Multicriteria decision making (MCDM) is one of the methods that popularly has been used in solving personnel selection problem. Alternatives, criteria, and weights are some of the fundamental aspects in MCDM that need to be defined clearly in order to achieve a good result. Apart from these aspects, fuzzy data has to take into consideration that it may arise from unobtainable and incomplete information. In this paper, we propose a new approach for personnel selection problem. The proposed approach is based on Hamming distance method with subjective and objective weights (HDMSOW’s). In case of vagueness situation, fuzzy set theory is then incorporated onto the HDMSOW’s. To determine the objective weight for each attribute, the fuzzy Shannon’s entropy is considered. While for the subjective weight, it is aggregated into a comparable scale. A numerical example is presented to illustrate the HDMSOW’s.
The rapid growth in globalization had created an intense competition between modern firms in global markets. These situations had urged the organization and firms to establish a comprehensive procedure during personnel selection process. The personnel selection can be defined as a process of selecting the individuals who match the requirement and qualification to perform a particular job in an excellent way [
Despite restructuring and reorganizing the personnel selection process, some of the firms had performed a socalled “strategic decision” to choose the best candidate during the selection process. Some decision makers try to utilize rigorous and costly selection procedure and some even used the traditional method which depends on only information stated on the application forms that turn out to be quickest and inexpensive methods [
Distance measure can be identified as one of the MCDM approaches that can be used in personnel selection process. This approach holds an important key to solve many problems related to biology, science, social, and technology due to its capability of constructing some related distance measures, notably similarity, and proximity which always become a norm in various problems [
Literally, evaluation of certain criteria or attributes to select an appropriate alternative for specified position could become tremendous and challenging task for the decision makers. It is because some of the criteria such as leadership, personality, and creativity are referred to as qualitative criteria in which exhibits imprecise and vagueness data. In general, this uncertainty and subjective scene that occurs during the evaluation of the alternatives based on respective criteria and criteria weight may come from various sources including unquantifiable information, incomplete information, unobtainable information, and partial ignorance [
The main objective of this paper is to propose an approach to solve personnel selection process by using Hamming distance method. Inspired by algorithm proposed by Canós et al. [
A fuzzy set
An intervalvalued fuzzy set
The multiplication of two intervalvalued fuzzy numbers,
Hamming distance methods to be used in this paper are presented as follows
Given two fuzzy subsets of
Then the Hamming distance is defined as
The weighted Hamming distance of dimension
Hamming distance is one of the distance measures that can be applied in personnel selection process. This is due to its ability in calculating the distance between ideal alternative and alternative. The ideal alternative is a virtual alternative in which the criteria values are expressed as close as possible to ideal values which is rationale for human thinking to achieve. There are several methods that focus on identifying and measuring the ideal alternative. However this measurement is beyond our scope of research. In this paper, the evaluation on the ideal alternative is made based on assumption of the optimum value of each criterion that alternatives should achieve for the specified job. We also disregard the usage of maximum value, for example,
The decision makers are genuinely aware that they cannot assume that all criteria are equally important as it holds its own meaning and neediness, especially when its focus is only to one subject or position. For example, when recruiting the appropriate applicant for position credit officer, the criteria that might be valued most are experienced in credit analysis and personality assessment. Generally, the other criteria are also valuable but they are not as important as these two criteria. Plus it is a human nature to have diverse opinion in evaluating process. Thus it is undeniable that the criteria weight plays an important role in MCDM problem as it depicted the relative weightiness of the criteria must be assigned [
The subjective weight are determined solely based on the preference of the decision makers [
One of the objective weighting measure that vastly has been used in MCDM field is Shannon’s entropy concept [
In this section, the description and algorithm for the HDMSOWs is constructed. To our best knowledge, the study of using a weighted Hamming distance method in solving personnel selection problem has rarely been done. Merigó and GilLafuente [
Let us assume that there is a set of
The decision matrix for ideal alternative is given as follows:
The decision matrix for performance alternatives is given as follows:
The weighting matrix for criteria weight;
By using
The interval decision matrix for the ideal alternative:
The interval decision matrix for performance alternatives:
The interval decision matrix for criteria weight
The criteria weight of
Subjective weight. The subjective weight of
Objective weight. The interval valued fuzzy number is transformed into crisp number before using Shannon’s entropy concept.
The details of Shannon’s entropy concept are defined as follows [
(a) Subjective weight. Before calculating the distance values, calculate the overall performance evaluation of ideal alternatives and alternatives by multiplying the aggregate weight with each criterion [
For the ideal alternative:
(b) Objective weight. For the objective weight, the distance values are calculated by using Definition
The alternatives are ranked in ascending order according to the distance values for respective
The alternatives are ranking according to the different values of
An example on the personnel selection in an academic institution is provided to validate the proposed algorithm. Suppose that the academic institution intends to employ a lecturer based on consideration of four main criteria which are experienced in teaching areas
Fuzzy linguistic terms and respective fuzzy numbers for each criterion weight.
Linguistic terms  Fuzzy numbers 

