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International Journal of Industrial Engineering, 21(3), 168-178, 2014

ISSN 1943-670X ©INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING

A VARIANT PERSPECTIVE TO PERFORMANCE APPRAISAL SYSTEM: FUZZY C – MEANS ALGORITHM

Coskun Ozkana, Gulsen Aydin Keskinb,*, Sevinc Ilhan Omurcac

[email protected], [email protected], [email protected] a Yıldız Technical University, Mechanical Engineering Faculty, Industrial Engineering Department, Istanbul – Turkey,

Tel: +90 212 383 2865, Fax: +90 212 383 2866 b Kocaeli University, Engineering Faculty, Industrial Engineering Department, Umuttepe Campus, Kocaeli – Turkey c Kocaeli University, Engineering Faculty, Computer Engineering Department, Umuttepe Campus, Kocaeli – Turkey

Performance appraisal and evaluating the employees for awarding is an important issue in human resource management. In performance appraisal systems, ranking scales and 360 degree are the most commonly used types of evaluating methods in which the evaluator gives a score for each criterion to assess all employees. Ranking scales are relatively simple assessment methods. Despite using ranking scales allows the management to complete the evaluation process in a short time, they have some disadvantages. In addition, although, all the performance appraisal methods evaluated the employees in different ways, the employees get scores for each evaluation criteria and then their performances are evaluated according to total scores. In this paper, the fuzzy c – means (FCM) clustering algorithm is applied as a new method to overcome the common disadvantages of the classical appraisal methods and help managers to make better decisions in a fuzzy environment. FCM algorithm not only selects the most appropriate employee(s), but also clusters them with respect to the evaluation criteria. To explain the FCM method clearly, a performance appraisal problem is discussed and employees are clustered both by the proposed method and the conventional method. Finally, the results obtained by the current system and FCM have been presented comparatively. This comparison concludes that, in performance appraisal systems, FCM is more flexible and satisfactory compared to conventional method. Key words: Performance appraisal, fuzzy c – means algorithm, fuzzy clustering, multi criteria decision making, intelligent analysis. 1. INTRODUCTION Employee performances such as capability, knowledge, skill, and other abilities are significantly important for the organizations (Gungor et al., 2009). Hence, accurate personnel evaluation has a significant role in the success of an organization. Evaluation techniques that allow companies to identify the best employee from the personnel are the key components of human resource management (Sanyal and Guvenli, 2004). However, this process is so complicated due to human nature. The objective of an evaluation process depends on appraising the differences between employees, and estimating their future performances. The main goal of a manager is to attain ranked employees who have been evaluated with regard to some criteria. Therefore, the development of efficient performance appraisal methods has become a main issue. Some authors define the performance appraisal problem as an unstructured decision problem, that is, no processes or rules have been defined for making decisions (Canos and Liern, 2008). Previous researches have shown that performance appraisal information is used especially in making decisions requiring interpersonal comparisons (salary determination, promotion, etc.), decisions requiring personal comparison (feedback, personal educational need, etc.), decisions orientated to the continuation of the system (target determination, human force planning, etc.) and documentation. It is clear that in a conventional way, there are methods and tools to do those tasks (Gürbüz and Albayrak, 2014); however, each traditional method has certain drawbacks. In this paper, fuzzy c – means (FCM) clustering algorithm is proposed to make a more efficient performance evaluation by removing these drawbacks. The proposed method enables the managers group their employees with respect to several criteria. Thus, managers can determine the most appropriate employee(s), in case of promotion, salary determination, and so on. In addition, in case of personal educational requirement, they will know which employee(s) needs training by the proposed method. This paper proposes an alternative suggestion to performance appraisal system. After a brief review of performance appraisal in Section 2, FCM algorithm is described in Section 3. A real-life problem is solved both by FCM and the conventional method to evaluate their performances and the findings are discussed in Section 4. Finally, this paper concludes with a discussion and a conclusion.

