PERSONNEL SELECTION THROUGH FUZZY ELECTRE I METHOD

Rahmi Baki, JMAS Vol 4 Issue 1 2016

The Journal of MacroTrends in Applied Science MACROJOURNALS

PERSONNEL SELECTION THROUGH FUZZY ELECTRE I METHOD Rahmi Baki Aksaray University/Management Information Systems, Turkey

Abstract In today’s conditions, where competition is becoming more severe, selection of personnel suitable for the posts offered by organizations is gaining greater importance. The current study deals with the issue of personnel selection for a sales engineer post of an international firm. Personnel selection criteria were determined through the analyses conducted by the human resources department and a literature review. The most suitable candidate was selected by evaluation of five criteria by three decision makers through Fuzzy ELECTRE method. Keywords: personnel selection, Fuzzy ELECTRE method

1. INTRODUCTION Personnel of a firm make up the most vital resource of it. Regardless of the type of the firm, each firm needs personnel. In this regard, the most important objective is to find the employee having the best qualifications for each position. Selection of suitable personnel has a strategic importance for organizations. Therefore, selection of personnel cannot be performed haphazardly. Personnel selection means finding the best employee from either inside the organization or outside of it for a position. Methods or techniques to be used in the selection process are expected to have a capacity of predicting the future performance of the candidate [1]. In the current study, Fuzzy ELECTRE I method was administered to the problem of selecting the best candidate for a sales engineer position. After the presentation of general information and a literature review about Fuzzy ELECTRE method, the stages of the method to be implemented for the solution of the problem are explained in the third section. After the discussion of the

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personnel selection operation, evaluation of the application and suggestions for future research are presented in the fifth section of the study. 2. LITERATURE REVIEW ABOUT FUZZY ELECTRE METHOD Multi-criteria decision making methods are used for risk evaluation and selection of alternatives competing with each other in terms of more than one criterion. In the present study, Fuzzy ELECTRE method was employed. ELECTRE method is a technique developed to order a series of alternatives. It is based on binary superiority comparisons between alternative decisions points for each evaluation factor. Following the first method known as ELECTRE I, different versions of this approach have been developed. In literature, there are ELECTRE I, ELECTRE II, ELECTRE III and ELECTRE IV methods[2]. When compared to the other methods, Fuzzy ELECTRE requires fewer inputs for the problems having high number of alternatives and criteria. Moreover, performances of alternatives can easily be analyzed and there is no obligation to make binary comparisons [3]. Requirement of certain performance value measurement and criterion weight is one disadvantage of ELECTRE technique. In real world problems, these cannot always be evaluated. Fuzzy set theories are ideal for the elimination of this disadvantage. As fuzzy logic can express uncertainties in linguistics variables and in the nature of the problem, it is frequently used for the improvement of ambiguous information and procedures. The method has the capacity to consider the scale of order by including a random interval without adapting the original scale. Unlike classical ELECTRE methods, clear data are not used while evaluating alternatives and criteria. Instead, fuzzy structures are constructed. Instead of clear data, fuzzy values are capitalized on. Fuzzy ELECTRE has been used for the solution of many real life problems. Sevkli developed a Fuzzy ELECTRE technique for the selection of the supplier to contribute to organizations’ attempts to establish strategies and supply chains [4]. Montazer et al. developed an expert decision system by using ELECTRE III method for the selection of a supplier [5]. Asghari et al. designed a Fuzzy ELECTRE application for the evaluation of 5 different mobile payment models in terms of 7 different criteria [6]. Kaya and Kahraman proposed an environmental effect evaluation methodology through Fuzzy ELECTRE approach. In their study, they evaluated the effect of six different industrial zones on environment to design the industrial structuring of the city of Istanbul and defined environmentally risky alternatives [7]. Aytac et al. compared five different catering services in the city of Denizli by using Fuzzy ELECTRE technique [8]. Hatami and Tavana developed an extension of ELECTRE I method in order to make decisions in fuzzy media and they presented the details of their method on a numerical sample. Moreover, Hamming developed a different technique based on distance [9]. Kabak et al. generated a combination of Fuzzy ANP, Fuzzy TOPSİS and Fuzzy ELECTRE methods and thus developed a multi-criteria decision making technique including both qualitative and quantitative factors for personnel selection [11]. Rouyendegh and Erkan investigated the role of potential boundary conditions and intellectual values in the selection of academicians [12]. Vahdani et al. compare the existing Fuzzy ELECTRE method with intuitional methods by analyzing the effect of a comprehensive sensitivity analysis and its corresponding threshold values. [13]. Hatami at al. 39


