PERSONNEL SELECTION USING GROUP FUZZY AHP AND SAW METHODS

Personnel evaluation and selection is a very important activity for the enterprises. Different job needs different ability and the requirement of criteria which can measure ability is different. It needs a suitable and flexible method to evaluate the performance of each candidate according to different requirements of different jobs in relation to each criterion. Analytic Hierarchy Process (AHP) is one of Multi Criteria decision making methods derived from paired comparisons. Simple Additive Weighting (SAW) is most frequently used multi attribute decision technique. The method is based on the weighted average. It successfully models the ambiguity and imprecision associated with the pair wise comparison process and reduces the personal biasness. This study tries to analyze the Analytic Hierarchy Process in order to make the recruitment process more reasonable, based on the fuzzy multiple criteria decision making model to achieve the goal of personnel selection. Finally, an example is implemented to demonstrate the practicability of the proposed method.


PERSONNEL SELECTION BACKGROUND
As in many decision problems, personnel selection problem is very complex in real life.Multi criteria decision making (MCDM) has been widely used to deal with decision-making problems involving multiple criteria selection of alternatives.To manage this personnel selection problem, various methods have been proposed to decide on the selection of human resources.Liang and Wang (1992) presented a model by using concepts of fuzzy set theory assess personnel fitness and job vacation.On the other hand, fuzzy sets decision theory suggested by Alliger, Feinzig, and Janak (1993) for the personnel selection problem.Liang and Wang (1994) developed a fuzzy MCDM methodology to find the final ranking values for candidates in personnel selection problem.Yaakob and Kawata (1999) used fuzzy methodology for solving workers' placement problem.Lovrich (2000) used fuzzy linguistic model for personnel selection.Capaldo and Zollo (2001) presented a model based on a case study in FIAT Research Centre (CRF) that is a major Italian company.Butkiewicz (2002) used fuzzy numbers for staff selection.Chen and Cheng (2005) combined Group decision support system (GDSS) with MCDM in fuzzy environment to solve the personnel selection problem.Golec and Kahya (2007) developed a hierarchical structure and used a fuzzy model for personnel selection.Zavadskas, Turskis, Tamošaitiene and Marina (2008) applied complex proportional assessment of alternatives with grey relations to select construction project manager.Liao and Chang (2009b) used ANP to choose public relations personnel for Taiwanese hospitals.Liao and Chang (2009a) applied ANP to select televised sportscasters for Olympic Games.Dağdeviren (2010) employed ANP and modified TOPSIS to select personnel.Dursun and Karsak (2010) used the principles of fuzzy information fusion, 2-tuple linguistic representation model, and TOPSIS to select personnel.Kelemenis and Askounis (2010) proposed a new approach on the basis of fuzzy TOPSIS to select information technology (IT) professionals.Lin (2010) combined ANP and fuzzy data envelopment analysis (DEA) to select personnel.Boran, Genç and Akay (2011) applied Intuitionistic fuzzy TOPSIS to select a sales manager in a manufacturing company.Keršulienė and Turskis (2011) integrated the principles of fusion of fuzzy information, additive ratio assessment method with fuzzy numbers and step-wise weight assessment ratio analysis technique to select architect.Zhang and Liu (2011) proposed an intuitionistic fuzzy multi-criteria decision making method with grey relational analysis (GRA) to select system analysis engineer.Baležentis, Baležentis and Brauers (2012) modified fuzzy multi objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) for personnel selection.Dadelo, Turskis, Zavadskas and Dadeliene (2012) presented The Use of a Hybrid MCDM Model for Public Relations Personnel Selection 391 model for personnel selection based on expert evaluation method and ARAS method.El-Santawy and El-Dean (2012) employ VIKOR to rank the candidates.Zolfani, Rezaeiniya, Aghdaie and Zavadskas (2012) used AHP and TOPSIS with grey relations to select a new drummer for a rock band.Kabak, Burmaoğlu and Kazançoğlu (2012) combine fuzzy ANP, fuzzy TOPSIS and fuzzy ELECTRE to select sniper.Rouyendegh and Erkan (2012) utilized fuzzy AHP to select most suitable academic staff.Afshari, Yusuff and Derayatifar (2013) propose a new linguistic extension of fuzzy measure and fuzzy integral for personnel selection.Dadelo, Turskis, Zavadskas and Dadeliene (2013) applied wisdom-of-crowds principle, TOPSIS, and SAW to select security guard.Hadad, Keren and Laslo (2013) proposed decision-making support system module to select project managers.Kabak (2013) applied fuzzy decision-making trial and evaluation laboratory DEMATEL-ANP model to select snipers.Rouyendegh and Erkan (2013) used fuzzy ELECTRE to select academic staff.Yu, Zhang and Xu (2013) explored aggregation methods for preferential hesitant fuzzy elements and their application on representative personnel evaluation.Ballı and Korukoğlu (2014) used fuzzy AHP and TOPSIS to select skilful basketball players.Dadelo et al. (2013) proposed 2 optimizing algorithms to select security guards.Keršulienė and Turskis (2014) integrated the principles of fusion of fuzzy information, ARAS method with fuzzy numbers, fuzzy weighted-product model and AHP to select a chief accounting officer.Md Saad, Ahmad, Abu and Jusoh (2014) presented a novel approach of handling personnel selection process by using the Hamming distance method.
In the current study personnel selection problem is considered as a multi criteria group decision making problem.In this paper, we proposed a personnel selection system based on Fuzzy Analytic Hierarchy Process (FAHP) and SAW method.The FAHP is applied to evaluate the best adequate personnel dealing with the rating of both qualitative and quantitative criteria.

