Revista de Matema´tica: Teor´ıa y Aplicaciones 2011 18(1) : 177–192
cimpa – ucr issn: 1409-2433
personnel selection based on
fuzzy methods
seleccio´n de personal basada en
me´todos difusos∗
Lourdes Cano´s† Trinidad Casasu´s‡ Enric Crespo§
Toma´s Lara¶ Juan C. Pe´rez‖
Received: 18 Feb 2010; Revised: 10 Sep 2010; Accepted: 18 Nov 2010
Abstract
The decisions of managers regarding the selection of staff strongly
determine the success of the company. A correct choice of employees
is a source of competitive advantage. We propose a fuzzy method for
staff selection, based on competence management and the compari-
son with the valuation that the company considers the best in each
competence (ideal candidate). Our method is based on the Hamming
∗This work has been partially supported by the project TIN2008-06872-C04-02 from
the Ministerio de Ciencia e Innovacio´n of Spain.
†Departamento de Organizacio´n de Empresas, Universidad Polite´cnica de Valencia,
Valencia, Spain. E-Mail: loucada@omp.upv.es
‡Departamento de Matema´ticas para la Economı´a y la Empresa, Universitat de Va-
lencia, Valencia, Spain. E-Mail: trinidad.casasus@uv.es
§Misma direccio´n que/same address as T. Casasu´s. E-Mail: enric.crespo@uv.es
¶Human Resources Manager, Faurecia, Valencia, Spain. E-Mail:
tomas.lara@faurecia.com
‖IES Andreu Sempere, Valencia, Spain. E-Mail: jcpc4655@telefonica.net
177
178 l. cano´s – t. casasu´s – e. crespo – t. lara – j.c. pe´rez
distance and a Matching Level Index. The algorithms, implemented
in the software StaffDesigner, allow us to rank the candidates, even
when the competences of the ideal candidate have been evaluated
only in part. Our approach is applied in a numerical example.
Keywords: fuzzy sets, personnel selection, management competences.
Resumen
Las decisiones de los directivos en cuanto a la seleccio´n de per-
sonal determinan en gran medida el e´xito de la empresa. Una eleccio´n
adecuada de los empleados proporciona una ventaja comparativa.
Proponemos un me´todo borroso para la seleccio´n de personal basado
en la gestio´n de competencias y la comparacio´n con la valoracio´n
que la empresa considera ma´s adecuada para cada trabajo (el can-
didato ideal). Nuestro me´todo utiliza la distancia de Hamming y
el Matching Level Index. Los algoritmos, implementados con el soft-
ware StaffDesigner, nos permite establecer un ranking de candidatos,
incluso cuando las competencias del candidato ideal han sido evalua-
das tan solo en parte. Nuestro enfoque esta´ aplicado en un ejemplo
nume´rico.
Palabras clave: conjuntos borrosos, conjuntos difusos, seleccio´n de per-
sonal, gestio´n de competencias.
Mathematics Subject Classification: 03B52, 68T37, 90B50.
1 Introduction
Nowadays, employees are considered strategic factors and a source of com-
petitive advantage towards generating long run sustainable profits. This
is the reason because the strategic management of human resources has
become a priority interest of firms. The objective is to have workers per-
fectly suited to their jobs (Pen˜a Bazta´n, 1990). As a result, workers will
perform excellently, not just satisfactorily, and this will give the company
advantage over competitors.
Following the papers of Spencer and Spencer (1993) and Boyatzis (1982),
we understand competence as individual knowledge, skills, attitudes and
behaviors that result in workers performing certain tasks and duties re-
markably well. Competences encompass not only knowledge and expe-
rience, but also other human attributes, objective and subjective, more
general and more complex (Cano´s & Liern, 2003).
The process usually begins by identifying the competences, their valu-
ation and the benchmark profile of these competences. Competences help
to use a common language in the firm, because as they take into account
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
personnel selection based on fuzzy methods 179
observable behavior it is easier for the human resource managers and the
other managers to agree (Hayes et al., 2000).
This approach makes the comparison between the requirement profile
of the job and the competence profile of the candidate, by taking as unit
of analysis the individual and not only the work job (Pereda & Berrocal,
1999).
A specific model per firm is implemented in a way that works with
a continuous feedback. The quantification difficulties must be taken into
account, because standard indicators could not be useful in this case given
human nature. Our proposal can be used in the acquisition policies as
well as in the developing policies, even when the target is to respect the
existing jobs.
