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Видшеш специфiчнi особливостi задач управлтня квалiфiкованими людськими ресурсами (УКЛР), що iдентифiкують гх як завдання багатокритерiального аналi-зу i прийняття ршень в нечткому серед-овищ^. Запропоновано модель прийняття ршень в задачах УКЛР. Обгрунтовано, що для тдвищення ефективностi та прозоро-стi ршень в УКЛР дощльно застосування багатокритерiальног оптимiзацiг на базi TOPSIS i показат його переваги
Ключовi слова: управлтня контентом, людськ ресурси, рекрутинг, прийняття ршень, нечтке середовище, нечтк мно-жини
Выделены специфические особенности задач управления квалифицированными человеческими ресурсами (УКЛР), позволяющие идентифицировать их как задачи многокритериального анализа и принятия решений в нечеткой среде. Предложена модель принятия решений в задачах УКЛР. Обосновано, что для повышения эффективности и прозрачности решений в УКЛР целесообразно применение многокритериальной оптимизации на базе TOPSISи показаны его преимущества
UDC 004.89
|dOI: 10.15587/1729-4061.2016.85454|
A METHOD FOR CONSTRUCTING RECRUITMENT RULES BASED ON THE ANALYSIS OF A SPECIALISTS COMPETENCES
V. Lytvyn
Doctor of Technical Sciences, Professor* E-mail: yevhen.v.burov@lpnu.ua V. Vysotska PhD, Associate Professor* E-mail: victoria.a.vysotska@lpnu.ua P. P u kac h
Doctor of Technical Sciences, Associate Professor** E-mail: petro.y.pukach@lpnu.ua I. Bo by k PhD, Associate Professor** E-mail: igor.bobyk@gmail.com B. Pakholok PhD, Associate Professor** E-mail: bogdanbp@ukr.net *Department of Information Systems and Networks*** **Department of Mathematics*** Lviv Polytechnic National University S. Bandery str., 12, Lviv, Ukraine, 79013
Under conditions of active development of innovative information technologies and software development, human resources (IT-professionals) are turning into the main strategic resource of organizations [1], which ensures their long-term competitiveness and achievement of goals, set by the organization [2]. Therefore, development of new conceptual approaches to recruiting IT-professionals is becoming increasingly important and relevant [3]. Recruitment is the process of searching for and selecting personnel for vacant positions in the staff of a company [4]. It is the main function and responsibility of human resources managers and recruiters [1]. Different approaches and information sources are used for recruitment [5]. The main sources are the internal database of a company or an agency, websites for a job search, social capital (or searching for candidates among acquaintances), media, social networks, forums, blogs, etc., the employees of companies-competitors (attracting professionals from other companies), higher educational establishments (inviting young specialists from higher education institutions), and cooperation with recruiting agencies [6].
It is a multifaceted extensive subjective procedure, extended over time and dependent mainly on the level of training of recruiters [7].
As a rule, people who are not qualified or partially qualified in the field and the level of expertise required by the position that the candidates apply for are involved in the recruitment at the initial stages [8]. At the next stages, specialists in subject areas usually take part in job interviews in order to analyse the level of expertise of the applicants who have already been approved after the interview or testing at the initial stages [9]. But they spend a lot of time filtering the information about candidates and their competence [10]. All of this takes a lot of time and resources from companies that offer a job or recruitment companies (it is impossible to have specialists and experts in all possible fields) [11]. It is necessary to automate the partial sub-processes of analysis of expertise of candidates for the positions and to develop approaches to the analysis of the competence level of
professionals [12]. Automation greatly reduces the time for selection of skilled workers and decreases the amount of data that need processing; it leads to a decrease in the subjectivity influence regarding recommendations of qualified people to the position. Taking into account the level of competences of applicants during recruiting makes it impossible to hire unqualified professionals [14].
Competences are the dynamic combination of knowledge, understanding, habits, abilities and skills [15]. Development of competences is the aim of training programs [16]. Competences are formed in a variety of academic disciplines and are evaluated at different stages [3].
Competences are divided into three types [2]:
A - Instrumental (cognitive, methodological, technological and linguistic abilities).
B - Interpersonal (communication skills, social interaction and cooperation).
C - System (combination of understanding, receptivity and knowledge, ability to plan changes for the improvement of systems, development of new systems).
In the European dictionary, the term "employability" (qualification for employment) is becoming increasingly popular; it describes the totality of knowledge, skills, habits, a good command of approaches to solving practical situations, as well as the ability and desire of continuous improvement and professional development [2]. Qualification for employment includes the following competences [17]:
- level of self-organization;
- ability to work in a group;
- ability to perform specific tasks;
- communication skills and literacy;
- knowledge of information technologies, etc.
