A Two-Phase Model for Personnel Selection Based on Multi-Type Fuzzy Information

From the viewpoint of human resource management, personnel selection is one of the more important issues for enterprises in a high-level competitive environment. In general, many influence factors, quantitative and qualitative, affect the decision-making process of personnel selection. For considering qualitative factors, decision-makers cannot always easily judge the suitable degree of each applicant. Under this situation, this research proposes a systematic decisionmaking method based on computing with linguistic variables. First, unsuitable applicants are filtered by considering the quantitative information of each applicant. At this stage, technique for order of preference by similarity to ideal solution (TOPSIS) and entropy methods are aggregated to eliminate unsuitable applicants in accordance with their closeness coefficient values. Second, experts (or decision-makers) use different types of 2-tuple linguistic variables to express their opinions of suitable candidates with respect to qualitative criteria. At this stage, we consider different preference functions in the preference ranking organization method for enrichment evaluation (PROMETHEE) method to calculate the outranking index of each suitable candidate. Next, we aggregate the closeness coefficient and outranking index of each suitable applicant to determine the ranking order. In order to illustrate the computational processes, an example demonstrates the practicability of the two-phase personnel selection method. The benefit of the proposed method is as follows. (1) It reduces the time for reviewing and evaluating the huge numbers of applicants. (2) It avoids subjective judgment by experts to determine the weights of all criteria. Finally, conclusions and contributions are discussed at the end of this paper.


Introduction
Human capital is one of the most important core assets for enterprises competing with other companies to survive in a high-level competitive environment. Personnel recruitment affects the quality of work and the operational performance of an enterprise [1]. In order to enhance an enterprise's competitiveness, it needs to select the right persons for the right jobs [2]. On the contrary, this will reduce the competitiveness of the enterprise and cost a lot of time and money for training workers to operate their jobs well if employees are assigned to the wrong position. Therefore, personnel selection is one of the important decision-making problems for managers of every enterprise. However, many quantitative and qualitative factors should be considered in dealing with the personnel selection problem. By considering the influential factors, a personnel evaluation and selection process can be formed like a multiple-criteria decision-making (MCDM) problem.
to compute the fuzzy fitness of each person to do the right jobs. Chien and Chen [30] proposed an effective data mining method based on the rough set theory to select the right person from a human resource database. Gungor et al. [31] considered many quantitative and qualitative factors and used fuzzy analytic hierarchy process (AHP) to cope with the personnel selection problem. According to maritime human resources data, Celik et al. [32] combined fuzzy AHP with fuzzy TOPSIS to deal with the academic personnel selection problem. Some researchers used the objective programming model and machine learning method to deal with the personnel selection problem for a project team [33,34].
Zhang and Liu [35] combined intuitionistic fuzzy numbers with the grey relational method to select suitable engineers for a software company. Chen et al. [36] used the linguistic VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) method and skill knowledge map to choose new staff in accordance with the job requirement. Bangerter et al. [37] selected a suitable person according to past performance of applicants based on the signaling theory. Afshari et al. [38] applied the fuzzy integral to perform personnel selection when the personnel selection criteria depended on each other. Sang et al. [39] used fuzzy number to evaluate the weight of each criterion and the performance of an applicant. Fuzzy TOPSIS was used to rank the applicants. Compared with the traditional TOPSIS method, their method can maintain computational efficiency to some extent and avoid information loss. Ji et al. [40] considered the risk preference of decision-makers by using a multi-valued linguistic variable to let experts express their opinions. After that, the projection-based iterative multi-criteria decision making (TODIM) method was applied to handle the personnel selection problem. The projection-based TODIM method was compared with some traditional MCDM methods for verifying feasibility of this method.
Heidary Dahooie et al. [41] designed the competency framework with five criteria in order to choose the best information technology expert. Grey additive ratio assessment (ARAS-G) and the stepwise weight assessment ratio analysis (SWARA) were integrated to derive the criteria weights and to determine the final ranking order of all candidates. Yalçın and Yapıcı Pehlivan [42] used the hesitant fuzzy linguistic terms to express the evaluation opinions of experts to deal with the personnel selection problem. In order to justify the usefulness of this method, fuzzy WASPAS (Weighted Aggregated Sum Product Assessment), fuzzy ARAS, fuzzy EDAS (Evaluation based on Distance from Average Solution), fuzzy TOPSIS, and fuzzy WASPAS were used to analyze and evaluate the personnel selection results by using the same data. The experiment result showed that this methodology is stable and efficient for solving personnel selection problems. Chuang et al. [43] designed a data-driven multi-attribute decision-making model. This model applied a machine learning mechanism to reduce the influence by the subjectivity experience of the experts. Rough set theory was used to derive an initial influential significance-relation matrix from real assessment data. A dynamic analytic network process was applied to acquire the influential significance-network relation map and influential weights from the initial matrix. PROMETHEE-AS can then be applied to evaluate the gap between the aspiration and current levels for each applicant. Kilic et al. [44] applied DEMATEL and ELECTRE methods to rank the air-filter manufacturing applicants. Krishankumar et al. [45] used intuitionistic fuzzy set (IFS) to express the opinions of experts and combined VIKOR method with IFS to effectively handle personnel selection problem. Ozdemir and Nalbant [46] used five main criteria for evaluating the applicants in Turkey. They combined consistent fuzzy preference relation (CFPR) with fuzzy analytic hierarchy process (FAHP) to rank the performances of those applicants.

