). The user ca see the compliace level value ad the compliace level tree (see Figure 5). Igeiería e Ivestigació vol. 35.º 2, august (89-95) 93

6 A quatitative defiitio of egieerig professioal profiles We eed a uique umeric value by each kowledge ad skill, i this case, we propose to use a kid of aggregatio operator (for example, maximum). These results allow us to build the idividual profile that ca be see i Table 6. Table 6. Idividual profile Kowledge/Skill OWA K: Cotrol 0.7 S: Experimetal Iquiry 0.72 Figure 5. Iformatio flow through the trees. We have used the Ratioal Uified Process (RUP) methodology of software desig. This prototype is a Web applicatio that has bee implemeted i PHP laguage ad it is based o a MySQL database. The database has ie tables with iformatio about the sets of skills ad kowledge, studets, courses of curriculum ad ideal profiles related with the Udergraduate Program of Electrical Egieerig from Uiversidad Nacioal de Colombia. I additio to this, the database records the iformatio regardig compliace levels of idividual profiles. Example The goal of this example is to show the applicatio of our model i order to fid the compliace level of a studet or idividual profile regardig a ideal profile. Suppose that we have a impact matrix that relates the kowledge Cotrol ad the skill Experimetal Iquiry with 3 courses Probability, Physics ad Cotrol Table 3 shows the values give to this relatioship. Table 3. Impact matrices Kowledge/Skill Courses Probability Physics Cotrol K: Cotrol S: Experimetal Iquiry A studet e has obtaied the ext grades, these have bee ormalized ad they ca be see i the Table 4. Suppose that we have ideal profiles defied by academic experts related with the kowledge Cotrol ad Skill Experimetal iquiry. Table 7 shows the structure established to each ideal profile: Table 7. Ideal Profiles Kowledge/Skill Professioal Profiles Power Distributio Systems Idustry Applicatios K: Cotrol S: Experimetal iquiry Through Fuzzy Implicatios it is possible to establish a relatioship betwee idividual ad ideal profiles i order to build the compliace level tree. The applicatio of Gödel implicatio is show i Table 8. Fially, we eed kow the compliace level of a studet respect to the Ideal profiles. I order to obtai this result we propose to apply a OWA operator over the compliace level tree of Table 8. I the Table 9 we show the results whe a OWA operator is applied, i this case we fid a expoetial OWA with a oress degree value 0.8. This outcomes show that the studet e has a compliace level i the profile Power distributio system greater tha the profile Idustry Applicatios. Table 8. Compliace level tree usig Gödel implicatio Kowledge/Skill Power Distributio Systems Professioal Profiles Idustry Applicatios K: Cotrol S: Experimetal Iquiry Table 9. Outcomes Table 4. Normalized grades Probability Physics Cotrol Studet e Power Distributio Systems Idustry Applicatios I order to fid the idividual profile, we propose to associate impact matrices ad studet grades, obtaiig the results show i the Table 5. Table 5. Impact matrices of a studet Kowledge/Skill Courses Probability Physics Cotrol K: Cotrol S: Experimetal Iquiry Coclusio ad Future Work A methodology to defie professioal profiles (ideal ad idividual) has bee proposed. The mathematical foudatios of the methodology have bee preseted. It is a quatitative model based o skills ad kowledge. Two mai tools take from the Kowledge Egieerig are used: fuzzy implicatios ad aggregatio operators. As those tools are ot uique, it is possible to coduct some sesitivity aalysis. As a example, we have tested: 1) the ifluece of the selectio of the fuzzy implicatio operatio, ad 2) the effect of the oress parameter i the aggregatio process. 94 Igeiería e Ivestigació vol. 35.º 2, august (89-95)