We will note that these are so-called general competences that are independent of the main profile of a chosen profession.
Survey [2], conducted among European employers (mostly representatives of industry and business), demonstrated that the chances of getting a proper place in the labour market depends on:
- skills that characterize employability - 78 %;
- positive attitude to work -72 %;
- appropriate practical experience (internship) - 54 %;
- area of the obtained education and training - 41 %;
- level of academic achievement at a higher educational establishment the applicant graduated from - 28 %;
- name (prestige) of educational institution the applicant graduated from - 8 %.
The aim of the work is the development of a multi-criteria optimization model of recruitment based on the analysis of competences of an IT-specialist. This will make it possible to automate the process of selection of IT-specialists in the recruitment departments of IT-companies through the development of appropriate software based on the developed model.
To achieve the aim, it was necessary to solve the following tasks:
- development of a formal model of classification of IT-professionals by the level of competence;
- development of the rules of competence evaluation of IT-specialists;
- development of the rules of recommendations for the positions of IT-specialists.
Paper [2] contains a prioritized list of 31 competences (K={kj, k2, ..., k31}) according to the programme Tuning (Table 1). The priority is calculated by the method of hierarchy analysis (analytic hierarchy process, AHP) [18]. Each competence belongs to one of the criteria {A, B, C} [2].
Let us sort out the criteria of the Ki competence by categories (Table 1). For each category we will find coefficient of relative importance of criteria of competence wi (as arithmetic mean of priorities of a category) [19]. Using the TOPSIS method [20, 21], we compute coefficients of relative importance of private criteria of competence wj and the weight coefficients of private criteria of competence w^ = w1 *wj (Table 1) [22].
In the course of studying, the profile of distant student S is formed considering each level of competence KA, KB, KC within [0;1]. A student is trained in certain specialty
P = {P1,P2,...,PNp}.
To acquire a specialty, it is necessary to complete several courses
C = {c1,c2,...,cnc} or CP = {Cp1,Cp2,C1P3}, CP c CP c C.
A course consists of disciplines
D = {d^,...^}.
Within each discipline, there are blocks of themes
L = {U2,..,1nl} or LD = {L°,L°,L°}, LDc LD c L,
Ki ^ (Di1,Di2,...,Din ) or Ki ^ (Di1,Di2,...,Din )
it is the choice of an expert group, which develops professional educational program. For each Dij, a group of experts
determines weight oij for competence Ki = 1) using
the AHP method [23]. For each Ci we construct a table of relationship between program competences and components of educational programs of a particular specialily (columns contain the list of disciplines, lines contain the list of competences). For example, for specialty 124 "Systems analysis" [24], the expert group defined 48 disciplines with the set of 28 competences and described the relationship between program competences and components of the educational program of a particular specialty. Each cell of this table is the presence or absence of a particular competence in a particular discipline. Accordingly, the matrix of weights of disciplines for the list of competences from the Tuning program is plotted.
S11 S12 ... S1N
Q= °21 °12 ... °2N . (1)
S31,1 S31,2 ... S31,N _
Coefficients of relative importance of criteria received by AHP and TOPSIS
Type Interpretation of criterion Ki Vector of priorities by AHP wi wi Wj = wi *wj
Ability to communicate in another language ki 0,081728 0.30812 0.130369
Ability to communicate orally and in writing in native language ks 0,081728 0.223483 0.094558
Ability to plan time and control it k5 0,073083 0.156996 0.066427
Ability to search for, process and analyze information from different sources k8 0,056095 0.108416 0.045872
A Ability to identify, formulate and solve problems kio 0,046394 0.423112 0.074296 0.031436
Ability to make well- grounded decisions ki2 0,036574 0.050915 0.021543
Knowledge and understanding of subject area and understanding of specialty ki5 0,026993 0.03516 0.014877
Ability to think abstractly, analyze and synthesize ki9 0,015431 0.0247 0.010451
Skills of using information and communication technologies k27 0,005086 0.017915 0.00758
Ability to be critical and self-critical k4 0,073083 0.286411 0.086828
Ability to demonstrate awareness of equal opportunities and gender issues k6 0,064504 0.217059 0.065803
Safety orientation k9 0,04951 0.156114 0.047327
Ability to work in a team ki4 0,028866 0.110389 0.033465
Ability to work in international context ki6 0,024721 0.077361 0.023453
B Ability to act based on ethical considerations ki7 0,020154 0.303159 0.054062 0.016389
Ability to communicate with non-specialists of the same area kis 0,016523 0.037886 0.011485
Interaction and interpersonal skills k2i 0,011812 0.02679 0.008122
Ability to act with social responsibility and civic consciousness k23 0,009635 0.019496 0.00591
Focusing on preservation of environment k28 0,004351 0.014431 0.004375
Ability to learn k2 0,081728 0.334658 0.091605
Ability to produce new ideas (creativity) k7 0,06124 0.262228 0.071779
Ability to apply knowledge in practical situations kii 0,041715 0.206098 0.056414
Ability to conduct research at the appropriate level ki3 0,032705 0.152891 0.04185
Entrepreneur spirit k20 0,013559 0.11133 0.030474
Ability to design and manage projects k22 0,011796 0.080632 0.022071
C Certainty and perseverance in performing received tasks and responsibilities k24 0,008331 0.273726 0.058299 0.015958
Correct understanding and respect for multiculture and differences k25 0,007182 0.042696 0.011687
Ability to work independently k26 0,005859 0.031049 0.008499
Ability to adapt to new situations k29 0,00363 0.023825 0.006522
Ability to evaluate and maintain the quality of completed work k30 0,003158 0.017331 0.004744
Ability to motivate people and to move towards common goals k3i 0,002823 0.013621 0.003728
Because of the lack of professional expert studies of the relationship between program competences from the Tuning program (Table 1) and the components of educational program of a particular specialty, in this paper we assume that
Ojj are equal among themselves and ^gj = 1.