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2. PERFORMANCE APPRAISAL Long term success of an organization depends heavily on its ability to measure the performances of its employees, and then use that information to insure that performances meet present standards and improve over time. This process is mentioned as performance appraisal or performance evaluation. It is a complex and challenging task. Several different performance appraisal methods can be examined. If it is used effectively, performance appraisal can improve the motivation and performance of an employee. It can also define the training needs of employees. If an employee is unable to meet the expectations, a training program may enable him/her to improve any skills or knowledge (Fisher et al., 1990). Since the appraisal process involves the evaluation of employees, based on a variety of criteria, it is a typical multi criteria decision making (MCDM) problem (Huang et al., 2009) and researchers show that fuzziness could be successfully applied to solve such problems (Chang et al., 2007). Various approaches have been developed to help organizations improve the loyalty of the employees to their work. Some of these are conventional methods which are used at the first practices of performance appraisal concept. Some others include developed modern methods to solve practical problems and to make more objective appraisal of conventional evaluation methods. The common methods used for performance appraisal are forced distribution, mixed standard scales, weighted checklist, critical incident technique, behaviorally anchored rating scale, self-evaluation, graphic rating scales, 360 degree and ranking and paired comparison ranking. When the related literature is examined in depth, ranking and 360 degree methods are found to be the most commonly used techniques. In ranking and paired comparison ranking, the evaluator ranks the employees in order from best to worst, with respect to their overall performances. Hence, the most preferred employee takes place on the top. This method requires the comparison of many pairs and it is easy to explain, understand and use. Also it is generally not time consuming and less expensive than other evaluation techniques; however, it has some disadvantages. The comparisons are highly subjective opinions, which the evaluator may have difficulty in supporting evidence. The ordering of employees depends on the size and character of the particular work group. Also, the method requires that one evaluator knows the performance of each employee and only one person can receive the top ranking. In large groups, this may not be possible (Fisher et al., 1990). In mixed standard scales, the manager marks the grade that describes the evaluated employee better for each category (the quantity and quality of the work, the attention to the work, decision making capability, etc). The method does not encourage an assessment to the employees. Instead, it can strengthen the emotion of “finishing the job as soon as possible”. While the assessment of a person is easy, the interpersonal comparisons can be difficult. Behaviorally anchored rating scale method requires greater attention since a behaviorally anchored rating scale is necessary for each job type. This method depends on the observable behavior of employees. Thus, judgments made during the evaluation still play a major role. A work analysis is required for a sensitive behavior based rating scale. Therefore, all the work analysis has to be updated. The cost of performing this method is high. In graphic rating scales, even though it is easy to assess the employees individually, interpersonal evaluations can be difficult. Using forced distribution method, performance of an employee is determined with respect to the other employees. To determine the performance of an employee, firstly the arithmetic mean and the standard deviation of the scores of the evaluated employees are computed. This is a time consuming method. In critical incident technique, the manager notes the critical incidents of the behaviours of each employee. Since it requires the examination of each employee in detail, it is time consuming, too. Furthermore, it is difficult to quantify the effects of critical incidents on the performances of employees, and hence interpersonal performance differences cannot be determined easily with this method. Using weighted checklist method, it is hard to develop the performance appraisal system. The preparation and application phases of the method also take a long time. Besides, the weights cannot be computed easily. In 360 degree method, performance appraisal process is based on the opinion of different groups of reviewers who socialize with the evaluated employees since they can truly respond to how an employee develops his/her job. This method has some limitations as: Businesses willing to implement this comprehensive method of assessment should be willing to spend the time and effort to train each anonymous evaluator in the process as well as correct ways to interpret questions. Besides, although quite a few information have been obtained related to employees, there is not a certain method how to evaluate this information (Espinilla et al., 2013). In the literature, there are several studies realized to overcome the drawbacks of traditional methods to evaluate the performances of the employees. Shaout and Al-Shammari (1998) present a proposed application of the fuzzy set theory to a personnel performance evaluation system. Aguinis et al. (1998) present a new procedure for computing equivalence bands to implement banding procedures in staffing decision making for employee evaluation. Capaldo and Zollo (2001) focus on the reliability of rating scales in employee assessment by applying fuzzy logic. Chang et al. (2007) develop a

