An Application of the Fuzzy ELECTRE Method for Academic Staff Selection Babak Daneshvar Rouyendegh and Turan Erman Erkan Department of Industrial Engineering, Atılım University, P.O. Box 06836, I˙ ncek, Ankara, Turkey
Abstract There are various methods regarding staff selection in different fields. Thanks to the increasing improvements in the field of education, universities around the world tend to demand high -quality and professional academic staff. Staff selection is a multi-criteria decision-making processes, and of strategic importance for most universities. This study deals with actual application of academic of staff selection using the opinion of experts to be applied into a model of group decision - making called the Fuzzy ELECTRE (Elimination Et Choix Traduisant la REaite) method. There are ten qualitative criteria for selecting the best candidate amongst five prospective applications. C 2012 Wiley Periodicals, Inc. Keywords: Academic Staff Selection, Multi-Criteria Decision-Making (MCDM), Fuzzy ELECTRE, Human Resources.
1. INTRODUCTION Staff recruitment is one of the primary steps in the process of universities’ human resources and education management. In the wake of an increase in the number of universities in Turkey, the need for recruiting academic staff has become inevitable. As a result, in the light of such demand the performance of staff, including research techniques, up-to-date knowledge, and language skills play an important role in finding a job successfully. As for their own share, the universities will not be able to keep their competitive advantages without the ability to recruit the right individuals in various departments. In recent years, the attention paid by researchers to the topic of skilled employee recruitment has increased considerably (Billsberry, 2007), (Breaugh, Macan & Correspondence to: Babak Daneshvar Rouyendegh (Babek Erdebilli), Department of Industrial Engineering, Atılım University, P.O. Box 06836. Phone: 90-312-586 83 11, Fax: 90-312-586 80 91; e-mail address:
[email protected] Received: 7 January 2011; revised 1 February 2011; accepted 4 February 2011 View this article online at wileyonlinelibrary.com/journal/hfm DOI: 10.1002/hfm.20301
Grambow, 2008). As globalization intensifies, human capital becomes a critical element for the success of firms (Kiessling & Harvey, 2005). In addition, successful recruitment is also crucial for a nation’s economic growth due to the shortage in qualifies labor force in many countries (Becker, 1995). Recruitment activities are processes aimed at singling out applicants with the required qualifications, and keeping them interested in the organization so that they will accept a job offer when it is extended. Substantial research has been conducted on recruitment due to its critical role in bringing human capital into organizations (Barber, 1998). In the literature, the techniques applied in staff selection, assessment, and evaluation include written and oral exams (Arvey & Campion, 1982). Although evaluating applicants by means of written and oral exams is essential for a company when employing the staff required, it is not sufficient all by itself. In this process, first of all, the criteria – or factors - that are to be the basis of assessment and evaluations have to be specified. What’s more, the weights of these criteria need to be determined, for each criterion possesses a different degree of importance - or weight - in staff assessment and evaluation. Therefore, unsatisfactory
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An Application of the Fuzzy ELECTRE Method for Academic Staff Selection
subjective selection may occur with conventional assessment and evaluation tools, such as written or oral exams, and tests which are not based upon any certain criteria and/or weights. The fuzzy linguistic models allow the translation of verbal expressions into numerical ones, thereby dealing quantitatively with imprecision in the expression of the importance of each criterion. There are a number of multi-criteria methods used for this purpose and based on fuzzy relations. The fuzzy set theory has been proposed by Liang & Wang (1992), Miller & Feinzing (1993), Liang & Wang (1994), Karsak (2001), Capaldo & Zollo (2001), Canos & Liern (2008), and Boran, Genc¸ & Akay (2011) to address the issue of staff selection. In addition, the fuzzy analytical approach has been applied by Mikhailov (2002) to the problem of selecting partnerships. Jessop (2004) has