Analyzing the obtained weights of disciplines, the expert group estimates the weight of semesters or courses
c^,...,^ (¿ce = 1) at Dj ece.
The set R contains specific learning outcomes by the theme blocks
R = (r1,r2,...,rNR) or RL = {ri,r2>».,0 RL c RL c R
or by disciplines Di. G are the learning outcomes by the category of competence at
G = {ga,gb,gc}, g = {
GA = {g1,g2,...,gm}, GB = {gm+1,gm+2,...,gm+nl,
G = {gm+n+1&gm+n+2&...&gNG}. (3)
Gf c Gf c G, Gf c Gf c G, Gf c Gf c G. (4)
Gf c Ga C G, Gf C Gb C G, Gf C Gc C G. (5)
gd={giD,gf,...,gfD}, gD={gfD+i,gmD+2,...,gmD+nD},
GD = {gmf+nf +1,gmf+nf+2,...,gNGD}. (6)
Fig. 1 displays tree of analysis of relationship between courses, disciplines, themes and learning outcomes.
Rf c Rd c R for discipline Di of students (expert assessment) is assessed by the ECTS scale (Table 3). For a more accurate assessment of a student&s level of competence, fuzzy trapezoidal numbers RO are used in the TOPSIS method. In the course of finding trapezoidal fuzzy numbers, correspondence between the ECTS scale and numeric grades was used, which is presented in Table 2.
Next, we find weights of competences for particular student Si
^ = QceR° (7)
and a student&s rating by the levels of acquired competences
To analyze learning outcomes of student Si, we calculate his level of competence through the calculation of Ri and Gi by the defined set of characteristics aS within [0;100] (Table 3).
Then we normalize RS ^ KS within [0;wi], taking into account the weights of competences (Table 1). For example, KA varies within [0;0.423112] , Kf within [0; 0.303159] and KC within [0; 0.273726]. An analysis of learning outcomes (aS) will be performed with the use of the TOPSIS method and compared with ai from Table 5, which presents the hierarchy of recommended key professions of IT profile and their criteria of importance. Column 3 contains results of calculation by the AHP. The limits of evaluation in case 1 - according to a general education assessment at higher education institutions considering factor of importance of
position (a| 100 = 50 + 50 Pj), and in case 2 - taking into
account the level of competence. Column "Assessment limits 1" was obtained considering the point scoring assessment of alternatives at higher education institution (that is, a student with total assessment for the entire period of studying, for example, 80,5 points, may qualify for all positions, starting with the 4th, whereas he can not qualify for the first 3 positions; to receive position 13, it is necessary to be assessed within [50; 74.52 87]). Column "Assessment limits 1" was obtained considering factor of importance by AHP (column 3 of Table 4). Column "Assessment limits 2" was obtained without considering significance by AHP (a2 -100 = 50 + (50/15)(i -1)).