In this paper we give a short introduction to management by com-
petences, model that we will use as basis for the proposed algorithms of
personnel selection. We propose a method to help in the managers’ deci-
sion, when the ideal competences associated to the offered job are defined.
We apply the method for the case of a development policy in a given firm.
2 Application of fuzzy techniques to human
resources management
In order to quantify and objectify the human resource variables, Math-
ematic Programming techniques are often required to back up decision
making and to help managers for carrying out their job as decision mak-
ers. However, the enormous number of interactions current firms are sub-
jected to, and how quickly they occur, as well as the uncertainty of many
of the available data they use, result in deterministic mathematics being
insufficient.
On one hand, to consider all the information the experts have, included
the subjective one, can provide benefits. On the other hand, in any de-
cision making process, the used mathematical model will be affected by
the introduced numerical values. Some times it is possible to assign prob-
ability distribution to some parameters (stochastic uncertainty), but some
times, this method is inappropriate, because there is no well-founded rea-
son to assume that the given parameter is following a specific distribution.
In that case we will speak about fuzzy uncertainty (Zimmermann, 1997,
Carlsson & Korhonen, 1986).
In Fuzzy Theory the basic idea is to substitute the characteristic func-
tion of a set A, which assigns the value 1 when the element belongs to A
and 0 when it does not, by a Membership Function µA which associates
each element to a real number in the interval [0, 1]. The value µA(x) is
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
180 l. cano´s – t. casasu´s – e. crespo – t. lara – j.c. pe´rez
understood as the membership degree of the element x in A (Kaufmann
& Gil-Aluja, 1987). A null membership degree is understood as not mem-
bership, 1 is understood as full membership in the Boolean sense, and the
intermediate values reflect an uncertainty membership (one speak of par-
tial membership) that will be interpreted in different ways, depending on
the case (Zadeh, 1965, Goguen, 1969).
If we consider the referential set X, a common representation of fuzzy
sets is the following:
A˜ = {(x, µA(x), x ∈ X)}.
Fuzzy Theory has been applied to the Human Resources Management in
various cases. Despite the variety of cases that can be represented by fuzzy
sets, when the value of µA(x) has to be given by one or many experts, one
way to make the job of the experts that must valuate easier is to extend
the concept of fuzzy set, by admitting µA(x) to be a tolerance interval,
this is, a multivaluated membership function
µΦ : X → P ([0, 1]),
given by µΦ(x) = [a1x, a2x] ⊆ [0, 1]. The set A˜Φ = {(x, µΦ(x)), x ∈ X} is
called interval- valued fuzzy set (Gil-Aluja, 1998). In general, when the
referential set is finite, X = {x1, x2, . . . , xn}, the way to express it uses to
be
A˜Φ = {(xj , µΦ(xj)), j = 1, . . . , n}. (1)
In this paper we will assume the competences, the ideal competences, as
well as the candidates’ competences, are valuated with intervals, so we will
handle the uncertainty by using interval-valued fuzzy sets or Φ-fuzzy. The
fuzzy processing for Human Resources Management has the difficulty of
using a suitable distance function (Chen & Cheng, 2005) and the difficulty
of ordering fuzzy sets according to that distance (Capaldo & Zollo, 2001).
2.1 Measuring distances to an ideal candidate
In order to valuate and rank the candidates for a job, we will study the
similarity among each candidate and the ideal candidate (the virtual can-
didate whose competences have the highest valuation given by the experts)
in two different ways, by means of the Hamming distance and by using a
Matching Level Index (Dubois & Prade, 2000).
One way of ordering the candidates is to calculate the distance from
each of them to the ideal candidate. Other definitions of distance can be
considered (Euclidean, Tchebichev, etc.) to select the “best fit”, but the
Hamming distance has recorded favorable results in ordering fuzzy sets in
the literature (Gil-Aluja, 1998).