applied the minimallybased weight method in staff selection. Chen & Cheng (2005) have proposed a Fuzzy Group Decision Support System (FGDSS) based on the metric distance method, in order to solve the IS (Information System) problem in staff selection (G¨ung¨or, Serhadlıo˘glu & Kesen, 2009). The Multi-Criteria Decision-Making (MCDM) is a modeling and methodological tool for dealing with complex engineering problems. In this field, the MultiAttribute Decision-Making (MADM) approach is the most well-known branch of the decision-making process and also a part of a general class of models for operations research that deal with decision problems under the presence of a number of decision criteria. The MADM approach requires that the selection be made among the decision alternatives described by their attributes. The problems concerning MADM are assumed to have a pre-determined, limited number of decision alternatives, and solving them involves sorting and ranking. The ELECTRE method for choosing the best action(s) from a given set of actions was devised in 1965, and later referred to as ELECTRE I (Electre One). The acronym ELECTRE stands for ELimination Et Choix Traduisant la REalite’or (ELimination and Choice Expressing the Reality), (Benayoun & Billsberry, 1966), Roy (1985) initialy cited for commercial reasons. This approach has evolved into a number of variants. Today, the used applied versions are known as ELECTRE II (Roy & Bertier 1973) and ELECTRE III (Roy 1978). ELECTRE is a popular approach to MCDM, and has been widely used in the literature (Vincke, 1992; Roy, 1996; Belton & Stewart, 2002; Almeida, 2007;
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Papadopoulos & Karagiannidisa, 2008; Wang & Triantaphyllou, 2008). This paper is divided into four main sections. The next section provides materials and methods, mainly the fuzzy sets and the ELECTRE method. The fuzzy ELECTRE method is introduced in section 3. How the proposed model is used in an actual example is explained in section 4. Finally, the conclusions are provided in the final section.
2. MATERIALS AND METHODS 2.1. Fuzzy Sets and Fuzzy Number Zadeh (1965) introduced the Fuzzy Set Theory to deal with the uncertainty due to imprecision and vagueness. A major contribution of this theory is its capability of representing vague data; it also allows mathematical operators and programming to be applied to the fuzzy domain. A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function, which assigns to each object a grade of membership ranging between zero and one (Kahraman, Ruan & Do˘gan, 2003). A tilde ‘∼’ will be placed above a symbol if the symbol represents a fuzzy set. A triangular fuzzy number ˜ is shown in Figure 1. A TFN is denoted sim(TFN) M ply as (l/m,m/u) or (l,m,u). The parameters l, m and u (l ≤ m ≤ u),respectively, denote the smallest possible value, the most promising value, and the largest possible value that describe a fuzzy event. The membership function of triangular fuzzy numbers is as follows: Each TFN has linear representations on its left and right side, such that its membership function can be defined as: ⎧ 0, x < l, ⎪ ⎪ ⎨ (x − l)/(m − l), l ≤ x ≤ m, x [1] μ( M ˜ ) = (u − x)/(u − m), m ≤ x ≤ u, ⎪ ⎪ ⎩ 0, x > u.
1.0 M l(y)
0.0
Human Factors and Ergonomics in Manufacturing & Service Industries
M r(y)
l Figure 1
m
u
˜ A triangular Fuzzy Number M.
DOI: 10.1002/hfm
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An Application of the Fuzzy ELECTRE Method for Academic Staff Selection
A fuzzy number can always be given by its corresponding left and right representation of each degree of membership as in the following: ˜ = (M l(y) , M r(y) = (l + (m − l)y, u + (m − u)y), M y ∈ [0, 1]
[2]
where l(y) and r(y) denote the left side representation and the right side representation of a fuzzy number, respectively. Many ranking methods for fuzzy numbers have been developed in the literature. These methods may provide different ranking result, and most of them are tedious in graphic manipulation requiring complex mathematical calculation (Kahraman, Ruan & Ethem 2002). While there are various operations on triangular fuzzy numbers, only the important operations used in this study are illustrated. If we define two positive triangular fuzzy numbers (l1, m1, u1) and (l2, m2, u2), then (l1, m1, u1) + (l2, m2, u2) = (l1 + l2, m1 + m2, u1 + u2),
[3]
∗
(l1, m1, u1) (l2, m2, u2) = (l1∗ l2, m1 + m2, u1∗ u2),
[4]
(l1, m1, u1) + k = (l1∗ km1∗ k, u1∗ k), wherek > 0.