Linguistic values and corresponding fuzzy trapezoidal numbers
N°. Linguistic values By ECTS Fuzzy values Grade R& Fuzzy trapezoidal numbers Conditional sign
Table 4 displays an approximate list of common positions in IT-cluster in Ukraine. Outside Ukraine (for instance, in the EU), this list is much wider. The list was formed and sorted based on the results of a survey of representatives of IT-cluster in Lviv. At present, much to our regret, there are no clearly formulated general requirements to each of the listed positions. Each company determines the range of qualifications for each of the enumerated positions. For example, in some of them, to take up the position of Programmer, it is sufficient to know one of the programming languages, and to take the position of Software Engineer, an applicant must know the basics of algorithmization. The position of Student was introduced to the table conditionally, in order to indicate minimum conditions for making recommendations for
d, d2... d7 d, d2... d7 d, d2... d7
gi G2...Gy ... /T\\
ga gb gc ga gb gc
gi g2...gN
ga gb gc ga gb gc
gi g2...gN ...
ga gb gc
ga gb gc
Fig. 1. Hierarchy of analysis of learning outcomes and the level of competences
Rules for the formation of competency profile of student
Course Discipline Theme RA RB RC Learning outcomes
Lk RAk Rjk RCk G,jt = + Rj + j
Ci Dj Lk+1 Rijk+1 Rijk+1 Rijk+1 1A b C Gijk+1 = 3(Rijk+1+Rijk+1+Rijk+1)
Lk+2 RAk+2 Rijk+2 R^k+2 1A B C Gijk+2 = 3 (^^+2 + Rijk+2 + Rijk+2)
Learning outcomes GA=¥ Ä GB=1 ?RBk GC=1 » Analysis of results aS*100
further positions. In Ukraine, according to the requirements of Ministry of Education and Science, postgraduate training requires higher qualification than that for other positions in IT-cluster. If recommendations for positions numbered 2-7 allow IT-companies immediately and without any hesitation to hire recommended graduates, the recommendations for positions numbered 8-15 only register the possibility for a graduate to take such positions after appropriate internship and gaining experience at previous positions. Recommendation for position 10, for example, indicates only that a graduate can take positions 2-7 with the prospect of a career growth to position 10 inclusive with the competences acquired in the course of studying. In future he can qualify for higher positions under condition of development of his skills and competences.
Coefficients of relative importance of the recommended basic IT-professions
No. Position Coefficient of importance by AHP pi Assessment limits
Case 1 -a1*100 Case 2-a2*100
To run an analysis of learning outcomes and to make recommendations, we divide all students into 3 levels of training. In accordance with the value of the competence priority (Table 1), we divide the sorted list of competences into three parts (equal). The first 10 competences (A-5, B-3, C-2) belong to part I, the next 11 competences belong to part II (A-3, B-5, C-3), and the remaining 10 belong to part III (A-1, B-2, C-7). An analysis of the level of competence of a subject according to learning outcomes will be used to make the rules of recommendations for a position or a choice of occupations (Table 5, 6, b is analysis of competences according to learning outcomes).
Rules of determining competence of student S for the analysis of competences according to learning outcomes (b)
level I level II level III
—wA < KA < wA 2 S 1 wA < KA < wA 2 S 1 wA < KA < wA 2 S
Rules of determining recommendations concerning professions of student S for the analysis of competences according to learning outcomes (b)
Rule 0 < KB <—wB, S 2 0 < KB < — wB, S 2 —wB < KB <3wB, 2 S 4
Position 2 3 4
Rule 0 < KB < — wB S 2 0 < KB < —wB S 2 —wB < KB <3wB, 2 S 4
Position 5 6 7
Rule —wB < K < wB, 2 S —wB < K < wB, 2 S —wB < K <3wB, 2 S 4
Position 8 9 10
Rule —wB <KB < wB, 2 S —wB < KB < 3wB, 2 S 4 —wB < KB < wB, 2 S
Position 11 12 13
Rule 1 wB < KB < 3wB, 2 S 4 —wB < KB < wB, 2 S —wB < KB < wB, 2 S
Position 14 15 16
According to the example of Table 1, KA ranges within [0;wA] ([0; 0.423112]), Kf - within [0;wB] ([0; 0.303159]) and KC - with [0;wC] ([0; 0.273726]).
The process of making recommendations for a position or classification of IT-specialists by the level of their competence is described by superposition
R = 5° g° P° a, (7)
where sign ° means superposition of functions (output results of function a are the input date for function b, that is, it is a sequence of performing processes from the right to the left); a is the analysis of learning outcomes and compiling the rating by acquired competences; b is the analysis of competences according to learning outcomes; g is the analysis of requirements for a position by the level of competences and learning outcomes; 5 is making recommendations to a student/candidate regarding his profession according to statistics of studying and attainment of competences (5f is compared with 5j(xi); 5f is calculated by learning outcomes of student Si; 5(xi) is the integral index, set within certain limits).
Integral index (coefficient of proximity of compared alternatives) 5(xi), obtained on the basis of evaluation of these private criteria, expresses a certain value of a degree of chance of hiring every candidate xi in the interval [0, 1]. The value of this magnitude allows making the final decision regarding each alternative candidate. In the process of conducting experiments connected with hiring an employee, we analysed the rules for choosing an alternative of recommendation for a position, according to the analysis of requirements for it (Table 7) [11].