The 2-Tuple Linguistic Variables
Many quantitative and qualitative factors in general will influence the decision-making of the personnel selection. For quantitative criteria, it is easy to use crisp values to express the evaluation values, such as working years, the grade of a language test such as TOEIC (Test of English for International Communication) grade or TOEFL (Test of English as a Foreign Language) grade, the level of education, and work licenses [1]. However, decision-makers always find it difficult to express their opinions for qualitative criteria, such as professionalism, working ability, leadership, communication skill, and emotional steadiness. In order to express the subjective opinions of experts, the 2-tuple linguistic variables are suitable for experts to express their opinions for the qualitative criteria. A 2-tuple linguistic variable can be defined as a triangular fuzzy number [47]. In this study, there are three types of 2-tuple linguistic variables used in the decision-making process. Different types of linguistic variables and the membership functions are shown as Table 1 and Figures 1-3, respectively.     Suppose that S = , , , … , is an ordered linguistic term set; g is the number used to represent the index of maximum linguistic variable in linguistic term set S; , , , … , are linguistic variables. A 2-tuple linguistic variable (L) can be expressed by two elements as ( , ) in accordance with the linguistic term set. The symbol is the central value of the ith linguistic variable in S, and symbol is the difference in values between L and the ith linguistic variable in S. Before the operation of 2-tuple linguistic variables, we must transform 2-tuple linguistic variables into crisp values. For the same reason, we can transform a crisp value into a 2-tuple linguistic variable to be expressed as a triangular fuzzy number. Applying the translation function ) (Δ , we can easily transform a crisp value β into a 2-tuple linguistic variable [47]. In this paper, the generalized translation function can be applied as [48]: where ∆ is symbol of translation function, = round(β × g) , = β − , β ∈ [0, 1] and ∈ [− , ).
A reverse function ∆ is applied to transform a 2-tuple linguistic information ( , ) into a crisp value. According to the generalized translation function, the crisp value can be computed as follows [48].
Suppose that x = {( , ), = 1,2, … , } is a set of 2-tuple linguistic variables. The term is the mean value, which is acquired from the set of the 2-tuple linguistic variable x = {( , ), = 1,2, … , }. It can be computed as [49]: As a result of different expertise backgrounds, knowledge, and experiences, experts use different types of linguistic terms to express their evaluation values in a decision-making process [50]. For example, if an expert has more knowledge or expertise background for the decision problem, then he/she will choose the type 3 linguistic variables (shown as Table 1) to present a more precise opinion in the decision-making process. To aggregate the opinions of all experts, one needs to transfer these different types of 2-tuple linguistic variables into a standard linguistic set. Herrera and Martinez [47] presented a method to transform different types of 2-tuple linguistic variables into a standard linguistic set, but the transform results cannot keep the same domain in accordance with their transform method. Therefore, a generalized transform method is applied here to transform the different types of linguistic variable into a common linguistic term at the same domain [48,51].
Suppose that the different types of linguistic variable sets can be defined by partitioning the interval [0, 1] (shown as Table 1). According to the generalized transform method, a crisp value β (β∈ [0, 1]) can be transformed into an ith linguistic term ( ( ) , ( ) ) of type t as: We therefore can transform the ith linguistic term ( ( ) , ( ) ) of type t into the kth linguistic term ( where g = ( + 1) − 1, and