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
personnel selection based on fuzzy methods 181
Definition 1 Given a reference set X = {x1, x2, . . . , xn} and two interval-
valued fuzzy numbers Φ-fuzzy A˜Φ, B˜Φ, whose membership functions are
µΦ
A˜
(xj) = [a1xj , a
2
xj ], µ
Φ
B˜
(xj) = [b1xj , b
2
xj ], j = 1, 2, . . . , n, the normalized
Hamming distance is defined as
d(A˜Φ, B˜Φ) =
1
n
 n∑
j=1
|µΦ
A˜
(xj)− µΦB˜(xj)|

=
1
2n
 n∑
j=1
(|a1xj − b1xj |+ |a2xj − b2xj |)
 . (2)
Definition 2 Given a reference set X = {x1, x2, . . . , xn} and two interval-
valued fuzzy numbers A˜Φ, B˜Φ, whose membership functions are µΦ
A˜
(xj),
µΦ
B˜
(xj), j = 1, 2, . . . , n, the matching level index of the interval-valued
fuzzy number B˜Φ with respect to the interval-valued fuzzy number A˜Φ is
defined as
µA˜Φ(B˜
Φ) =
1
n
n∑
j=1
µ
xj
A˜Φ
(B˜Φ)
where
µ
xj
A˜Φ
(B˜Φ) =

1 if [b1xj , b
2
xj ] ⊆ [a1xj , a2xj ]
length([b1xj ,b
2
xj
]∩[a1xj ,a2xj ])
length([b1xj ,b2xj ]∪[a1xj ,a2xj ])
if [b1xj , b
2
xj ] 6⊆ [a1xj , a2xj ].
(3)
3 Our problem
By personnel selection we understand the process through one or several
people that better fit the characteristics of a job are chosen. As in the most
cases of management, this process is complicated and it must be taken into
account concepts as validation, reliance and fixing of approach.
Specifically, if we consider a job with n appropriated competences, that
we will denote as our referential finite set X = {c1, c2, . . . , cn}, and we have
R possible candidates, Cand = {P1, P2, . . . , PR}, to fill the job, the selec-
tion should be done by evaluating each candidate in the n competences.
This evaluation can be understood as the membership degree to a fuzzy
set or Φ-fuzzy set (Cano´s & Liern, 2008).
Let’s assume the R candidates have been valuated in the n competences
by a set of p experts, Exp = {E1, E2, . . . , Ep}, and the valuation of each
competence and each expert has been done with intervals. The way to fix
the extremes of the intervals is very important. First, it should be easy
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
182 l. cano´s – t. casasu´s – e. crespo – t. lara – j.c. pe´rez
for the experts to express and quantify their valuation. Second, it must be
clear enough to differentiate among the given valuations. In our case, we
propose values between 0 and 1, taken with one figure. This is, 11 different
values to build the intervals. In some cases could be excessive, but we have
checked that an odd number of values, 7 or 9, are adequate.
Once established that point, the firm managers have to fix the most
suitable valuation of each competence. In this way, the ideal candidate for
the firm is defined. The way to define the ideal candidate is done by means
of intervals valuated by other (or the same) set of experts. An applicant
will fill better the job as much “similar” to the given ideal candidate is.
Definition 3 A fuzzy number M˜ is said to be a LR-fuzzy number,
M˜ = (mL,mR, αL, αR)LR
if its membership function has the following form:
µM˜ =

L
(
mL−x
αL
)
if x < mL
1 if mL < x < mR
R
(
x−mR
αR
)
if x > mR
(4)
where L and R are reference functions, i.e. L,R : [0,+∞[→ [0, 1] are
strictly decreasing in suppM˜ = {x : µM˜ (x) > 0} and upper semi-continuous
functions such that
L(0) = R(0) = 1.
If suppM˜ is a bounded set, L and R are defined on [0, 1] and satisfy L(1) =
R(1) = 0. If there exist an inverse for the functions L and R, the α-cuts
are:
M(α) = [M1(α),M2(α)] = [mL − αLL−1(α),mR + αRR−1(α)], α ∈ [0, 1].
In particular, when L and R are linear functions, we are
M(α) = [M1(α),M2(α)] = [mL − αLα,mR + αRα], α ∈ [0, 1].
In this paper our interest is, not only to obtain intervals (α-cuts) from a
fuzzy number, but also the inverse process, this is, to build fuzzy numbers
from the aggregation of intervals. The following lemma gives us the way
to do it.
Lemma 1 Let us consider h intervals {[a1r , a2r ], 1 ≤ r ≤ h} and two refer-
ence functions L,R : [0,+∞[→ [0, 1]. Given the values
mL = min
r
a1r + a
2
r
2
,mR = max
r
a1r + a
2
r
2
,ML = min
r
a1r,M
R = max
r
a2r,
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
personnel selection based on fuzzy methods 183
αL = mL −ML, αR = mR −MR,
M˜ = (mL,mR, αL, αR)LR is a LR-fuzzy number and the intervals [mL,mR]
and [ML,MR] are the peak and support, respectively, of M˜ .