A level of competence depends on the learning outcomes over a certain period (for example, 4 years of studying). Each period (year) may have its coefficient of importance according to the expert assessment. As a result of pairwise comparison of the importance of attainment of competences for each of the 4 years of training, the following values of coefficients of importance depending on the year of study were obtained for case I: e1=0,375, e2=0,125, e3=0,125, e4=0,375. Table 8 presents 5 cases (5 different opinions of different groups of experts) of distribution of coefficients of importance of competences for each year of studying out of 4.
As an example, we will analyze learning outcomes of any arbitrary 3 students (x1, x2, x3) over four years for the purpose of their correspondence to 31 competences for the position of Senior Manager (position numbered 13 in Table 4). To do this, with the use of the TOPSIS method, we will calculate trapezoidal fuzzy numbers in Table 9, reflecting one of the equivalents of assessing a student&s level of knowledge (Table 2).
According to Table 9, a student can score maximum 12400 points (31*4*100). For example, candidate x1 scored 11160 points (5f = 11160/12400 = 0.9 by general educational requirements for knowledge assessment), candidate x2 scored 9080 (52 = 0.732258), candidate x3 scored 11160 (53 = 0.9). Candidates x1 and x3 have the same number of
points, but there is a difference in their level of training. Candidate x1 studied better in the 1st year, worse - during the remaining years. x3, on the contrary, studied worse at the beginning of training, but had better results in the end. That is why they have different levels of competences according to the chosen specialty. Special subjects are usually taught in senior courses. Accordingly, x1 and x3 have equal rights to claim for a position without taking into account their level of competence in all 31 criteria. Taking into account the competence of years of studying, a matrix of trapezoidal fuzzy numbers is plotted (Table 10). Table 10 also displays aggregated trapezoidal fuzzy numbers. Elements of the matrix of aggregated trapezoidal fuzzy numbers are multiplied by weights of private criteria and results are normalized (Table 11).
List of alternatives of recommendations for selection of position
No. Alternative Candidate Explanations concerning hiring
Coefficients of competence according to year of studying
Pairwise comparison ce Variants of coefficients of importance of competences for each year of studying (cases)
I II III IV V
Year ce 0,375 0.25 0.463184 0.413265 0.568093
Year ce2 0,125 0.25 0.275411 0.292222 0.287771
Year c3 0,125 0.25 0.175972 0.186714 0.10758
Year c4 0,375 0.25 0.085433 0.107799 0.036557
Example of learning outcomes of students x-| x2 x3
No. Criteria Alternatives Expert assessment R& Matrix of trapezoidal fuzzy numbers RO
ce c2 c3 c4 ce c2 c3 c4
X2 A B B C (8,9,10,10) (7,8,8,9) (7,8,8,9) (5,6,7,8)
X3 B B A A (7,8,8,9) (7,8,8,9) (8,9,10,10) (8,9,10,10)
X2 A B D C (8,9,10,10) (7,8,8,9) (4,5,5,6) (5,6,7,8)
X3 B B A A (7,8,8,9) (7,8,8,9) (8,9,10,10) (8,9,10,10)
X2 A B D C (8,9,10,10) (7,8,8,9) (4,5,5,6) (5,6,7,8)
X3 B B A A (7,8,8,9) (7,8,8,9) (8,9,10,10) (8,9,10,10)
X2 A B D C (8,9,10,10) (7,8,8,9) (4,5,5,6) (5,6,7,8)
X3 B B A A (7,8,8,9) (7,8,8,9) (8,9,10,10) (8,9,10,10)
X2 A B B C (8,9,10,10) (7,8,8,9) (7,8,8,9) (5,6,7,8)
X3 B B A A (7,8,8,9) (7,8,8,9) (8,9,10,10) (8,9,10,10)
Table 10