employed Fuzzy ELECTRE method to evaluate the hazardous waste recycling plants in terms of human health, environmental protection and safety [14]. Zandi and Roghanian developed an alternative Fuzzy ELECTRE technique based on VİKOR method [15]. Kheirkhah and Dehghani evaluate the quality of public transportation by using Fuzzy ELECTRE technique. [16]. Xu and Shen developed a technique for multi-criteria decision making problems by using ELECTRE I method for Atanassov’s intuitionistic fuzzy sets model [17]. Wu and Chen developed a method that can yield ideal solutions to multi-criteria decision making problems even with erroneous or incomplete data for Atanassov’s intuitionistic fuzzy sets model Moreover, they analyzed their method on two samples 18]. Anojkumar et al. analyzed Fuzzy TOPSİS, Fuzzy VİKOR, Fuzzy ELECTRE and Fuzzy PROMETHEE methods for the selection of materials for pipe production in sugar industry. They developed a systematic approach to the selection of best alternative material based on seven evaluation criteria [19]. Chen and Xu combined ELECTRE II method with indecisive fuzzy logic to develop an alternative Fuzzy ELECTRE technique [20]. Lupo conducted a study based on Fuzzy ELECTRE method to evaluate the service quality of three international airports in Sicilia region and to make detailed suggestions [21]. 3. STAGES OF FUZZY ELECTRE METHOD In many studies in literature, ELECTRE method and fuzzy logic have been synthesized. Hatami and Tavana developed a different technique based on Hamming distance. They then compared the developed technique with TOPSİS technique, which is one of the accepted techniques in literature. Their analyses revealed that this new technique yields more effective results [10]. In the current study, the technique developed by Hatami and Tavana was also used. The stages of the technique are presented below: Stage 1: First, a group of decision makers is constituted to determine the performances of alternatives and significance levels of criteria. Significance levels of criteria to be used to evaluate alternatives are classified. These restricted significant levels are evaluated through fuzzy values. Stage 2: Levels of achievement to be used in the evaluation of alternatives based on the criteria are classified and then evaluated through fuzzy values. Stage 3: Decision makers evaluate each criterion according to significance levels determined in Stage 1. Stage 4: Each of the decision makers evaluates each alternative according to each criterion based on achievement levels classified in Stage 2. Stage 5: Means of importance weights of the criteria evaluated by the decision makers are taken. 𝑅̂ = (a, b, c), k= 1, 2, 3…K

(1)

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1

1

1

𝐾 𝐾 a= 𝐾 ∑𝐾 𝑘=1 𝑎𝑘 , b = 𝐾 ∑𝑘=1 𝑏𝑘 , c = 𝐾 ∑𝑘=1 𝑐𝑘

Stage 6: Means of the achievement levels of the alternatives evaluated by the decision makers according to the criteria are taken. (𝑥𝑖𝑗 ) = (𝑎𝑖𝑗 , 𝑏𝑖𝑗 , 𝑐𝑖𝑗 ) 1

(2) 1

1

𝐾 𝐾 𝑎𝑖𝑗 = 𝐾 ∑𝐾 𝑘=1 𝑎𝑖𝑗𝑘 , 𝑏𝑖𝑗 = 𝐾 ∑𝑘=1 𝑏𝑖𝑗𝑘 , 𝑐𝑖𝑗 = 𝐾 ∑𝑘=1 𝑐𝑖𝑗𝑘

With these values, fuzzy decision matrix is constructed. 𝑥̂11 ̂ =[ ⋮ 𝐷 𝑥̂𝑚1

⋯ 𝑥̂1𝑛 ⋱ ⋮ ] ⋯ 𝑥̂𝑚𝑛

(3)