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fuzzy group decision support system including three ranking methods to help making better decision under fuzzy circumstances. Golec and Kahya (2007) present a comprehensive hierarchical structure for evaluating an employee by fuzzy model. Kuo and Chen (2008) apply fuzzy delphi method to construct key performance appraisal indicators for mobility of the service industries. Secme et al. (2009) use integrated fuzzy analytic hierarchy process and TOPSIS for performance evaluation of banks. Moon et al. (2010) use a fuzzy set theory, electronic nominal group technique and TOPSIS for ranking decisions through the multi criteria performance appraisal process for the promotion screening of employees. Wu and Hou (2010) develop an integrated model for employee performance estimation and reduced the work load of 3PL (third party logistics) decision makers. Özdaban and Özkan (2010) suggest a fuzzy model on determining of job and personnel evaluation. Moon et al. (2010) discussed an approach based on fuzzy set theory and nominal group technique for the promotion screening of candidates applying for a particular commission in a military organization. Kelemenis et al. (2011) present a fuzzy TOPSIS for the ranking of the personnel alternatives. Özdaban and Özkan (2011) study to evaluate personnel and jobs jointly with fuzzy distance sets. Sepehrirad et al. (2012) aim to develop a mathematical model for 360 degree performance appraisal in which subjective assessments are weighted and aggregated based on mathematical model, delphi method, fuzzy AHP, simple additing weighting method and TOPSIS. Min-peng et al. (2012) use fuzzy comprehensive evaluation and AHP to model the R&D staff performance appraisal. Meng and Pei (2013) propose the weighted unbalanced linguistic aggregation operators to synthesize linguistic evaluation value, belief degree and experts’ weights. Espinilla et al. (2013) present an integrated model for 360 degree performance appraisal that can manage heterogeneous information and compute a final linguistic evaluation for each employee, applying an effective aggregation that considers the interaction among criteria and reviewers relevance by means of weights. Gürbüz and Albayrak (2014) add an engineering point of view to this process by giving a hybrid MCDM approach to evaluate employees’ performances working for a same task and explain an efficient way of handling the qualitative and quantitative data simultaneously. Although, all the performance appraisal methods evaluated the employees differently, the employees get scores for each evaluation criteria and then their performances are evaluated according to total scores. Alternatively, our proposed method evaluates the employees by each evaluation criteria separately. Recently, researchers have been developing decision support systems and expert systems to improve the outcomes of human resource management. How the proposed method in this study contributes to the literature is summarized as follows:

1. When the literature is examined in depth, it is confirmed that the ranking methods and 360 degree method are used most commonly for performance appraisal problems. In these methods, employees are sorted in a descending order according to their total scores based on the evaluation criteria and the appropriate employee(s) is determined by this ordering. In conventional methods; however, all the evaluation criteria are rated separately, sorting of employees is done according to the total score of each employee. However, the total score can cause the loss of separated effects of all criteria. Divergently in FCM, employees having the same total score can be in different clusters. It means that different employees having the same total score can be dissimilar. Additionally, in this paper, the employees are categorized in four classes instead of sorting. Thus, a performance improvement can be applied when necessary.

2. To the best of our knowledge, there is not any performance classification study published in the literature. In this paper, each employee is assigned to a cluster and the membership degrees of employees to all the clusters are determined by FCM method. In this way, it is possible to know the membership degree of each employee to each cluster.

3. FCM does not do hard clustering, which is one of its major advantages. Consequently, the final decision belongs to the decision maker. In case membership degrees of the employee to a couple of clusters are close to each other, the decision maker is able to make further qualitative analysis and assign this employee to another cluster.