Example of filling the matrix with aggregated trapezoidal fuzzy numbers with regard to competence of years of studying for
case IV from Table 8
Criteria Alternatives Years of studying c° Aggregated trapezoidal fuzzy numbers
ce (e1=0.413265) c2 (e2=0.292222) c3 (e3=0.186714) < (e4=0.107799)
k1 X1 (3.30612, 3.719385, 4.13265, 4.13265) (2.33778, 2.630002, 2.922225, 2.922225) (1.306995, 1.493708, 1.493708, 1.680422) (0.754593, 0.862392, 0.862392, 0.970191) (0.754593, 2.176372, 2.352744, 4.13265)
X 2 (3.30612, 3.719385, 4.13265, 4.13265) (2.045557, 2.33778, 2.33778, 2.630002) (1.306995, 1.493708, 1.493708, 1.680422) (0.538995, 0.646794, 0.754593, 0.862392) (0.538995, 2.049417, 2.179683, 4.13265)
X 3 (2.892855, 3.30612, 3.30612, 3.719385) (2.045557, 2.33778, 2.33778, 2.630002) (1.493708, 1.680422, 1.867135, 1.867135) (0.862392, 0.970191, 1.077991, 1.077991) (0.862392, 2.073628, 2.147256, 3.719385)
k3 X1 (3.30612, 3.719385, 4.13265, 4.13265) (2.33778, 2.630002, 2.922225, 2.922225) (1.306995, 1.493708, 1.493708, 1.680422) (0.754593, 0.862392, 0.862392, 0.970191) (0.754593, 2.176372, 2.352744, 4.13265)
X 2 (3.30612, 3.719385, 4.13265, 4.13265) (2.045557, 2.33778, 2.33778, 2.630002) (0.746854, 0.933568, 0.933568, 1.120281) (0.538995, 0.646794, 0.754593, 0.862392) (0.538995, 1.909382, 2.039648, 4.13265)
X3 (2.892855, 3.30612, 3.30612, 3.719385) (2.045557, 2.33778, 2.33778, 2.630002) (1.493708, 1.680422, 1.867135, 1.867135) (0.862392, 0.970191, 1.077991, 1.077991) (0.862392, 2.073628, 2.147256, 3.719385)
k5 X1 (3.30612, 3.719385, 4.13265, 4.13265) (2.33778, 2.630002, 2.922225, 2.922225) (1.306995, 1.493708, 1.493708, 1.680422) (0.754593, 0.862392, 0.862392, 0.970191) (0.754593, 2.176372, 2.352744, 4.13265)
X 2 (3.30612, 3.719385, 4.13265, 4.13265) (2.045557, 2.33778, 2.33778, 2.630002) (0.746854, 0.933568, 0.933568, 1.120281) (0.538995, 0.646794, 0.754593, 0.862392) (0.538995, 1.909382, 2.039648, 4.13265)
X 3 (2.892855, 3.30612, 3.30612, 3.719385) (2.045557, 2.33778, 2.33778, 2.630002) (1.493708, 1.680422, 1.867135, 1.867135) (0.862392, 0.970191, 1.077991, 1.077991) (0.862392, 2.073628, 2.147256, 3.719385)
k30 X1 (3.30612, 3.719385, 4.13265, 4.13265) (2.33778, 2.630002, 2.922225, 2.922225) (1.306995, 1.493708, 1.493708, 1.680422) (0.754593, 0.862392, 0.862392, 0.970191) (0.754593, 2.176372, 2.352744, 4.13265)
X 2 (3.30612, 3.719385, 4.13265, 4.13265) (2.045557, 2.33778, 2.33778, 2.630002) (0.746854, 0.933568, 0.933568, 1.120281) (0.538995, 0.646794, 0.754593, 0.862392) (0.538995, 1.909382, 2.039648, 4.13265)
X 3 (2.892855, 3.30612, 3.30612, 3.719385) (2.045557, 2.33778, 2.33778, 2.630002) (1.493708, 1.680422, 1.867135, 1.867135) (0.862392, 0.970191, 1.077991, 1.077991) (0.862392, 2.073628, 2.147256, 3.719385)
k31 X1 (3.30612, 3.719385, 4.13265, 4.13265) (2.33778, 2.630002, 2.922225, 2.922225) (1.306995, 1.493708, 1.493708, 1.680422) (0.754593, 0.862392, 0.862392, 0.970191) (0.754593, 2.176372, 2.352744, 4.13265)
X 2 (3.30612, 3.719385, 4.13265, 4.13265) (2.045557, 2.33778, 2.33778, 2.630002) (1.306995, 1.493708, 1.493708, 1.680422) (0.538995, 0.646794, 0.754593, 0.862392) (0.538995, 2.049417, 2.179683, 4.13265)
X 3 (2.892855, 3.30612, 3.30612, 3.719385) (2.045557, 2.33778, 2.33778, 2.630002) (1.493708, 1.680422, 1.867135, 1.867135) (0.862392, 0.970191, 1.077991, 1.077991) (0.862392, 2.073628, 2.147256, 3.719385)
Elements of normalized matrix of decision making
Criteria Alternatives Weight coefficient of criteria Elements of weighed fuzzy matrix (*100) Elements of normalized matrix of decision making