[5]
2.2. Steps of ELECTRE Method The ELECTRE (ELiminiation Et Traduisant la REalite) method was originated by Roy in the late 1960s. This method is based on the study of outranking relations using concordance and discordance indexes to analyze such relation among the alternatives. The concordance and discordance indexes can be viewed as measurements of dissatisfaction that a decision–maker uses in choosing one alternative over the other. Suppose an MCDM problem has m alternatives (A1 , A2 , . . . , Am ) and n decision criteria/attributes (C1 , C2 , . . . , Cn ). Each alternative is evaluated with respect to the n criteria/attributes. All the values/rating assigned to the alternatives with respect to each criterion form a decision matrix denoted byX = (xij )m×n . Let W = (w1 , w2 , . . . , wn ) bethe relative weight vector of the criteria, satisfying nj=1 wj = 1. Then, the ELECTRE method can be summarized as follows (Yoon & Hwang, 1995).
Normalise the decision matrix X = (xij )m×n by calculating, which represents the normalised criteria/attributes value/rating. 1/ xxij rij = m 1 i=1
xij2
For the minimisation objective, [6]
where i = 1, 2, . . . , m and j = 1, 2, . . . , n xıj rij = m
2 i=1 xij
For the maximisation objective, [7]
where i = 1, 2, . . . , m and j = 1, 2, . . . , n Calculate the weighted normalised decision matrix V = (vij )m×n vij = rij .wij ,
[8]
wherei = 1, 2, . . . , m and j = 1, 2, . . . , n, Where Wj is the relative weight of the j th criterion or attribute, and n
Wj = 1
[9]
j =1
Determine the concordance and discordance sets. For each pair of alternative Ap and Aq (p, q = 1, 2, . . . , m and, p = q), the set of criteria is divided into two distinct subsets. If the alternative Ap is preferred over alternative Aq for all the criteria, then concordance set is composed. This can be written as: C(p, q) = {j |vpj > vqj }
[10]
Where Vpj is the weighted normalised rating of the alternative Ap with respect to the jth criterion. In other words, C(p, q) is the collection of attributes where Ap is better than, or equal, to Aq . The complement of C(p, q), the discordance set, contains all the criteria for which Ap is worse than Aq . This can be written as D(p, q) = {j |vpj < vqj },
[11]
Calculate the concordance and discordance indexes. The concordance index of C(p, q) is defined as Wj ∗ , [12] Cpq = j∗
where j ∗ are the attributes contained in the concordance set C(p, q). The discordance index D(p, q) represents the degree of disagreement in (Ap → Aq ), and
Human Factors and Ergonomics in Manufacturing & Service Industries
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An Application of the Fuzzy ELECTRE Method for Academic Staff Selection
can be defined as
Then the normalised aggregated fuzzy importance ˜ = [w ˜ 2, w ˜ n ]. ˜ 1, w weight matrix is constructed as W
Dpq =
Rouyendegh and Erkan
j+
j
|νpj + − vqj + | |vpj − vqj |
[13]
,
Step 2. A decision matrix is formed as: ⎡
Where j + are the attributes contained in the discordance set D(p, q) and vij is the weighted normalised evaluation of the alternative i on criterion j . Outranking the relationships, this method the defines that Ap outranks Aq when Cpq ≥ C¯ and Dpq ≤ ¯ where C¯ and D ¯ are the averages of Cpq and Dpq , D, respectively.