4 Personnel selection model
In the models we are going to work with, the selection is based on n
necessary competences for occupying one job. Our referential set is the set
of competences
X = {c1, c2, . . . . , cn},
and each candidate will be valuated on them. Let’s assume p experts who
valuate all candidates on the n competences through intervals.
One very used way for ordering the candidates is to compare them
with an ideal candidate (Gil-Aluja, 1998, Cano´s et al., 2008, Cano´s &
Liern, 2008). Bigger is the intersection among the candidate and the ideal,
more suitable is the candidate for the job (Gil-Aluja, 1998). Depending on
the job, it would be possible to assign different weights to the competences,
although in this paper we will assume all the competences weighted in a
similar way. The process to follow is similar in any case.
The Hamming distance calculates the difference between the extremes
of the intervals. In this method there is no difference between one excess or
one defect with respect to the ideal, so we evaluate both in a similar way.
In case of the Matching Level Index, it implicitly includes an adjustment
of the excesses or defects. This is the reason because these two techniques
can give different results to the same process of personnel selection.
4.1 Comparison with the ideal candidate
As we have seen above, for each α ∈ [0, 1] we have R Φ-fuzzy numbers,
P˜Φi (α), 1 ≤ i ≤ R, which represent each one of the candidates, and another
one, I˜Φ(α), which represents the ideal candidate. The goal is to measure
the distance or the similarity of each one of the candidates to the ideal
one, by applying the Hamming distance or the Matching Level Index, this
is
di(α) = d(P˜Φi (α), I˜
Φ(α)), 1 ≤ i ≤ R (5)
where d represents the Hamming distance (Definition 1) or the Matching
Level Index (Definition 2). The process we have followed is given in the
scheme showed in Figure 1.
When the set of real numbers {di(α)}Ri=1 is ordered, the candidates are
ordered for the level α of requirement. If we repeat this process for values
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
184 l. cano´s – t. casasu´s – e. crespo – t. lara – j.c. pe´rez
Valuation of the competences
of the i-th candidate
{c˜i1, c˜i2, . . . , c˜in}
'
&
$
%
Valuation of competences
of the ideal candidate
{I˜1, I˜2, . . . , I˜n}
'
&
$
%
For each α
0 ≤ α ≤ 1

ffi
fi
fl
⇓
P˜Φi (α) =
{
(cij , [c1ij(α), c
2
ij(α)]), j = 1, . . . , n
}
I˜Φ(α) =
{
(cj , [I1j (α), I
2
j (α)]), j = 1, . . . , n
}
'
&
$
%
⇓
d(P˜Φi (α), I˜
Φ(α))
ff



Figure 1: Scheme for the comparison of the candidates with the ideal one.
α ∈ [0, 1] which are of interest for the decisor, we have an order of the
candidates in different cases.
In general, it is possible to offer to the Human Resources Department
of the firm different rankings of candidates for different levels of demand
α ∈ [0, 1]. Each level of demand determines a final position of the candi-
dates, because the level of requirement could change the valuation of one
candidate, depending on his/her situation inside or outside of the stab-
lished level of requirement.
4.2 The algorithm
According to what has been stated above, we have built the following
algorithm:
Step 1. Construct a fuzzy number for each one of the competences for
the ideal candidate, {I˜1, I˜2, .., I˜n}, given the valuation of q experts.
Step 2. Construct a fuzzy number for each one of the competences for
each candidate, {c˜i1 , c˜i2 , . . . , c˜in}, from the valuation of p experts.
Step 3. For each one of the competences, and given an exigency level
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
personnel selection based on fuzzy methods 185
α ∈ [0, 1], construct interval-valued fuzzy numbers for each candidate
and for the ideal candidate:
P˜Φi (α) =
{
cij , [c1ij(α), c
2
ij(α)], 1 ≤ j ≤ n
}
, i = 1, 2, . . . , R
I˜Φ(α) =
{
(cj , [I1j (α), I
2
j (α)]), 1 ≤ j ≤ n
}
Step 4. For the chosen exigency level α ∈ [0, 1], compare each candidate
to the ideal candidate,
di(α) = d(P˜Φi (α), I˜
Φ(α)), 1 ≤ i ≤ R
Step 5. Order candidates for the exigency level α.