ki xi 0.i3037 (9.83756, 28.3731, 30.6725, 53.8769) (0.18259, 0.52663, 0.56931, 1)
X2 (7.02683, 26.718, 28.4163, 53.8769) (0.13042, 0.49591, 0.52743, 1)
X3 (11.2429, 27.0337, 27.9936, 48.4892) (0.23186, 0.55752, 0.57731, 1)
ks Xi 0.09456 (7.13528, 20.5793, 22.2471, 39.0775) (0.18259, 0.52663, 0.56931, 1)
X2 (5.09663, 18.0547, 19.2865, 39.0775) (0.13042, 0.46202, 0.49354, 1)
X3 (8.15461, 19.6078, 20.304, 35.1698) (0.23186, 0.55752, 0.57731, 1)
k5 Xi 0.06643 (5.01254, 14.457, 15.6286, 27.452) (0.18259, 0.52663, 0.56931, 1)
X2 (3.58038, 12.6834, 13.5488, 27.452) (0.13042, 0.46202, 0.49354, 1)
X3 (5.72861, 13.7745, 14.2636, 24.7068) (0.23186, 0.55752, 0.57731, 1)
k30 Xi 0.00474 (0.35798, i.03247, i.ii6i4, i.96053) (0.i8259, 0.52663, 0.5693i, i)
X2 (0.2557, 0.9058i, 0.9676i, i.96053) (0.i3042, 0.46202, 0.49354, i)
X3 (0.409i2, 0.98373, i.0i866, i.76448) (0.23i86, 0.55752, 0.5773i, i)
k3i Xi 0.00373 (0.28i3i, 0.8ii35, 0.877i, i.54065) (0.i8259, 0.52663, 0.5693i, i)
X2 (0.20094, 0.76402, 0.8i259, i.54065) (0.i3042, 0.4959i, 0.52743, i)
X3 (0.32i5, 0.77305, 0.8005, i.38659) (0.23i86, 0.55752, 0.5773i, i)
Next, integral matrix of fuzzy ideal positive (best, x*) and fuzzy ideal negative (worst, x-) decisions is plotted, which is presented in Table 12.
Table 12
Integral matrix of IPD and IND
Criteria of competence x*, IPD x-, IND
Ki (i,i,i,i) (0.i30424, 0.i30424, 0.i30424, 0.i30424)
Results of distances of alternatives to IPD, calculated by the value of each individual criterion, are presented in Table 13 (columns 2-4). Results of distances of alternatives to IND, calculated by the value of each individual criterion, are presented in Table 14 (columns 5-7).
Table 13
Distances of alternatives to IPD and by the value of each criterion
Criteria D(xi,x*) D(X2,X*) D(x3,x*) D(xi,x-) D(X2,X-) D(x3,x-)
ki 0.26943 0.3084 0.24ii2 0.277i2 0.26i839 0.287i44
ka 0.26943 0.32552 0.24ii2 0.277i2 0.249495 0.287i44
k5 0.26943 0.32552 0.24ii2 0.277i2 0.249495 0.287i44
k30 0.26943 0.32552 0.24ii2 0.277i2 0.249495 0.287i44
k3i 0.26943 0.3084 0.24ii2 0.277i2 0.26i839 0.287i44
Using the TOPSIS method, we will estimate the limits of criteria of competence and the level of competence
for each of the three candidates. Taking into account the competences of years of studying, the matrix of trapezoidal fuzzy numbers is plotted, and aggregated trapezoidal fuzzy numbers are displayed. Elements of the matrix of aggregated trapezoidal fuzzy numbers are multiplied by weights of private criteria and the results are normalized. Then the integral matrix of IPD and IND, respectively, is plotted. For example, for case IV (Table 12), the limits of criteria of competence are [0.130424; 1] by the TOPSIS. Thus, for ki when assessing IPD, we have x1=0.51907, x2=0.57054, x3=0.49104. Distances of alternatives to IPD by the value of each individual criterion ki are D(x1,x*)=0.26943, D(x2,x*)=0.32552 and D(x3,x*)=0.24112. For ki, when assessing IND, we have x1=0.526422, x2=0.499494, x3=0.535858. Distances of alternatives to IND by the value of each individual criterion ki are D(x1,x-)=0.27712, D(x2,x-)=0.249495 and D(x3,x-)=0.287144.
We defined distances of each alternative to IPD and IND according to each variant of coefficients of importance for each year of studying (5 cases are considered as an example, see Table 8). Then we calculated values of integral index that expresses the degree of proximity of each compared alternative to the ideal solution by TOPSIS, and based on the results, the ranks of each alternative were determined (Table 14).