3. THE FUZZY ELECTRE METHOD The basic steps of the fuzzy ELECTRE proposed be Sevkli (2010) can be described in the following way. Step 1. In the first step, a panel of decision- makers (DMs) knowledgeable in the field of staff selection is established. The group has k decision- makers (i.e, D1 , D2 , . . . , Dk ) responsible for the ranking (yj k ) of each criterion (i.e. C1 , C2 , . . . , Cn )in an increasing order. Then, the aggregated fuzzy importance weight for each criterion can be described as fuzzy trian˜ j = (lj , mj , uj ) for K = 1, 2, . . . , k gular numbers w and j = 1, 2, . . . , n. The aggregated fuzzy importance weight can be determined as follows:
X11 ⎢ X21 X=⎢ ⎣ ··· Xm1
⎤ · · · X1n · · · X21 ⎥ ⎥ ··· ··· ⎦ · · · Xmn
X12 X22 ··· Xm2
[16]
Step 3. After forming the decision matrix, normalisation is applied. The calculation is performed using formulae [6] and [7]. Then, the normalised decision matrix is obtained as ⎡ ⎤ r11 r12 · · · r1n ⎢ r21 r22 · · · r21 ⎥ ⎥ X=⎢ [17] ⎣· · · · · · · · · · · ·⎦ rm1 rm2 · · · rmn Step 4. Considering the different weights of each criterion, the weighted normalised decision matrix is computed by multiplying the importance weight of the evaluation criteria and the values in the normalised decision matrix. The weighted normalised decision matrix V˜ for each criterion is defined as V˜ = [˜vij ]m×n
for
j = 1, 2, . . . , n,
i = 1, 2, . . . , m and where
˜j. v˜ij = rij × w
and 1 yj k, lj = min{yj k } mj = k k
⎡
k
uj = max{yj k } k
k=1
[14] Then, the aggregated fuzzy importance weight for each criterion is normalised as:
···
1 v22
···
···
···
1 vm1
1 vm2
1 · · · vmn
2 v11
2 v12
···
2 v22
···
···
···
2 vm1
2 vm2
2 · · · vmn
3 v11
3 v12
···
3 v22
···
···
···
3 vm2
3 · · · vmn
⎢ 1 ⎢ v21 V =⎢ ⎢ ⎣··· 1
⎡ ˜ j = (wj 1 , wj 2 , wj 3 ), w
1 v12
1 v11
⎢ 2 ⎢ v21 V =⎢ ⎢ ⎣··· 2
Where wj 1 = n
1 /l
j =1
wj 3
4
j 1/ l
⎡
1 /m
j
1 uj = n 1 j =1 uj
j 1 /m j j =1
wj 2 = n
⎢ 3 ⎢ v21 V =⎢ ⎢ ⎣··· 3
[15]
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3 vm1
DOI: 10.1002/hfm
1 v1n
⎤
1 ⎥ v2n ⎥ ⎥, ⎥ ···⎦
2 v1n
⎤
2 ⎥ v2n ⎥ ⎥ ⎥ ···⎦
3 v1n
⎤
3 ⎥ v2n ⎥ ⎥. ⎥ ···⎦
[18]
Rouyendegh and Erkan
An Application of the Fuzzy ELECTRE Method for Academic Staff Selection
Here, v˜ij denote normalised positive triangular fuzzy numbers. Step 5. The concordance and discordance indexes are calculated for different weightes of each criterion (wj 1 , wj 2 , wj 3 ). The concordance index Cpq represents the degree of confidence in pair-wise - judgments (Ap → Aq ). The concordance index Cpq for the proposed model is defined as 1 2 2 Cpq = wj 1 , Cpq = wj 2, , Cpq = wj 3 , j∗
j∗
j∗
[19] Where J ∗ are the attributes contained in the concordance set C(p, q). Step 6. The discordance index, on the other hand, measures the power of D(p, q). The discordance index D(p, q), which represents the degree of disagreement in (Ap → Aq ), can be defined as 1 1 j + vpj + − vqj + 1 Dpq = 1 1 j vpj − vqj 2 2 − v v + + j + pj qj 2 Dpq = 2 v − v 2 j pj qj 3 3 v + − vqj + j + pj 3 Dpq [20] = 3 v − v 3 j
pj
qj
J+
Where are the attribute contained in the discordance set D(p, q), and vij is the weighted normalised evaluation of the alternative i on the criterion j. Step 7. The final concordance and discordance indexes are computed using the following formula: ∗ = Cpq
z
Z
z Cpq
z=1
∗ Dpq =
z
Z
z Dpq
z=1
Where,
Z = 3.