Step 6. Repeat steps 2, 3, 4, and 5 for different values of α.
Step 7. The company chooses the exigency level and selects the most
suitable candidate.
5 Computational proof
In our example, we consider n = 5 competences, k = 20 candidates, p = 4
experts who valuate the candidates’ competences and q = 1 expert (we
are assuming that the firm has totally defined the requirements of the
ideal candidate, the generalization to several experts for determining the
ideal candidate would not have influence on the proposed method) who
has valuated the ideal competences required for the job. We consider this
number of candidates (20), because the managers confirmed us that these
kind of tools are very useful when the number of applicants is high and
they face up a duty of ranking them.
We will consider 11 values for α, α ∈ {0, 0.1, 0.2, . . . , 0.9, 1}.
5.1 Competences of the ideal candidate
The valuation of competences of the ideal candidate, given by the expert
of the firm, is shown in table 1.
In this valuation the opinion of the experts about the competences of
an ideal candidate not always gives the value 1 to the highest value. This
would mean that the expert could consider not necessary for the candidate
to have the highest performance in this competence.
5.2 Valuation of the competences of the candidates
The valuation given by each expert, about the competences of each candi-
date are shown in Tables 2, 3, 4 and 5.
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
186 l. cano´s – t. casasu´s – e. crespo – t. lara – j.c. pe´rez
Low value Highest value
Competence 1 0.65 0.70
Competence 2 0.80 1.00
Competence 3 0.50 0.80
Competence 4 0.80 0.85
Competence 5 0.50 0.90
Table 1: Valuation of the ideal candidate competences.
Expert 1 Expert 2 Expert 3 Expert 4
L H L H L H L H
C
an
di
da
te
1 Comp. 1 0.3 0.65 0.3 0.8 0.35 0.8 0.7 1
Comp. 2 0.2 0.7 0.7 0.9 0.4 0.6 0.35 0.6
Comp. 3 0.35 0.5 0.5 0.7 0.25 0.9 0.4 0.8
Comp. 4 0.4 0.8 0.5 0.6 0.35 0.9 0.25 0.65
Comp. 5 0.15 0.55 0.5 0.6 0.35 0.9 0.25 0.65
C
an
di
da
te
2 Comp. 1 0.25 0.6 0.25 0.7 0.4 0.8 0.35 0.7
Comp. 2 0.35 0.8 0.35 0.6 0.3 0.6 0.7 0.8
Comp. 3 0.4 0.6 0.4 0.5 0.7 0.8 0.35 0.7
Comp. 4 0.45 0.75 0.5 0.8 0.35 0.8 0.4 0.6
Comp. 5 0.5 0.7 0.5 0.8 0.35 0.8 0.4 0.6
C
an
di
da
te
3 Comp. 1 0.25 0.7 0.35 0.7 0.3 0.55 0.5 0.9
Comp. 2 0.35 0.65 0.3 0.6 0.4 0.7 0.2 0.7
Comp. 3 0.3 0.55 0.5 0.9 0.6 0.85 0.35 0.65
Comp. 4 0.4 0.9 0.6 0.85 0.25 0.7 0.35 0.6
Comp. 5 0.55 0.75 0.5 0.7 0.35 0.6 0.3 0.65
C
an
di
da
te
4 Comp. 1 0.6 0.8 0.5 0.7 0.4 0.6 0.7 0.7
Comp. 2 0.7 0.9 0.8 1 0.9 0.95 0.8 1
Comp. 3 0.35 0.8 0.6 0.9 0.5 0.8 0.7 0.7
Comp. 4 0.75 0.8 0.85 0.85 0.8 0.8 0.8 0.85
Comp. 5 0.5 0.9 0.6 0.8 0.7 0.7 0.5 0.8
C
an
di
da
te
5 Comp. 1 0.25 0.6 0.25 0.7 0.4 0.8 0.35 0.7
Comp. 2 0.35 0.8 0.35 0.6 0.3 0.5 0.7 0.8
Comp. 3 0.3 0.7 0.4 0.5 0.7 0.8 0.35 0.7
Comp. 4 0.5 0.6 0.5 0.8 0.02 0.7 0.3 0.6
Comp. 5 0.6 0.65 0.5 0.8 0.2 0.8 0.3 0.6
Table 2: Valuation of the candidates 1–5.