Very low (VL)  (0, 0, 0.2) 
Low (L)  (0.05, 0.2, 0.35) 
Medium low (ML)  (0.2, 0.35, 0.5) 
Medium (M)  (0.35, 0.5, 0.65) 
Medium high (MH)  (0.5, 0.65, 0.8) 
High (H)  (0.65, 0.8, 0.95) 
Very high (VH)  (0.8, 1, 1) 
Fuzzy linguistic terms and respective fuzzy numbers for each criterion.
Linguistic terms  Fuzzy numbers 

Very poor (VP)  (0, 0, 0.2) 
Poor (P)  (0.05, 0.2, 0.35) 
Medium poor (MP)  (0.2, 0.35, 0.5) 
Fair (F)  (0.35, 0.5, 0.65) 
Medium good (MG)  (0.5, 0.65, 0.8) 
Good (G)  (0.65, 0.8, 0.95) 
Very good (VG)  (0.8, 1, 1) 
Decision makers’ evaluation on each criterion weight.
Criteria 






VH  H  H  MH 

H  VH  MH  H 

VH  VH  H  H 
Decision makers’ evaluation on ideal alternative.
Criteria 






VG  G  VG  MG 
Decision makers rating on alternative performance.
Alternatives 



 












 

G  G  F  F  MG  F  G  VG  VG  G  VG  MG 

F  G  G  F  F  F  G  MG  G  MG  G  G 

F  VG  F  MG  VP  G  VG  G  MG  VG  G  G 

G  G  G  MG  G  G  VG  VG  VG  G  G  MG 
Subjective weight for each criterion at
Criteria 




(0.75, 0.9833)  (0.84166, 0.95833) 

(0.75, 0.9833)  (0.84166, 0.95833) 

(0.60, 0.90)  (0.675, 0.825) 

(0.60, 0.90)  (0.675, 0.825) 
Each criterion projection value at
Criteria 


 









(0.34615)  (0.35185)  (0.30769)  (0.29630)  (0.34615)  (0.35185) 

(0.30769)  (0.29630)  (0.34615)  (0.35185)  (0.34615)  (0.35185) 

(0.35556)  (0.35556)  (0.28889)  (0.28889)  (0.35556)  (0.35556) 

(0.28889)  (0.28889)  (0.35556)  (0.35556)  (0.35556)  (0.35556) 
Shannon’s entropy based weight.
Criteria 


 









0.99864  0.99713  0.00136  0.00287  0.12385  0.20439 

0.99864  0.99713  0.00136  0.00287  0.12385  0.20439 

0.99585  0.99585  0.00415  0.00415  0.37615  0.29561 

0.99585  0.99585  0.00415  0.00415  0.37615  0.29561 
Distance value of subjective and objective weights at
Distance 



 










Subjective  0.12604  0.13993  0.15181  0.17915  0.17305  0.20001  0.04979  0.06338 
Objective  0.23685  0.32263  0.31193  0.40220  0.36193  0.45220  0.11239  0.14087 
Ranking of alternatives at
Ranking  Subjective weight  Objective weight  






1 




2 




3 




4 




Ranking of alternatives at
Ranking  Subjective weight  Objective weight  






1 




2 




3 




4 




The fuzzy linguistic variables for each criterion weight.
The fuzzy linguistic variables for each alternative.
Based on the results obtained, the proposed HDMSOWs can be summarized as follows.
Ideal alternative matrix (
Decision matrix for alternatives evaluation on each criterion (
The weighting matrix (
By using the
The objective and subjective weights are identified. The subjective weight is measured based on (
The distance values between the ideal alternative and the alternatives are calculated by using the Hamming distance method. For the subjective weight, the overall performance evaluation for the ideal alternative (
The ranking of the alternatives is made based on the distance values obtained before. The alternative with the less distance value is considered as a preferable alternative to be selected. Table
The steps are repeated by using different values of
The decision makers then will select the suitable alternative to fill the vacancy based on the ranking of the alternatives. The decision makers also can make the decision based on the preferable
In this paper, we have presented a novel approach of handling personnel selection process by using the Hamming distance method. Based on the fact that most of criteria assessment is in qualitative or in subjective measurement, fuzzy set theory has been applied to overcome this limitation. Furthermore, realizing the importance of weighting the criteria in determining which criteria are valued the most; two types of weights have been applied in this paper which are objective and subjective weights. The objective weight is determined by the application of Shannon’s entropy concept and the subjective weight is obtained based on the preference of the decision maker. With the use of the weighted Hamming distance, the distance values between the ideal alternative and the alternatives are identified and the ranking of the alternatives based on the overall evaluation of the criteria is made. The final results showed that the criteria
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was funded by the Ministry of Education of Malaysia under Research Acculturation Grant Scheme (RAGS): 901800004.