[21]
This formula can be considered as the defuzzification procedure. The dominance relationship of the alternative Ap over the alternative Aq becomes stronger with a larger final concordance index Cpq and a smaller final discordance indexDpq . The outranking relation is obtained by applying the following equation procedure to gain the kernel as the subset of the best alternatives: If
C(p, q) ≥ C¯
and
¯ D(p, q) ≥ D
[22]
¯ are the averages of Cpq and Dpq , Where C¯ and D respectively.
4. DETERMINING THE WEIGHTS OF THE FACTORS IN THE STAFF SELECTION MODEL In 2009, using ten criteria, one university in Turkey selected the best candidate among five others, all of whom had passed the initial examination. In this study, the objective is to determine the most eligible individual for a certain position. The decisive factors were classified into three main criteria; work factors, academic factors, and individual factors. These criteria are, again, divided into various sub-criteria, namely: Work factors: C1 = GRE and Foreign language, C2 = GPA - Bachelor degree, C3 = Oral Presentation. Academic factors: C4 = Academic Experience, C5 = Research Paper Writing, C6 = Technical Information, C7 = Team Work. Individual factors: C8 = Self Confidence, C9 = Compatibility, C10 = Age. The optimal staff selection chart appears in Figure 2. The weights of the criteria are calculated using a comparison matrix. Meanwhile, data is calculated from five experts’ decisions, shown in Table 1, and by calculating the normalised matrix, as Table 2, respectively. After that, the concordance and disconcordance sets are separated as in Table 3. Finally, the result and determination of the priorities of the candidates are extracted from Table 4 and Table 5. Finally, the result score is always, the-bigger-thebetter. As visible in Table 5, candidate 2 has the highest score due to its best choice. This is while candidate 5 has the lowest score and is, therefore, position in the last column. Other related results are also reflected in same Table 5. Obviously, the choice is candidate 2. Therefore, the result is:
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An Application of the Fuzzy ELECTRE Method for Academic Staff Selection
Rouyendegh and Erkan
Best Candidate
Work Factors
Academic Factors
Individual Factors
GRE and Foreign
Academic
language
Experience
GPA (Bachelor
Research Paper
Degree)
Writting
Oral Presentation
Information
Self Confidence
Compatibility
Technical Age
Team Work
Figure 2
Staff Selection Chart.
Candidate 2 Candidate 3 Candidate 1 Candidate 4 Candidate 5. We also Fuzzy ELECTRE method, and compared the results with Fuzzy AHP method. Fuzzy AHP approach and Fuzzy ELECTRE method propose the same candi-
date 2 as the best choice. They came from different theoretical backgrounds and relate differently to the discipline of multi-criteria decision-making. Because data needed for Fuzzy AHP and Fuzzy ELECTRE method approach are different, we do not necessarily expect to
TABLE 1. Determining the weights of criteria by comparison matrix (If X1 criteria is preferable over X2, we put “p”, otherwise, X.) Criteria
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
Weights
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
– X X X X X X X X X
P – X X X X X X X X
P P – X X X X X X X
P P P – X X X X X X
P P P P – X X X X X
P P P P P – X X X X
P P P P P P – X X X
P P P P P P P – X X
P P P P P P P P – X
P P P P P P P P P –
0,272727 0,136363 0,090909 0,081553 0,101942 0,058252 0,058252 0,074380 0,066116 0,059504
6
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TABLE 2. The normalised decision matrix
CA 1 CA 2 CA 3 CA 4 CA 5
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
0,049 0,146 0,016 0,146 0,049
0,098 0,033 0,011 0,011 0,033
0,055 0,011 0,004 0,033 0,033
0,049 0,029 0,010 0,003 0,029
0,015 0,015 0,015 0,005 0,077
0,001 0,002 0,035 0,021 0,021
0,001 0,002 0,035 0,021 0,021
0,029 0,049 0,010 0,010 0,010
0,027 0,045 0,003 0,002 0,003
0,004 0,004 0,011 0,033 0,033
TABLE 3. Stage of Concordance and Disconcordance sets
C12 C13 C14 C15 C23 C24 C25 C34 C35 C45
1
2
3
4
5
6
7
8
9
10
C
D