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
personnel selection based on fuzzy methods 187
Expert 1 Expert 2 Expert 3 Expert 4
L H L H L H L H
C
an
di
da
te
6 Comp. 1 0.25 0.55 0.3 0.7 0.2 0.9 0.5 0.7
Comp. 2 0.35 0.7 0.5 0.6 0.35 0.7 0.2 0.8
Comp. 3 0.5 0.65 0.35 0.5 0.35 0.9 0.35 0.55
Comp. 4 0.5 0.6 0.3 0.45 0.3 0.5 0.3 0.7
Comp. 5 0.45 0.9 0.4 0.55 0.4 0.5 0.4 0.7
C
an
di
da
te
7 Comp. 1 0.25 0.45 0.25 0.7 0.3 0.55 0.35 0.7
Comp. 2 0.35 0.55 0.35 0.6 0.5 0.7 0.3 0.8
Comp. 3 0.3 0.7 0.3 0.45 0.2 0.7 0.3 0.9
Comp. 4 0.5 0.65 0.3 0.6 0.35 0.6 0.4 0.7
Comp. 5 0.3 0.9 0.5 0.9 0.35 0.65 0.35 0.7
C
an
di
da
te
8 Comp. 1 0.25 0.5 0.25 0.65 0.3 0.6 0.35 0.6
Comp. 2 0.35 0.45 0.35 0.6 0.4 0.65 0.3 0.65
Comp. 3 0.3 0.75 0.4 0.5 0.6 0.9 0.4 0.6
Comp. 4 0.4 0.55 0.35 0.8 0.25 0.7 0.6 0.9
Comp. 5 0.6 0.7 0.3 0.8 0.35 0.55 0.3 0.7
C
an
di
da
te
9 Comp. 1 0.25 0.65 0.4 0.45 0.2 0.9 0.4 0.7
Comp. 2 0.35 0.9 0.3 0.55 0.35 0.7 0.2 0.55
Comp. 3 0.25 0.5 0.5 0.6 0.7 0.9 0.35 0.9
Comp. 4 0.55 0.6 0.5 0.9 0.12 0.7 0.7 0.9
Comp. 5 0.6 0.75 0.35 0.8 0.2 0.6 0.12 0.7
C
an
di
da
te
10 Comp. 1 0.5 0.5 0.3 0.3 0.55 0.55 0.7 0.7
Comp. 2 0.35 0.65 0.4 0.45 0.5 0.7 0.3 0.8
Comp. 3 0.3 0.7 0.6 0.85 0.65 0.65 0.7 0.7
Comp. 4 0.6 0.6 0.7 0.7 0.35 0.6 0.3 0.55
Comp. 5 0.35 0.5 0.5 0.65 0.35 0.8 0.4 0.7
C
an
di
da
te
11 Comp. 1 0.1 0.9 0.2 0.9 0.4 0.6 0.25 0.8
Comp. 2 0.35 0.5 0.6 1 0.25 0.9 0.35 0.7
Comp. 3 0.45 0.6 0.35 0.8 0.6 0.8 0.4 0.6
Comp. 4 0.65 0.9 0.8 1 0.3 0.6 0.9 1
Comp. 5 0.65 0.9 0.8 1 0.3 0.6 0.2 0.6
C
an
di
da
te
12 Comp. 1 0.25 0.6 0.25 0.65 0.4 0.6 0.4 0.9
Comp. 2 0.35 0.55 0.35 0.6 0.3 0.65 0.6 0.97
Comp. 3 0.25 0.7 0.4 0.5 0.2 0.9 0.3 0.7
Comp. 4 0.5 0.9 0.5 0.8 0.35 0.7 0.4 0.9
Comp. 5 0.6 0.7 0.5 0.8 0.2 0.55 0.2 0.7
Table 3: Valuation of the candidates 6–11.