Stage 7: At this stage, the constructed decision matrix is normalized. In the normalization operation, the highest fuzzy numerical data for one criterion in the decision matrix is determined and all the numerical data in this criterion are divided by this number. This operation is repeated for all the criteria. In this way, normalized decision matrix is formed. 𝑅̂ = [𝑟̂𝑖𝑗 ]𝑚𝑥𝑛 𝑟̂𝑖𝑗 = (

𝑎𝑖𝑗 𝑐̂𝑗

,

i= 1, 2, 3, ... m; j=1, 2, 3, ... n

𝑏𝑖𝑗 𝑐𝑖𝑗 𝑐̂𝑗

,

𝑐̂𝑗

(4)

), 𝑐̂𝑗 = max 𝑐𝑖𝑗

Stage 8: Fuzzy values in the obtained fuzzy decision matrix are multiplied with the importance weights of the criteria found in Stage 5 according to each criterion. In this way, weighted normalized decision matrix is obtained. This matrix is shown with “v”.

𝑣̂11 ̂ 𝑉=[ ⋮ 𝑣̂𝑚1

⋯ ⋱ ⋯

𝑣̂1𝑛 ⋮ ] 𝑣̂𝑚𝑛

(5)

Stage 9: At this stage, by administering “Hamming Distance” method, the table showing the distances of binary alternatives between the criteria that will help us to construct inconsistency matrices is formed. Each alternative is compared with all the other alternatives. The purpose for the use of this method is to find the number of two values. That is, we can find out how different the alternatives are from each other. Stage 10: At this stage, by capitalizing on the weighted normalized decision matrix, conformity matrix is constructed. One alternative is compared with each of the other alternatives. Importance weights of the criteria in which the alternative is superior or equal to another with 41


which it is compared are summed up. The conformity matrix obtained in this way is shown with 𝐶̂ . 𝑐̂11 ̂ 𝐶=[ ⋮ 𝑐̂𝑚1

⋯ ⋱ ⋯

𝑐̂1𝑛 ⋮ ] 𝑐̂𝑚𝑛

(6)

Stage 11: At this stage, by capitalizing on the table showing the distances of binary alternatives between the criteria, inconsistency matrix is obtained. Each alternative is compared with each of the other alternatives. The criteria in which an alternative is inferior to another are determined. This value is divided by the highest value in this column. This operation is repeated ̂. for all the alternatives. The inconsistency matrix obtained in this way is shown with 𝐷 𝑑̂11 ̂ =[ ⋮ 𝐷 𝑑̂𝑚1

⋯ ⋱ ⋯

𝑑̂1𝑛 ⋮ ] ̂ 𝑑𝑚𝑛

(7)

Stage 12: Each value in the conformity matrix is compared with the mean of all the values in this matrix. Values bigger than the mean are evaluated as 1 and those smaller than it are evaluated as 0. In this way, Boolean conformity matrix is obtained and shown with B vector. 𝑏11 B=[ ⋮ 𝑏𝑚1

⋯ ⋱ ⋯

𝑏1𝑛 ⋮ ] 𝑏𝑚𝑛

(8)

𝑐̂𝑚𝑛 ≥ 𝐶̅ => 𝑏𝑚𝑛 = 1

(9)

𝑐̂𝑚𝑛 < 𝐶̅ => 𝑏𝑚𝑛 = 0

(10)

Stage 13: Each value in the inconsistency matrix is compared with the mean of all the values in the matrix. Values bigger than the mean are evaluated as 1 and those smaller than it or equal to it are evaluated as 0. In this way, Boolean inconsistency matrix is obtained and shown with H vector. ℎ11 H=[ ⋮ ℎ𝑚1

⋯ ⋱ ⋯

ℎ1𝑛 ⋮ ] ℎ𝑚𝑛

(11)

̅ => ℎ𝑚𝑛 = 1 𝑑̂𝑚𝑛 < 𝐷

(12)

̅ => ℎ𝑚𝑛 = 0 𝑑̂𝑚𝑛 ≥ 𝐷

(13)

Stage 14: Boolean conformity matrices are multiplied with each other and thus, spherical matrix is obtained. This matrix is represented with Z.