– 1 – 1 1 1 1 – – 1
1 1 1 1 1 1 1 1 – –
1 1 1 1 1 – – – – 1
1 1 1 1 1 1 1 1 – –
1 1 1 – 1 1 – 1 – –
– – – – – – – 1 1 1
– – – – – – – 1 1 1
– 1 1 1 1 1 1 1 1 1
– 1 1 1 1 1 1 1 1 –
1 – – – – – – – – –
2,3,4,5,10 1,2,3,4,5,8,9 2,3,4,5,8,9 1,2,3,4,8,9 1,2,3,4,5,8,9 1,2,4,5,8,9 1,2,4,8,9 2,4,5,6,7,8,9 6,7,8,9 1,3,6,7,8,10
1,6,7,8,9 6,7,10 1,6,7,10 5,6,7,10 6,7,10 3,6,7,10 3,5,6,7,10 1,3,10 1,2,3,4,5,10 2,4,5,9
TABLE 4. Determination of the Alternatives C12 C13 C14 C15 C23 C24 C25 C34 C35 C45 C21 C31 C41 C51 C32 C42 C52 C43 C53 C54
0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0
TABLE 5. Prioritizing Candidates 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0
Candidates First Candidate Second Candidate Third Candidate Fourth Candidate Fifth Candidate
Weight 1,11981 59,72175 32,19688 −26,2574 −118,248
natives by each method is very close to each other. This indicates that when the decision maker is consistent with himself in determining the data of each method independently, the ranking results will be necessarily the same. In fact, it was confirmed the same results, and second candidate was selected.
5. CONCLUSION have same result for the same personnel selection problem. But, in comparing the ranking derived by using Fuzzy AHP method and Fuzzy ELECTRE method, the best alternative is (candidate 2), and ranking of alter-
In this article, the role of intellectual values, and were examined, the potential key boundary conditions for the application of a multi-criteria recruitment framework in an academic context revealed.
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An Application of the Fuzzy ELECTRE Method for Academic Staff Selection
An MCDM is presented based on the fuzzy set theory in order to select the best candidate. In order to achieve consensus among the decision-makers, all pairwise comparisons were converted into triangular fuzzy numbers to adjust the fuzzy rating and the fuzzy attribute weight. The fuzzy set theory in the decisionmaking process implies that this practice,yet, is not absolute. Academic staff selection is a process that also contains uncertainties. This problem can be overcome by using fuzzy numbers and linguistic variables to achieve accuracy and consistency. In short, our analysis suggests that recruitment within an academic environment is a complex issue, thus human resources cannot be measured quantitatively using the traditional decision-making tools such as crisp ELECTRE. To overcome this deficiency, fuzzy numbers, can be applied to make accurate and consistence decisions by reducing subjective assessment. The main contribution of this study lies in the application of a fuzzy approach to the academic staff selection decision - making processes, drawing on an actual case in human resources. Using the appropriate MCDM tools, this study deals with one of the most important subjects in the field of human resources managment, allowing for more objective decisons. Fuzzy set theory is capable of dealing with uncertainty. ELECTRE is one of the decision making method based on pair wise comparison. The advantages of the Fuzzy ELECTRE method for staff selection problem, more research is called for within the context of studying a more complex staff selection with multiple criteria as well as investigating other MCDM to find the optimum staff selection solution. In this study, we tried to design a multi-criteria decisionmaking model based on fuzzy set theory to select the most adequate person. Unlike other decision methods, this method can adaptively find a suitable person for the job. As for future work, it is suggested that other multicriteria approaches - such as, the fuzzy analytic network process and PROMETHEE outranking methods be applied and compared in staff selection and recruitment procedures. References Almeida, A. T. (2007). Multicriteria decision model for outsourcing contracts selection based on utility function and ELECTRE. Computers & Operations Research, 34 (12), 3569–3574. 8
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Human Factors and Ergonomics in Manufacturing & Service Industries
DOI: 10.1002/hfm
9