The TPMCDM Method
As we know, a personnel selection problem can be regarded as a MCDM problem with multiple experts (or decision-makers). Basically, the problem structure of personnel selection can be divided into five parts by means of the following sets.
( (v) The crisp performance ratings of applicants with respect to quantitative criteria can be represented as ij x , i = 1,2,…,m and j = 1,2,…,z. The linguistic performance ratings of each applicant with respect to qualitative criteria can be described as ij x , i = 1,2,…,m and j = z + 1,z + 2,…,n.
According to the definitions of symbols, the decision matrix by aggregating the evaluations of experts can be formulated as: According to the decision matrix, the performance of the ith applicant with respect to the jth criterion by the kth expert can be expressed as a crisp value ( ) for the quantitative criteria ( ∈ ). The mean value of all can be represented as . The performance of the ith applicant with respect to the jth criterion by the kth expert can be represented as a 2-tuple linguistic variable = ( , ) for the quantitative criteria ( ∈ ). The aggregated linguistic rating ( ) of the ith applicant with respect to the jth criterion can be calculated as: (8) is used to integrate experts' opinions. The concept of Formula (8) is that an expert's opinion is transferred as a crisp value by Formula (2). The average value of experts' opinions (crisp value type) can be calculated. Finally, experts' integrated opinions (crisp value type) will be transferred as a 2-tuple linguistic variable by Formula (1).
The aim of this paper is to provide the two-phase multiple-criteria decision-making (TPMCDM) method to deal with the personnel selection problem. It can be divided into two phases. In the first stage, the evaluation values of each applicant with respect to quantitative criteria are considered to eliminate some unsuitable applicants by using the TOPSIS method. In the second stage, the different preference functions of the qualitative criteria are applied to evaluate the suitable candidates by using the PROMETHEE method. By considering the quantitative and qualitative criteria simultaneously, a comprehensive support index is defined to determine the ranking order of all suitable candidates in accordance with the closeness coefficients of TOPSIS and outranking indices of PROMETHEE simultaneously. The whole process of the TPMCDM method is shown in Figure 4.

The First Phase
In order to compare the performance ratings of applicants with respect to quantitative criteria more objectively, the performance ratings of applicants can be normalized as: The entropy value of the jth quantitative criterion ( ) can be computed as: Therefore, the weight of the jth quantitative criterion (w ) can be computed as: We construct the weighted normalized decision matrix as: ( ) The closeness coefficient ( ( )) of each applicant is calculated as: where 0 ≤ ( ) ≤ 1.
If ( ) = 1, then is the best applicant. If ( ) = 0, then is the worst applicant. If ( ) ≥ ( ), then applicant is preferred to . Therefore, we can determine the ranking order of all applicants in accordance with closeness coefficients.
From the closeness coefficients of all applicants, we choose some suitable applicants to evaluate in accordance with their ranking order. If we set the elimination ratio as , then the number of qualified applicants can be determined as: where represents the set of qualified applicants.
( ) represents the rank of applicant in accordance with the closeness coefficient.
( * (1 − )) represents the number of applicants needed to be evaluated at the next stage. According to the closeness coefficients of qualified applicants, a support ratio of each qualified applicant with respect to quantitative criteria can be defined as: where

The Second Phase
At the second stage, we evaluate the qualified applicants (suitable applicants or candidates) in accordance with qualitative criteria. For any two suitable applicants and ( i A , s A ∈ b G ), the difference value between them with respect to qualitative criterion j can be expressed as . Therefore, a preference degree of suitable applicant over for qualitative criterion j is defined as: For dealing with qualitative information, we express the criterion with a linear preference and indifference function (shown in Figure 5) as: Here, p and q are threshold values, and are two-tuple linguistic variable, and ∆ is the function that transforms 2-tuple linguistic information into a crisp value. Level criterion with a linear preference function (shown in Figure 6) for qualitative information is expressed as: The entropy value of the jth qualitative criterion ( ) can be computed as: The overall preference index of suitable applicant over can be represented as: The leaving flow of i A can be calculated as: where + ( ) is the dominating degree of over the other suitable applicants. The entering flow of can be calculated as: where φ ( ) is the dominating degree of by the other suitable applicants. The net flow of can be calculated as: We define the outranking index of candidate as: According to the outranking index of each suitable applicant by using the PROMETHEE method, a support ratio of each suitable applicant with respect to qualitative criteria is calculated as: where We can therefore define a comprehensive support index of each suitable applicant by considering the quantitative and qualitative criteria simultaneously as: where is the preference index of the final decision-maker, and 0 ≤ ≤ 1. If = 1, then it means that the decision-maker selects a qualified applicant according to quantitative information. If = 0, then it means that the decision-maker depends on qualitative information to select the qualified applicants. The higher the comprehensive support index ( ) is, the better suitable applicant is. Finally, the ranking order of all suitable applicants in can be determined in accordance with the comprehensive support indices.