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Z=BxH

(14)

Each element in these matrices (𝑧𝑚𝑛 ) is obtained by multiplying each value in Boolean conformity and inconsistency matrices with each other. 𝑧𝑚𝑛 = 𝑏𝑚𝑛 x ℎ𝑚𝑛

(15)

Stage 15: By analyzing the spherical matrix, superiorities of the alternatives to each other are determined. An alternative having the value of 1 in the matrix is superior to the other. However, this does not mean that an alternative having the value of 0 is inferior to the other. Under the conditions of the spherical matrix, a superiority scheme is drawn. By interpreting this scheme, selection order of the alternatives is determined. 4. APPLICATION In the current study, the procedure followed by an international prefab manufacturing firm in recruiting a sales engineer was investigated. In the application, criteria and alternatives were evaluated by three decision makers (DM1, DM2, DM3). For the selecting of the best candidate, 6 candidates (P1, P2, P3, P4, P5, P6) were evaluated. The candidates were evaluated according to 5 different criteria. These criteria were determined through the interpretations of the decision makers and a literature review. The criteria on which the alternatives are compared are experience, education, foreign language competency, computer competency and personal features. These criteria are shown as C1, C2, C3, C4 and C5; respectively.

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STAGE 1: Variables to be used in the determination of importance weights of the criteria are determined. Table 1: Variables used in the evaluation of the criteria

Importance Level Fuzzy Values

Very Little Important (VLI) (0,0,0.2)

Lıttle Important (LI)

Normal (N)

Important (I)

(0,0.2,0.4)

(0.2,0.4,0.6)

(0.4,0.6,0.8)

Very Important (VI) (0.6,0.8,1)

STAGE 2: Variables to be used in the evaluation of the performances of the alternatives are determined. Table 2: Variables used in performance evaluation Successful Level Fuzzy Values

Too Few Successful (TFS) (0,0,2)

Few Successful (FS) (0,2,4)

Normal (N)

Successful (S)

(2,4,6)

(4,6,8)

Very successful (VS) (6,8,10)

STAGE 3: The decision makers evaluate the significance levels of the criteria. Table 3: Evaluation of the criteria by the decision makers Experience (C1) Education (C2) Foreıgn Language (C3) Computer Skılls (C4) Personal Characteristics (C5)

DM 1 Very Important Important Important Very Important Normal

DM 2 Important Normal Very Important Normal Lıttle Important

DM 3 Very Important Important Important Lıttle Important Normal

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STAGE 4: The decision makers evaluate the performances of the alternatives according to the criteria. Table 4: Evaluation of the alternatives by the decision makers Criteria

C1

C2

C3

C4

C5

Alternative P1 P2 P3 P4 P5 P6 P1 P2 P3 P4 P5 P6 P1 P2 P3 P4 P5 P6 P1 P2 P3 P4 P5 P6 P1 P2 P3 P4 P5 P6

DM1 N AFS S VS FS FS S FS VS FS FS S S TFS VS N N N N FS S N N N FS S FS S FS N

Decision Makers DM2 N N S S TFS FS VS TFS S FS N S S FS S FS FS S S N S N FS N FS S N VS FS S

DM3 TFS FS S S FS N S FS S TFS N S VS FS VS N FS S N FS S FS FS N N S N S FS S

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STAGE 5: Evaluation of decision makers is calculated by averaging. Table 5: Weight means of the criteria Criteria C1 C2 C3 C4 C5

Importance Level (0,533, 0,733, 0,933) (0,333, 0,533, 0,733) (0,466, 0,733, 0,933) (0,266, 0,466, 0,666) (0,133, 0,333, 0,533)

STAGE 6: By taking the means of the performance evaluations of the decision makers for the alternative criteria, fuzzy decision matrix is formed. Table 6: Fuzzy decision matrix P1 P2 P3 P4 P5 P6