4. Finally, the proposed method is quite flexible and adaptive and has a quite fast computation time. 3. FUZZY C- MEANS CLUSTERING Clustering plays an important role in many engineering fields such as pattern recognition, system modeling, image processing, communication systems, data mining, taxonomy, medicine, geology, and business. Clustering methods divide a set of N input vectors into c groups so that the members of the same group are more similar to one another than to the members of other groups. The number of clusters may be predefined or it may be determined by the method (Tushir and Srivastava, 2010). Unlike traditional hard clustering schemes, such as k-means, which assign each data point to a specific cluster, fuzzy c – means (FCM) algorithm employs fuzzy partitioning such that each data point belongs to a cluster to some degree specified by a membership grade (Chen and Wang, 2009). Dunn (1974) is the first to construct a fuzzy clustering method based on the objective function minimization. Bezdek (1981) generalizes the

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objective function minimization to FCM algorithm by using weighted exponent on the fuzzy memberships (Tushir and Srivastava, 2010; Hung et al., 2008). Teppola et al. (1998) use a combined approach of partial least squares and FCM clustering for the monitoring of an activated-sludge waste-water treatment plant. Liao et al. (2003) develop a modified FCM clustering and apply it to generate fuzzy membership functions for a data set obtained from an industrial application. D’Urso and Giordani (2006) propose a fuzzy clustering model for fuzzy dataset. De Carvalho (2007) introduces adaptive and non-adaptive FCM clustering for symbolic interval data partitioning. Pedrycz and Rai (2008) introduce the concept of collaborative fuzzy clustering. Chen and Wang (2009) use FCM clustering to create the relationship between image blocks. If data groups are well-separated, hard clustering approach can be a natural solution. However, if the clusters are overlapped and some of data belong partially to several clusters, then fuzzy clustering is a natural way to deal with this situation. In this case, the membership degree of a data object to a cluster is a value from the interval [0,1]. The illustration of fuzzy clustering is seen at Figure 1. FCM is an unsupervised clustering algorithm that has a wide domain of applications such as agricultural engineering, astronomy, chemistry, geology, medical diagnosis, pattern recognition and image processing (Ayvaz et al., 2007; Rezaee et al., 1998). In FCM, the clusters are identified based on a known number of clusters (c), level of fuzziness (q); and initial membership values for the input vector. The memberships of the clusters are defined with corresponding membership values, and clusters are described by prototypes that represent the cluster centers.

Figure 1. Illustration of fuzzy clustering (Mingoti and Lima, 2006)

FCM is an iteratively optimal algorithm based on the iterative minimization of the objective function in eq. (1).

( ) ( )∑∑ = =

−= c

j kj

q kjq vxXVJ

1 1

2 ,, µµ (1)

s.t. ∑ =

= c

k kju

1, [ ]1,0∈kju , ∑ =

≤≤ n

j kj nu

1 0

(2) where n denotes the number of data objects and c denotes the number of clusters. Paracompanymeter kjµ is the membership degree of thj data object to cluster k set which is defined as in eq (3). jx represents the

thj data object,

kv represents the center of cluster k which is defined in eq (4). kj vx − denotes the Euclidean distance between data object jx and cluster k . Parameter q is the membership function weighting exponent that determines the amount of fuzziness of the resulting partition (e.g., m = 1 means hard clustering, m = ∞ means completely fuzzy). This parameter can influence the performance of FCM and it is generally suggested to choose a value between1.5 and 2.5 (Wu, 2012). Therefore, in this study, q is set at 2. By minimizing eq. (1) using the Lagrange multiplier method, the updated equations of membership function and cluster center are presented in eq. (3) and eq. (4) respectively.