MATERIAL AND METHODS
In real-world cases, most problems have more than one decision criterion.As the result, MCDM methods have been developed to solve complex problems.The aim in MCDM is to determine overall preferences among alternatives.

Analytic Hierarchy Process (AHP)
The analytic hierarchy process (AHP) is a widely used multi criteria decision making method introduced by Saaty (1980).It resolves decisionmaking problems by structuring each problem into a hierarchy with different levels of criteria.In other words, AHP structures a decision problem into a hierarchy and evaluates multi-criteria tangible and intangible factors systematically.AHP also has been applied in numerous fields including many personnel selection decisions, (Vaidya & Kumar, 2006).The purpose of AHP is to capture the expert's knowledge; the conventional AHP still cannot reflect the human thinking style.Therefore, fuzzy AHP, a fuzzy extension of AHP, was developed to solve the hierarchical fuzzy problems.In the fuzzy-AHP procedure, the pair wise comparisons in the judgment matrix are fuzzy numbers that are modified by the designer's emphasis.Zadeh (1965), introduced the fuzzy set theory which was oriented to the rationality of uncertainty due to imprecision or vagueness.A major contribution of fuzzy set theory is its capability of representing vague data.The theory also allows mathematical operators and programming to apply 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.A tilde "~" will be placed above a symbol if the symbol represents a fuzzy set.A triangular fuzzy number (TFN), M is shown in Figure 1.

Linguistic variables
According to Zadeh (1975), it is very difficult for conventional quantification to express reasonably those situations that are overtly complex or hard to define; so the notion of a linguistic variable is necessary in such situation.A linguistic variable is a variable whose values are words or sentences in a natural or artificial language.Here, we use this kind of expression to compare two criteria by nine basic linguistic terms from one to nine respectively, as 'Equal Importance', 'Weak or Slight', 'Moderate Importance', 'Moderate Plus', 'Strong Importance', 'Strong Plus', 'Very Strong', 'Very, very Strong' and 'Extreme Importance' with respect to a fuzzy nine level scale (see Table 1).