C1 (1,333, 2,666, 4,666) (0,666, 2,666, 4,666) (4, 6, 8) (4,666, 6,666, 8,666) (0, 1,333, 3,333) (0,666, 2,666, 4,666)

C2 (4,666, 6,666, 8,666) (0, 1,333, 3,333) (4,666, 6,666, 8,666) (0, 1,333, 5,333) (1,333, 3,333 5,333) (4, 6, 8)

C3 (4,666, 6,666, 8,666) (0, 1,333, 3,333) (4,666, 6,666, 8,666) (1,333, 3,333, 5,333) (0,666, 2,666, 4,666) (3,333, 5,333, 7,333)

C4 (2,666, 4,666, 6,666) (0,666, 2,666, 4,666) (4, 6, 8) (1,333, 3,333, 5,333) (0,666, 2,666, 4,666) (2, 4, 6)

C5 (0,666, 2,666, 4,666) (4, 6, 8) (1,333, 3,333, 5,333) (0, 2, 4) (0, 2, 4) (3,333, 5,333, 7,333)

46


STAGE 7: While conducting this operation, the fuzzy decision matrix in Table 6 is normalized. In the normalization operation, the highest numerical data in the decision matrix for each criterion is determined and all the numerical data in this criterion are divided by this value. This operation is repeated for all the criteria. In this way, normalized decision matrix is constructed. Table 7: Normalized fuzzy decision matrix P1 P2 P3 P4 P5 P6

C1 (0,153, 0,307, 0,538) (0,076, 0,307, 0,538) (0,461, 0,692, 0,923) (0,538, 0,769, 1) (0, 0,153, 0,384) (0,076, 0,307, 0,538)

C2 (0,538, 0,769, 1) (0, 0,153, 0,384) (0,538, 0,769, 1) (0, 0,153, 0,615) (0,153, 0,384, 0,615) (0,461, 0,692, 0,923)

C3 (0,538, 0,769, 1) (0, 0,153, 0,384) (0,538, 0,769, 1) (0,153, 0,384, 0,615 (0,076, 0,307, 0,538) (0,384, 0,615, 0,846)

C4 (0,333, 0,583, 0,833) (0,083, 0,333, 0,583) (0,5, 0,75, 1) (0,166, 0,416, 0,666) (0,083, 0,333, 0,583) (0,25, 0,5, 0,75)

C5 (0,083, 0,333, 0,583) (0,5, 0,75, 1) (0,166, 0,416, 0,666) (0, 0,25, 0,5) (0, 0,25, 0,5) (0,416, 0,666, 0,916)

STAGE 8: Fuzzy values in the obtained fuzzy decision matrix in Stage 7 are multiplied with the importance weights of the criteria found in Stage 5 according to each criterion. In this way, weighted normalized decision matrix is obtained. Table 8: Weighted normalized fuzzy decision matrix P1 P2 P3 P4 P5 P6

C1 (0,081, 0,225, 0,501) (0,040, 0,225, 0,501) (0,245, 0,507, 0,861) (0,286, 0,563, 0,933) (0, 0,112, 0,358) (0,040, 0,225, 0,501)

C2 (0,179, 0,409, 0,733) (0, 0,081, 0,281) (0,179, 0,409, 0,733) (0, 0,081, 0,450) (0,050, 0,204, 0,450) (0,153, 0,368, 0,676)

C3 (0,250, 0,563, 0,933) (0, 0,081, 0,358) (0,250, 0,409, 0,933) (0,071, 0,204, 0,573) (0,034, 0,163, 0,501) (0,178, 0,327, 0,789)

C4 (0,088, 0,271, 0,554) (0,022, 0,155, 0,388) (0,133, 0,349, 0,666) (0,044, 0,193, 0,443) (0,022, 0,155, 0,388) (0,066, 0,233, 0,499)

C5 (0,044, 0,194, 0,443) (0,011, 0,110, 0,310) (0,066, 0,249, 0,533) (0,022, 0,138, 0,354) (0,011, 0,110, 0,310) (0,033, 0,166, 0,399)