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
188 l. cano´s – t. casasu´s – e. crespo – t. lara – j.c. pe´rez
Expert 1 Expert 2 Expert 3 Expert 4
L H L H L H L H
C
an
di
da
te
13 Comp. 1 0.25 0.55 0.25 0.45 0.4 0.9 0.35 0.9
Comp. 2 0.35 0.7 0.3 0.6 0.3 0.7 0.7 0.9
Comp. 3 0.35 0.65 0.5 0.9 0.5 0.9 0.22 0.7
Comp. 4 0.5 0.9 0.35 0.65 0.3 0.5 0.2 0.6
Comp. 5 0.4 0.5 0.3 0.8 0.25 0.7 0.3 0.55
C
an
di
da
te
14 Comp. 1 0.4 0.55 0.4 0.7 0.35 0.6 0.5 0.7
Comp. 2 0.35 0.7 0.6 0.65 0.2 0.7 0.3 0.7
Comp. 3 0.3 0.9 0.4 0.45 0.35 0.65 0.4 0.9
Comp. 4 0.4 0.5 0.5 0.55 0.6 0.65 0.35 0.7
Comp. 5 0.6 0.65 0.5 0.7 0.25 0.8 0.3 0.6
C
an
di
da
te
15 Comp. 1 0.25 0.6 0.25 0.65 0.35 0.55 0.4 0.65
Comp. 2 0.35 0.8 0.35 0.6 0.3 0.7 0.6 0.9
Comp. 3 0.35 0.7 0.3 0.5 0.5 0.6 0.25 0.7
Comp. 4 0.5 0.55 0.5 0.8 0.04 0.75 0.35 0.9
Comp. 5 0.45 0.7 0.6 0.65 0.2 0.65 0.3 0.7
C
an
di
da
te
16 Comp. 1 0.25 0.65 0.25 0.9 0.2 0.6 0.4 0.7
Comp. 2 0.35 0.9 0.35 0.45 0.35 0.65 0.7 0.9
Comp. 3 0.2 0.5 0.4 0.55 0.7 0.75 0.06 0.7
Comp. 4 0.5 0.6 0.5 0.7 0.3 0.6 0.2 0.6
Comp. 5 0.6 0.65 0.5 0.65 0.5 0.55 0.3 0.9
C
an
di
da
te
17 Comp. 1 0.1 0.9 0.2 0.9 0.4 0.6 0.25 0.8
Comp. 2 0.35 0.5 0.6 1 0.25 0.9 0.35 0.7
Comp. 3 0.4 0.6 0.35 0.8 0.6 0.8 0.4 0.6
Comp. 4 0.55 0.85 0.8 0.95 0.3 0.6 0.8 1
Comp. 5 0.65 0.85 0.8 0.95 0.3 0.6 0.2 0.6
C
an
di
da
te
18 Comp. 1 0.25 0.5 0.6 0.7 0.6 0.75 0.4 0.9
Comp. 2 0.35 0.8 0.35 0.65 0.25 0.7 0.6 0.7
Comp. 3 0.25 0.7 0.4 0.6 0.35 0.6 0.25 0.6
Comp. 4 0.5 0.6 0.5 0.9 0.04 0.6 0.35 0.65
Comp. 5 0.6 0.9 0.3 0.8 0.2 0.8 0.2 0.9
C
an
di
da
te
19 Comp. 1 0.25 0.55 0.3 0.7 0.2 0.9 0.5 0.7
Comp. 2 0.35 0.9 0.35 0.45 0.35 0.65 0.7 0.9
Comp. 3 0.35 0.7 0.3 0.5 0.5 0.6 0.25 0.7
Comp. 4 0.4 0.5 0.5 0.55 0.6 0.65 0.35 0.7
Comp. 5 0.5 0.9 0.5 0.9 0.5 0.9 0.5 0.9
Table 4: Valuation of the candidates 12–19.
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
personnel selection based on fuzzy methods 189
Expert 1 Expert 2 Expert 3 Expert 4
L H L H L H L H
C
an
di
da
te
20 Comp. 1 0.25 0.6 0.4 0.65 0.4 0.6 0.5 0.7
Comp. 2 0.35 0.9 0.6 0.65 0.3 0.65 0.2 0.95
Comp. 3 0.3 0.5 0.3 0.6 0.5 0.9 0.35 0.7
Comp. 4 0.35 0.7 0.5 0.9 0.3 0.7 0.35 0.7
Comp. 5 0.45 0.45 0.5 0.5 0.5 0.5 0.7 0.7
Table 5: Valuation of the candidate 20.
5.3 Solutions for various levels of exigency
We show the results obtained by columns in Table 6. Each one of them
represents the candidates ordered from the best to the worst, and it is
obtained for a given value of α, where α = 0, 0.1, 0.2, . . . , 1, respectivly.