Simple Additive Weighting (SAW)
Simple Additive Weighting which is also known as weighted linear combination or scoring methods is a simple and most often used multi attribute decision technique.The method is based on the weighted average.An evaluation score is calculated for each alternative by multiplying the scaled value given to the alternative of that attribute with the weights of relative importance, directly assigned by decision maker and followed by summing of the products for all criteria.The advantage of this method is that it is a proportional linear transformation of the raw data which means that the relative order of magnitude of the standardized scores remains equal.
then development analysis of m objectives will be computed as below: M by using fuzzy operator (⊕): is the amount of development analysis for i th goal, we will compute S i as follow: , , is a weight of i th criteria with fuzzy numbers.The rest will be found in the same way.In group fuzzy AHP, the weights of each criteria for each expert should be computed in geometrical mean and the result of this step will be done in next step.
Step 2: , ,  then the preference of S i and S k (the degree of possibility of k i S S  ) will be calculated as below: The equation of triangle fuzzy number will be extracted as followed: Step 3: By finding the preference of S i and S k in step 2, we should calculate the degree of possibility for a convex fuzzy number as follow: Personnel selection using group fuzzy AHP and SAW methods JEMC, VOL. 7, NO. 1, 2017, 3-10 7 For k=1, 2… n, i k  .Then the weight vector is given by: Step 4: By normalizing this vector, we can get: Step 5: Construct a decision matrix (m × n) that includes m personnel's and n criteria.So calculate the normalized decision matrix for positive criteria: And for negative criteria: * j r is a maximum number of r in the column's j.
Step 6: Evaluate each alternative, A i by the following formula: Where x ij is the score of the ith alternative with respect to the jth criteria, w j is the weighted criteria which have been found from Fuzzy AHP [3].
As a result, by comparing A i (i=1,2,…,m), the greater one is the best personnel and will be followed by rests.

CASE STUDY
One sector of Telecommunication Company should employ just one staff.The numbers of 40 people contributed in the written exam.In the first step, five of them were accepted and only one of them was chosen as the best one by using Group Fuzzy AHP and SAW methods in the second step.
The authors used the opinions of three experts who contributed in the interview.A linguistic variable is a variable whose values are words or sentences in a natural or artificial language.So, three experts have filled up this kind of expression to compare two criteria by nine basic linguistic terms (Table 2 of first expert), based on table 1.The smallest possible value, the most promising value and the largest possible value for each expert was extracted.Each linguistic variable will be transformed to three terms, therefore the authors did them in Table 3.In order to make geometrical mean, the authors used each experts' viewpoint and computed fuzzy weights in Table 4 (step1).
In steps 3 and 4, in order to calculate the degree of possibility for a convex fuzzy number and finally the normalized weight vector of criteria (Table 5), the preference of S i and S k should be used (steps 2, 3, 4).
To calculate the normalized decision matrix, it is necessary to construct a decision matrix (5 × 7) that includes m personnel and n criteria as follows (steps 5, 6) that will be shown in Table 6:   As a result, the rank of alternatives will be shown in Table 7. (Step 6) Finally, Table 7 shows that personnel 3 is the best for the considered job and it will be followed by P2, P1, P5 and P4 respectively.

CONCLUSION
Decision-makers face vagueness in the decision making process.In many cases, group decision making can improve the consistency of the human decision making process and using fuzzy numbers helps to reach a more effective decision.In this paper, personnel evaluation process is modeled by using the FAHP based on Chang's Algorithm.In order to validate the practicality of the proposed model, it is applied to a personnel selection problem in a Telecommunication company.There are many other multi-attribute evaluation methods that can be combined with fuzzy logics such as TOPSIS and ELECTRE as presented in the literature.The application of these methods to personnel evaluation problem with more evaluation criteria might be suggested for further research.

Figure 1 :
Figure 1: A triangular fuzzy number

Table 1 :
Membership function of linguistic scale

Table 2 :
Linguistic variable of first expert

Table 4 :
Criteria's weight with fuzzy set

Table 5 :
Weights of criteria

Table 6 :
Normalized decision matrix with alternatives' weights