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STAGE 9: At this stage, by administering “Hamming Distance” method to the weighted normalized decision matrix in Table 8, the criteria are compared to each other. The table showing the distances of binary alternatives between the criteria is formed. Each alternative is compared with all the other alternatives. Table 9: The distances of binary alternatives between the criteria 𝑋11

C1

C2

C3

C4

C5

𝑋21 𝑋31 𝑋41 𝑋51 𝑋61 𝑋12 𝑋22 𝑋32 𝑋42 𝑋52 𝑋62 𝑋13 𝑋23 𝑋33 𝑋43 𝑋53 𝑋63 𝑋14 𝑋24 𝑋34 𝑋44 𝑋54 𝑋64 𝑋15 𝑋25 𝑋35 𝑋45 𝑋55 𝑋65

𝑋11 -

𝑋21 (0,0)

𝑋31 (0,09, 0)

𝑋41 (0,11, 0)

𝑋51 (0, 0,11)

𝑋61 (0, 0)

𝑋12 𝑋13 𝑋14 𝑋15 -

𝑋22 (0, 0,10) 𝑋23 (0, 0,16) 𝑋24 (0, 0,03) 𝑋25 (0, 0,02) -

(0,09, 0) 𝑋32 (0, 0) (0,10, 0) 𝑋33 (0, 0,05) (0,10, 0) 𝑋34 (0,02, 0) (0,06, 0) 𝑋35 (0,01, 0) (0,04, 0) -

(0,11, 0) (0,01, 0) 𝑋42 (0, 0,10) (0, 0) (0, 0,10) 𝑋43 (0, 0,11) (0,04, 0) (0, 0,06) 𝑋44 (0, 0,02) (0,01, 0) (0, 0,05) 𝑋45 (0, 0,01) (0,01, 0) (0, 0,03) -

(0, 0,11) (0, 0,13) (0, 0,15) 𝑋52 (0, 0,06) ( 0,041, 0) (0, 0,06) (0,04, 0) 𝑋53 (0, 0,13) (0,027, 0) (0, 0,08) (0, 0,01) 𝑋54 (0, 0,03) (0, 0) (0, 0,06) (0, 0,01) 𝑋55 (0, 0,02) (0, 0) (0, 0,04) (0, 0,01) -

(0, 0) (0, 0,09) (0, 0,11) (0,03, 0) 𝑋62 (0, 0,13) (0,09, 0) (0, 0,01) (0,09, 0) (0,05, 0) 𝑋63 (0, 0,07) (0,08, 0) (0, 0,02) (0,04, 0) (0,05, 0) 𝑋64 (0, 0,01) (0,02, 0) (0, 0,03) (0,01, 0) (0,02, 0) 𝑋65 (0, 0,01) (0,01, 0) (0, 0,02) (0,01, 0) (0,01, 0) -

-

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STAGE 10: By capitalizing on the weighted normalized decision matrix in Table 8, conformity matrix is constructed. Each alternative is compared with each of the other alternatives. Importance weight means of the criteria in which the alternative is superior or equal to another with which it is compared are summed up Table 10: Confirmatory matrix P1

P2

P3

P4

P5

P6

P1 -

(0,533, 0,733, 0,933) (1,731, 2,798, 3,798) (0,533, 0,733, 0,933) (0, 0, 0)

(0,533, 0,733, 0,933) 𝐶̅ = (0,826, 1,558, 2,111)

P2 (1,731, 2,798, 3,798) -

P3 (0,799, 1,266, 1,666) (0, 0, 0)

(1,731, 2,798, 3,798) (1,731, 2,798, 3,798) (1,198, 2,065, 2,857) (1,731, 2,798, 3,798)

-

(0,533, 0,733, 0,933) (0, 0, 0)

(0, 0, 0)

P4 (1,198, 2,065, 2,865) (0,333, 0,533, 0,733) (1,198, 2,065, 2,865) -

(0,333, 0,5333, 0,733) (1,198, 2,065, 2,857)