According to the obtained results, the best (optimum) option of decision in this case is IV, at which x3, that is, candidate x3, is an alternative. Chances of candidate x3 are assessed by value 5T(x3) = 0.521822 when 5(x3)e[0.50; 0.65). The same concerns candidate x2 (5T(x2) = 0.503516 at 5(x2)e [0.50; 0.65)), but he has a chance only if x3 rejects the offer. Accordingly, hiring a candidate is associated with a low risk, which can be compensated in the process of work by high indices of other competences. As for candidate x1 (5 T(x1) = 0.470902 at 5(x1)e[0.25; 0.50)), hiring him is associated with greater risk.
Distances of compared alternatives to IPD and IND, coefficient of their proximity to ideal solution and corresponding ranks by TOPSIS
Case from Table 9 Alternatives x* x * i -x + x ST(xi) Ranks
X1 2.697018 2.883112 5.58013 0.516675 1
I + + - x 2 3.019768 2.730049 5.749817 0.474806 2
x 3 2.697018 2.883112 5.58013 0.516675 1
X1 0.974359 2.41648 3.390839 0.71265 1
II + — x 2 1.845603 1.965006 3.810609 0.515667 2
x 3 0.974359 2.41648 3.390839 0.71265 1
X1 3.144922 2.979148 6.12407 0.486465 2
III --- x 2 3.346642 2.881048 6.22769 0.462619 3
x 3 3.040106 3.007715 6.047821 0.497322 1
x1 2.890055 2.930995 5.82105 0.503516 2
IV + + + x 2 3.149538 2.803118 5.952656 0.470902 3
x 3 2.734 2.983532 5.717531 0.521822 1
x1 3.534842 3.076006 6.610848 0.465297 1
V --- x 2 3.64263 3.01851 6.661141 0.453152 3
x 3 3.526551 3.062903 6.589454 0.464819 2
tion under condition that some indices can be easily filled in in the process of adaptation.
The obtained results of experimental calculations based on TOPSIS for the task of selecting the best candidate were compared with results of the selection, obtained using the point-scoring assessment system. Table 16 presents results of the two approaches to the estimation of the level of competence and the analysis of alternatives by the degree of proximity to the ideal decision regarding making recommendations for a conditionally selected position 13 (Table 4, Fig. 2), which allows conducting their comparative analysis.
Table 16
For objectivity of decision making, the experts carried out the point-scoring assessment of alternatives, closest to ideal decisions. To assess the alternatives, the correspondent calculations based on the point-scoring system of linguistic values according to Table 2 were carried out. On the basis of statistical data, obtained with the use of the point-scoring system of assessing alternatives, proximity of each alternative to the ideal decision by TOPSIS was established, with the component of 12400 points. Results of decision making on the basis of the point-scoring system of assessing three alternatives (candidates for a vacant position) are given in Table 15.
Results of priority of alternatives
Candi- Results based on AHP and TOPSIS Results based on general educational scale of assessment Data from Table 7
date Case 1 Case 2
x1 3 5 5 5
x2 2 4 4 4
x3 3 5 5 5
Comparison of results of the calculations with the use of two methods with regard to coefficients of relative importance of the basic recommended IT-professions (Table 4) reveals obvious discrepancy of the latter.
Educational professional program
Table 15
Results of point-scoring assessment of alternatives
ra MriflplK lipMMrJCTTH pÜB mi
Alternative Total point -scoring assessment Analysis of alternatives according to general educational level of studying Analysis of alternatives according to the calculations by AHP and TOPSIS
x1 11160 0.9 0.503516
x2 9080 0.732258 0.470902
x3 11160 0.9 0.521822
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The best alternative is x3, which scored 11160 points similar ti x1, it is followed by priority by alternative x2. According to the degree of proximity to the ideal decision, a correspondent conclusion is drawn for each alternative using a point- scoring system of assessment of alternatives:
Relevance of position %
Systems Architect 40
IT Project Manager 4H
Senior manager 51
Manager (¡3
Fig. 2. Example of implementation of the calculation of coefficients of relative importance for the recommended basic IT-professions for a particular student
Moreover, those candidates whose hiring in accordance with the proposed method is associated with great risk, with the use of the point-scoring assessment of alternatives fall into the category of the most preferred. Thus, the results of testing show sufficient sensitivity of the TOPSIS method in the process of selection of the best alternative among the best, while the method of point-scoring assessment does not actually allow distinguishing among several most prioritized candidates by the degree of proximity to the ideal alternative. This proves the effectiveness of the proposed methodological approach when solving the tasks of MQHR.
A general formal model for the classification of IT-professionals by the level of their competence was established and described. Its essence lies in a sequential analysis of the competence level of IT-specialist according to his learning outcomes in the chosen specialty. Thanks to it, recommendations for the positions in IT-industry are compiled according to the requirements of IT-cluster that automates the process of recruiting.
References