Numerical Example
In order to illustrate the computational process of the two-phase multiple-criteria decisionmaking (TPMCDM) method for the personnel selection clearly, a selection problem of an overseas marketing manager is shown in this section. A decision-making committee consists of three experts to choose the best overseas marketing manager from twenty applicants. The influence factors of personnel selection were first collected from the literatures and a questionnaire was designed for asking managers of enterprises to obtain the evaluation criteria. There are eight criteria (shown as Table 2) used to evaluate the applicants. Quantitative criteria include English ability ( ), educational background ( ), work experience ( ), and license ( ). Qualitative criteria include communication skill ( ), innovation ability ( ), advertise design ability ( ), and emotional steadiness ( ). According to the TPMCDM method, the computational steps of this selection problem are summarized as follows.

The Computational Steps Based on Quantitative Criteria
Step 1. The quantitative data of the twenty applicants are shown as Table 3. English ability ( ) is represented by TOEIC grade. Educational background ( ) means the education degree of each applicant. Work experience ( ) is represented by the length of working time (years). License ( ) means the number of professional licenses that each applicant possesses.
Step 2. Based on Table 3, calculate the normalized values and the weights of quantitative criteria by using the entropy method as Table 4.
Step 3. Calculate the weighted normalized matrix and determine the positive ideal solution (A * , PIS) and the negative ideal solution (A , NIS).
Step 4. For each applicant, the distances from PIS and NIS as well as the closeness coefficient (CC) can be computed as Table 5.
Step 5. Supposing that the elimination rate is 50%, ten qualified applicants are selected in accordance with closeness coefficient values of all applicants as Table 5. Therefore, the set of qualified applicants is { , , , , , , , , , }.
Step 6. The support ratios of ten qualified applicants based on quantitative criteria can be calculated as Table 5.

The Computational Steps of the Final Ranking Order
Step 1. Each expert chooses the linguistic variable type to express his/her opinion. In this paper, expert chooses type 1, chooses type 2, and chooses type 3. The definitions of linguistic variables are shown as Table 1. The membership functions of linguistic variables are shown as Figures  1-3.
Step 2. Three experts use the linguistic variables to express their performance ratings of each qualified applicant with respect to qualitative criteria as Table 6.
Step 3. Transform the different types of linguistic ratings of three experts into type 2. Aggregate the linguistic ratings of each qualified applicant with respect to qualitative criteria.
Step 4. Transform the aggregation linguistic ratings into crisp values and calculate the weights of qualitative criteria by using the entropy method as Table 7.
Step 5. Determine the threshold values of preference functions for each qualitative criterion as Table 8.
Step 6. Calculate the overall preference indices between a pair of qualified applicants.
Step 7. According to PROMETHEE, the leaving flow, the entering flow, the net flow, and the outranking index of each qualified applicant can be calculated as Table 9.
Step 8. Based on the support ratios of quantitative and qualitative criteria, a comprehensive support index of each qualified applicant can be calculated as Table 10. If the preference index of the final decision-maker is 0.5 ( i. e. , = 0.5), then the ranking order of all qualified applicants in accordance with comprehensive support indices is If the preference index of the final decision-maker changes, then the comprehensive support index of each qualified applicant will be different as Figure 7. In addition, the ranking order of qualified applicants will change in accordance with as Figure 8. As we know, the final decisionmaker can select the suitable applicants flexibly with a different preference index ( ).   Table 9. The leaving flow, the entering flow, the net flow and outranking index of each candidate.