P5 (1,731, 2,798, 3,798) (0,932, 1,532, 2,132) (1,731, 2,798, 3,798) (1,398, 2,265, 3,065) -

P6 (1,731, 2,798, 3,798) (0,533, 0,733, 0,933) (1,731, 2,798, 3,798) (0,533, 0,733, 0,933) (0, 0, 0)

(1,731, 2,798, 3,798)

-

49


STAGE 11: Inconsistency matrix is constructed. By capitalizing on the table showing the distances of binary alternatives between the criteria in Table 9, inconsistency matrix is obtained. Each alternative is compared with each of the other alternatives. The criteria in which an alternative is inferior to another are determined. It is obtained from the maximum value from the criteria in the table.. This value is divided by the highest value in this column. This operation is repeated for all the alternatives. In this way, inconsistency matrix is obtained. Table 11: Inconsistency matrix P1 P2 P3 P4 P5 P6 ̅ 𝐷 = 0,633

P1 -

P2 0

P3 0,900

P4 1

P5 0

P6 0

1 0 1 1 1

0 0 1 0

1 1 1 1

1 1 1 0,846

0,866 0 0,400 0

1 0 1 1 -

STAGE 12: Boolean conformity matrix is formed. Each value in the conformity matrix in Table 10 is compared with the mean of all the values in this matrix. Values bigger than the mean are evaluated as 1 and those smaller than it are evaluated as 0 and in this way, Boolean conformity matrix is obtained. Table 12: Boolean conformity matrix P1 P2 P3 P4 P5 P6

P1 0 1 0 0 0

P2 1 1 1 1 1

P3 0 0 0 0 0

P4 1 0 1 0 1

P5 1 1 1 1 1

P6 1 0 1 0 0 -

50


STAGE 13: Each value in the inconsistency matrix in Table 11 is compared with the mean of all the values in this matrix. Values bigger than the mean are evaluated as 1 and those smaller than it or equal to it are evaluated as 0 and in this way, Boolean inconsistency matrix is obtained Table 13: Boolean inconsistency matrix P1

P1 -

P2 1

P3 0

P4 0

P5 1

P6 1

P2 P3 P4 P5 P6

0 1 0 0 0

1 1 0 1

0 0 0 0

0 0 0 0

0 1 1 1

0 1 0 0 -

STAGE 14: Boolean conformity matrix in Table 12 and Boolean inconsistency matrix in Table 13 are multiplied with each other and thus, spherical matrix is obtained. Table 14: Spherical matrix P1

P1 -

P2 1

P3 0

P4 0

P5 1

P6 1

P2 P3 P4 P5 P6

0 1 0 0 0

1 1

0 0 0 0

0 0 0 0

0 1 1 1

0 1

1

0 -

STAGE 15: Through the analysis of the spherical matrix, superiority scheme of the alternatives is drawn. By evaluating the superiority scheme, the alternatives are interpreted.

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Figure 1: Superiority of the alternatives to each other When the figure is examined, it is seen that first P3 and then P4 should take the priority in the recruitment. In the following stage, P1 is preferred. After these candidates, the most positive candidate is P5. P2 and P5 are observed to be weaker than the other alternatives. 5. RESULT The current study dealt with the issue of personnel selection for a sales engineer post of an international firm by means of Fuzzy ELECTRE I method. The candidates were evaluated by 3 decision makers based on 5 criteria. Among the alternatives, the number 3 candidate should be selected first. Moreover, the experience and foreign language competency criteria were observed to be the most important criteria. As the number 3 candidate is strong in terms of these two criteria, he became the first to be selected. Future research may try multi-criteria decision making methods such as VİKOR, TOPSİS, DEMATEL and their fuzzy versions. In addition, the same method can be used for other positions after the reevaluation of the criteria. REFERENCES 1. Thomson, R. (1993). Managing People (First Edition). USA: Butterworth-Heinemann, 27-29 2. Wang, X., Triantaphyllou, E. (2008). “Ranking Irregularities When Evaluating Alternatives by Using Some ELECTRE methods”, Omega, 36(1), 45-63. 3. Özcan, T., Çelebi, N., Esnaf, S. (2011). “Comparative Analysis of Multi Criteria Decision Making Methodologies and Implementation of a Warehouse Location Selection Problem”, Expert Systems with Applications, 38, 9773–9779. 4. Sevkli, M. (2010). “An Application Of The Fuzzy ELECTRE Method For Supplier Selection”, International Journal of the Production Research, 48:12, 2292-3405.