7 BARRERA, DUARTE, SARMIENTO, AND SOTO As further work, more experimetatio is eeded i order to adjust the methodology. Aalysis of real cases is required. A close work with the domai experts must be doe i order to defie the skills ad kowledge trees ad the impact matrix. The potetial of the methodology is broad: for example, it ca be used i program assessmet tasks sice it is possible to measure if the expectatios from orgaizatios ad society are beig fulfilled. From aother perspective, it ca be used for studets as a iformatio tool about their idividual learig processes. Curretly, our methodology is the basis of a project whose goal is to recommed learig pathways for studets i the Electrical Egieerig curriculum from Uiversidad Nacioal de Colombia. As the optimal pathway depeds o the desire professioal profile, this quatitative model is the keystoe of the project. Refereces Alles, M. (2009). Diccioario de competecias, La trilogía: Las 60 competecias más usadas, Bueos Aires, Argetia: Editorial Garica. Cosejo de Facultad de Igeiería. (2009). Resolució 181 de 2009, Uiversidad Nacioal de Colombia, sede Bogotá. Crawley, E. F. (2001). Creatig the CDIO Syllabus a Statemet of Goals for Udergraduate Egieerig Educatio, Departmet of Aeroautics ad Astroautics, Massachusetts Istitute of Techology. Crawley, E. F. (2002). The CDIO Syllabus a uiversal template for Egieerig Educatio, ASEE/IEEE Frotiers i Educatio Cofer-ece. Crosthwaite, C., Camero, I., Lat, P. ad Litster, J. (2006). Balacig curriculum processes ad cotet i a project cetred curriculum. i pursuit of graduate attributes, Icheme (Istitutio of Chemical Egieers), 84(7), DOI: /ece Davies, J., Fesel, D. ad va Harmele, F. (2003). Towards the Sematic Web. Otology-Drive Kowledge Maagemet, New York, USA: Jho Willey ad Sos. Departameto de Igeiería Eléctrica y Electróica, Uiversidad Nacioal de Colombia. (2008). CDIO Syllabus e español, do-cumeto de aplicació de la metodología CDIO al departameto de Igeiería Eléctrica y Electróica, Uiversidad Nacioal de Colombia, sede Bogotá. Detyiecki M. (2001). Fudametals o Aggregatio Operators., Computer Sciece divisio, Uiversity of Califoria. Driakov, D., Helledoor, H. ad Reifrak, M. (1993). A Itroductio to Fuzzy Cotrol, Berli, Germay: Spriger-Verlag. DOI: / Fesel, D., Holger, L., Polleres, A., de Bruji, J., Stollberg, M., Roma, D. ad Domigue, J. (2007). Eablig Sematic Web Services. The Web Service Modelig Otology, Berli, Germay: Spriger-Verlag. DOI: / Filev, D., ad Yager, R. (1998). O the issue of obtaiig OWA operator weights, Fuzzy Sets ad Systems, DOI: /S (96) Ghisays, A. (2013). Represetació del Programa Curricular de Pregrado de Igeiería Eléctrica de la Uiversidad Nacioal e el Área de Circuitos, Señales y Sistemas mediate Otologías, Bogotá, Colombia: Facultad de Igeiería, Uiversidad Nacioal de Colombia. Herádez Díaz, A. (2004). Perfil Profesioal, Revista Pedagógica Uiversitaria, 9(2), Hor, E. ad Kupries, M. (2003). A study program for professioal software egieerig, Proceedigs of the 16th Coferece o Software Egieerig Educatio ad Traiig (CSEET 03). DOI: /csee Merigó, J.M. (2011). A uified model betwee the weighted average ad the iduced OWA operator, Expert Systems with Applicatios, 38(9), DOI: /j.eswa Merigó, J.M. ad Casaovas, M. (2011). The ucertai iduced quasi-arithmetic OWA operator. Iteratioal Joural of Itelliget Systems, 26(1), DOI: /it Sarmieto, C. (2010). Represetació del Programa Curricular de Pregrado de Igeiería Eléctrica de la Uiversidad Nacioal, mediate Otologías, Bogotá, Colombia: Facultad de Igeiería, Uiversidad Nacioal de Colombia. Soto, R. (2012). Represetació del área de Electrotecia y Sistemas de Potecia del programa curricular de Igeiería Eléctrica, mediate Otologías, Bogotá, Colombia: Facultad de Igeiería, Uiversidad Nacioal de Colombia. Yager, R. (1988). O ordered weighted averagig aggregatio operators i multicriteria decisio makig. IEEE Trasactios o Systems, Ma ad Cyberetics, 18(1), DOI: / Yager, R. (2004). OWA aggregatio over a cotiuous iterval argumet with applicatios to decisio makig, IEEE Trasactios o Systems, Ma ad Cyberetics, 34(2), DOI: /TSMCB Igeiería e Ivestigació vol. 35.º 2, august (89-95) 95