Simulation and Effectiveness Explanation
In order to illustrate the effectiveness of the TPMCDM method for dealing with the personnel selection problem, we implement data simulation to compare TPMCDM with TOPSIS [6][7][8] and PROMETHEE [51] methods with linguistic variables. The linguistic TOPSIS (L-TOPSIS) and linguistic PROMETHEE (L-PROMETHEE) methods are one phase for determining the ranking order of all applicants in accordance with quantitative and qualitative criteria simultaneously. Based on the proposed example, we generate new data of each applicant by using random variables. The range of generating new data with respect to criteria are shown in Table 11, and 100,000 simulations are executed to make the comparisons between TPMCDM and the others. If the better applicants are selected by the TPMCDM method, which overlaps with other methods, then the two-phase method is effective for reducing the cost of interview time. In order to compute the overlapped ratios between the TPMCDM method and the other methods, the top ten applicants are selected from all applicants by the TPMCDM, L-TOPSIS, and L-PROMETHEE methods, respectively. Therefore, we define the coverage rate to express the overlap degree of the top ten applicants between the TPMCDM method and L-TOPSIS. We then define the coverage rate to express the degree of overlap of the top ten applicants between the TPMCDM method and L-PROMETHEE. We compute and as: where ( ) is the rank order of applicant i A by the L-TOPSIS method.
( ) is the rank order of applicant by the L-PROMETHEE method.
( ) is the rank order of applicant by the TPMCDM method. As we know, the TPMCDM method eliminates some applicants in the first step for saving on interview time and cost. Under this situation, the elimination ratio and coverage rate exhibit a tradeoff relationship to select the better applicants for managers. A higher elimination ratio at the first step may produce a lower coverage rate. A lower elimination ratio at the first step cannot reduce the interview time and cost for managers effectively.
According to the results of Table 12 and Figure 9, we find that larger elimination ratios truly produce smaller coverage rates. For example, if managers want to save 20% of interview time (elimination rate is 20%) to select applicants, then the coverage ratios are 84.17% and 80.64% between the TPMCDM method and the L-TOPSIS and L-PROMETHEE methods, respectively. However, if managers want to save 10% of interview time (elimination rate is 10%) to select the applicants, then the coverage ratios are 92.81% and 91.16% between the TPMCDM method and L-TOPSIS and L-PROMETHEE methods, respectively. Thus, the elimination ratios and coverage rates have a tradeoff relationship. A decision-maker should consider and decide the relative importance between experts' time and personnel selection decision quality.
The average rank order of each selected applicant by the TPMCDM method is computed to compare with the linguistic TOPSIS and linguistic PROMETHEE methods, respectively. According to experiment result (shown as Figure 10), we know that a lower rank order of the applicant in the TPMCDM method acquires a lower average rank order in the L-TOPSIS and L-PROMETHEE methods, respectively. The rank order distribution of each selected applicant by the TPMCDM method is also computed in the linguistic TOPSIS method as Figure 11. The rank order distribution of each selected applicant by the TPMCDM method is also computed in the linguistic PROMETHEE method as Figure 12. Based on the above analysis results, we find that the TPMCDM method can help managers to select suitable employees and can effectively reduce the interview time and cost during the process of personnel recruitment.

Conclusions
When facing a global competitive environment, enterprises know that the selection of suitable persons is key to their survival. However, it is costly to review and evaluate huge numbers of applicants. In order to cope with the personnel selection problem efficiently and effectively, a twophase multiple-criteria decision-making (TPMCDM) method is presented herein to select suitable persons for the right positions by considering quantitative and qualitative factors at the same time. The contributions and advantages of the systematic method proposed in this paper can be summarized as follows.
(1) According to the two-phase MCDM method, some unsuitable applicants will be filtered effectively by considering quantitative information at the first stage. In other words, the two-phase MCDM method can reduce the time for reviewing and evaluating the huge numbers of applicants at the same time.
(2) To avoid subjective judgment by experts to determine the weights of all criteria, the entropy method automatically computes according to the data distribution.
(3) By combining the support ratios of qualitative with quantitative information, a comprehensive support index is defined to determine the ranking order of all candidates effectively. Considering the different importance of qualitative and quantitative factors, managers can adjust their preference to compute the comprehensive support index and select the suitable employee.
(4) In this research, the elimination ratios and coverage rates have a trade-off relationship. Enterprises can use the proposed method by justifying that the elimination ratios save decision makers' time according to the enterprises' actual demand.
The proposed model can reduce the overload of reviewing applicants for managers. The TPMCDM method of personnel recruitment provides an objective and systematic process to handle the personnel selection problem with huge numbers of applicants. The multi-type linguistic variables based on 2-type linguistic terms are used to express the evaluation values of decision-makers in this paper. However, it is not easy to define the suitable type linguistic variables for experts to express their subjective opinions. It is the limitation of the proposed method to deal with the personnel selection problem based on huge amounts of applicants. To enhance the practical value of the twophase multiple-criteria decision-making (TPMCDM) method, one can design and develop a decision support system based on the proposed model in the near future.