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ELECTRE III Method For Vendor Selection”, Expert System with Applicatons, 36, 10837-10847.

7. Asgari, F., Amidian, A.A., Muhammadi, J., Rabiee, H.R. (2010). “A Fuzzy ELECTRE Approach for Evaluating Mobile Payment Business Models”, International Conference on Management of eCommerce and e-Government, 351-355. 8. Kaya, T., Kahraman, C. (2011). “An Integrated Fuzzy AHP–ELECTRE Methodology for Environmental Impact Assessment”, Expert Systems with Applications, 38, 8553–8562. 9. Aytaç, E., Işık, A.T., Kundakçı, N. (2011). “Fuzzy ELECTRE I Method for Evaluating Catering Firm Alternatives”, Ege Acedemical Review, 11, 125-134. 10. Hatami, A., Tavana, M. (2011). “An Extension of the ELECTRE I Method for Group Decision Making Under a Fuzzy Environment”,Omega, 39, 373–386. 11. Kabak, M., Burmaoğlu, S., Kazançoğlu, Y. (2011). “A Fuzzy Hybrid MCDM Approach for Professional Selection”, Expert Systems with Applications,39, 3516–3525. 12. Rouyendegh, B.D., Erol, S. (2012). “Selecting the Best Project Using the Fuzzy ELECTRE Method”, Mathematical Problems in Engineering, 1-12. 13. Rouyendegh, B.D., Erkan, T.E. (2012). “An Application of the Fuzzy ELECTRE Method for Academic Staff Selection”, Human Factors and Ergonomics in Manufacturing & Service Industries, 23 (2) 107–115. 14. Vahdani, B., Mousavi, S.M., Tavakkoli, R., Hashemi, H. (2013), “A New Design of the Elimination and Choice Translating Reality Method for Multi Criteria Group Decision Making in an Intuitionistic Fuzzy Environment”, Applied Mathematical Modelling, 37, 1781–1799. 15. Hatami, A., Tavana, M., Moradi, M., Kangi, F. (2013). “A Fuzzy Group ELECTRE Method for Safety and Health Assessment in Hazardous Waste Recycling Facilities”, Safety Science, 51, 414–426. 16. Zandi, A., Roghanian, E. (2013). “Extension of Fuzzy ELECTRE Based on VİKOR Method”, Computers & Industrial Engineering, 66, 258–263. 17. Kheirkhah, A.S., Dehghani, A. (2013). “The Group Fuzzy ELECTRE Method to Evaluate the Quality of Public Transportation Service”, International Journal of Engineering Mathematics and Computer Sciences, 1,3. 18. Xu, J., Shen, F. (2014). “A New Outranking Choice Method for Group Decision Making Under Atanassov’s Interval Valued Intuitionistic Fuzzy Environment”, Knowledge Based Systems, 70, 177–188. 19. Wu, M., Chen, T. (2014). “The ELECTRE Multicriteria Analysis Approach Based on Atanassov’s Intuitionistic Fuzzy Sets”, Expert Systems with Applications,38, 12318–12327. 53


20. Anajkumar, L., Ilangkumuran, M., Sesirekha, S. (2014). “Comparative Analysis of MCDM Methods for Pipe Material Selection in Sugar Industry”, Expert Systems with Applications, 41, 2964–2980. 21. Chen, N., Xu, Z. (2015). “Hesitant Fuzzy ELECTRE II AApproach: A New Way to Handle 4 Multi Criteria Decision Making Problems”, Information Sciences, 292-20, 175-197. 22. Lupo, T. (2015), “ Fuzzy ServPerf Model Combined with ELECTRE III to Comparatively Evaluate Service Quality of International Airpoerts in Sicily”, Journal of Air Management, 42, 249-259.

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PERSONNEL SELECTION THROUGH FUZZY ELECTRE I METHOD

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