α
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
The best 4 4 4 4 4 4 4 4 4 4 4
17 17 17 17 11 11 20 20 11 11 11
19 11 11 11 17 17 11 11 20 20 17
11 19 19 19 19 19 17 17 17 17 19
6 6 6 6 6 6 19 19 19 19 20
20 20 20 20 10 3 3 10 10 10 10
2 2 2 2 2 10 10 3 3 3 3
1 1 1 1 12 2 9 9 9 9 9
12 12 12 12 3 12 6 2 2 2 13
16 10 7 10 20 9 2 6 13 13 18
10 7 10 3 1 1 1 12 5 5 2
7 16 13 7 9 8 12 1 1 18 5
13 13 16 8 8 7 14 5 12 1 1
5 9 3 9 7 14 7 7 18 12 12
9 5 9 13 14 20 5 14 6 7 7
14 14 8 14 5 5 8 13 7 14 14
8 3 5 5 13 13 13 18 14 8 8
3 8 14 16 16 18 18 8 8 6 16
18 18 18 18 18 16 16 16 16 16 6
The worst 15 15 15 15 15 15 15 15 15 15 15
Table 6: Selection of candidates using the Matching Level Index.
In Table 7 we show the results obtained using the Hamming distance.
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
190 l. cano´s – t. casasu´s – e. crespo – t. lara – j.c. pe´rez
α
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
The best 4 4 4 4 4 4 4 4 4 4 4
2 2 20 20 20 11 11 11 11 11 11
19 20 2 2 2 20 17 17 17 17 17
20 19 19 19 11 17 2 19 19 19 19
10 10 10 10 19 2 20 2 2 2 2
7 7 17 17 10 19 19 10 10 12 3
12 17 11 11 17 10 10 20 12 10 12
6 12 12 12 12 12 12 12 20 3 9
17 11 7 7 14 14 14 3 3 9 18
14 14 14 14 7 8 3 14 9 20 10
11 6 8 8 8 7 1 9 14 14 14
8 8 6 6 6 3 9 1 1 18 5
13 13 13 13 1 1 8 13 18 1 20
5 1 1 1 3 6 13 18 5 5 1
16 5 5 3 13 13 7 5 13 13 13
1 16 3 5 5 9 18 8 16 16 16
15 15 16 16 9 5 5 7 8 15 15
3 3 15 15 18 18 6 16 15 8 8
18 18 18 18 15 16 16 6 7 7 7
The worst 9 9 9 9 16 15 15 15 6 6 6
Table 7: Selection of candidates using the Hamming distance.
6 Conclusions
Human Resources are considered an important source of competitive ad-
vantage in any company. One way companies can profit from these re-
sources is through competence management.
From one side, the use of mathematical models in decision making pro-
vide some advantages as the obtaining of clear and quick solutions which
are easy to understand. From the other side, the difficulties appear be-
cause, in general, mathematical models are objectives and quantify figures
difficult to relate with this topics. To avoid these problems, we use Fuzzy
Sets Theory which allows adding uncertainty and subjectivity to the prob-
lem. To represent accurately real life by a model is a hard work. The fuzzy
logic does not add difficulty to traditional mathematics and it is closer to
human thought. Fuzzy Theory allows avoiding the requirements of rigidity
which could do a model not to make sense and it provides us with ignoring
solutions that could be useful. In the personnel selection process an inflex-
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(1): 177–192, January 2011
personnel selection based on fuzzy methods 191
ible treatment of valuations of candidates can interfere with the ordering
process because it does not consider all the necessary requirements. Also,
a global valuation neutralizes positive valuation of competences with neg-
ative ones, being not fair. We propose a personnel selection model flexible
and complementary, useful to order applicants to a post. Moreover, the use
of intervals provides the expert with great flexibility to decide the suitable
valuation in each case.
We emphasize in our practical case, as well as in any other, that it
would be very risky to decide, not only the best candidate. But also an
absolute and certain order of all candidates. Clearly, from the obtained
results, the method point out the applicants more qualified and that less
qualified. Our three preferred candidates would be P4, P11, and P20, and
any one of them would be a good choice for the firm, but manager could
add other specific requirements of the firm, outside of the method, to take
the final decision. In the same way, the Human Resources Manager could
add some specific conditions to decide the final order.
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