∑ =

−

⎟ ⎟

⎠

⎞

⎜ ⎜

⎝

⎛

−

− =

1/2

1 µ (3)

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∑

= =

q kj

x v

)(

µ (4)

3.1. Fuzzy C-Means (FCM) Algorithm Inputs: Data objects to be clustered, number of clusters (c), threshold value, clustering error (error_ rate) and the maximum number of iteration (max_iteration). 1. Initialize kjµ (k=1, 2,…,c ; j=1,2,…,n) 2. FOR t = 1, 2, 3, …,max_iteration 2.1. Update cluster centers using eq. (4). 2.2. Update membership values )(newkjµ using eq. (3) 2.3. Update objective function using eq. (1).

2.4. IF ( ( ) ( ) rateerrorXVJXVJ oldq new

q _,,,, )( ≤− µµ ) then stop.

Output: Final data clusters. MATLAB 2008b is used to perform FCM performance appraisal method that mentioned above. In the next section, we introduce a case study and explain how FCM algorithm for a performance appraisal problem is implemented. 4. CASE STUDY The company under consideration is a part of a conglomerate and its business scope covers the production of fiberglass for composites industry. Since the start of production in 1976, the company has continually increased its capacity and grown to one of the valuable European glass fiber manufacturers. The company’s specialized glass fiber reinforcements find applications in advanced moulding and compounding techniques throughout the world. Market requirement continuously leads to the adaptation of existing reinforcement products and to the development activities of new products. Through application research, the performance and properties of the fiber glass and polyester products are tested and evaluated in order to guarantee quality, efficient application on optimal price/performance relationship and the required properties for end products. The company evaluates the performance of its employees conventionally using classical rating method. A decision team is organized in order to evaluate the performance of the employees. Evaluation team is composed of three decision makers (DMs) namely, the human resource manager, the supervisor and the department manager. These experts primarily prepared an evaluation form as seen in Table 1 including performance criteria. Three DMs selected fifteen criteria from the literature for performance appraisal (Golec and Kahya, 2007; Jereb et al., 2005; Heath and Mills, 2000; Gungor et al., 2009). The DMs rate all criteria using a scale from 1 (low performance) to 5 (high performance). Average ratings are calculated for every criterion. To get the Total Performance Point (TPP) for each personnel, the formula below is used:

TPP = (∑Average Rate)*100/75 The existing method uses TPP values for distinguishing performance levels. The current rating method classifies employees into four groups. Hence, TPP for each employee is calculated with respect to the performance evaluation criteria. These employees are grouped according to the score intervals that defined by the company as shown in Table2. We propose an alternative performance appraisal system based on FCM and explain how it is applied for this company. In the proposed method, employee data are clustered by FCM algorithm. Thus, employees are separated into different clusters according to their performances. Different performance levels of employees are represented by the formed clusters which are also represented by their centers. The major advantage of FCM algorithm is not only attaching data objects to precisely one cluster, but also defining the membership degrees to all clusters. An employee with higher membership degree (the closest member to cluster center) indicates the characteristic of cluster better than the other members. The cluster members are arranged based on this consideration.

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Table 1. Existing performance evaluation form Criteria

Nr. Criteria Definition DM1 Rate

DM2 Rate

DM3 Rate

Average Rate

Cr1 Written and unwritten communication skills, non-verbal communication

Cr2 Administrative orientation Cr3 Tolerance for stress Cr4 Leadership Cr5 Negotiation Cr6 Ability to work as part of a team Cr7 Reliability and punctuality Cr8 Appearance of self confidence Cr9 Technical/ professional proficiency

Cr10 Ability to analyze a situation or problem logically Cr11 Planning and organizing Cr12 Delegation and control Cr13 Work experience Cr14 Foreign language Cr15 Decision making

∑Average Rate

Table 2. Company’s existing performance levels

TPP Performance Class Performance Level

80 ≤ TPP Group 1 Excellent 65 ≤ TPP ≤ 79 Group 2 High 50 ≤ TPP ≤ 64 Group 3 Sufficient

TPP ≤ 49 Group 4 Low

This study consists of two parts. In the first part, data are clustered by FCM algorithm to find out performance levels. Membership degrees of each employee regarding all clusters are calculated. Each cluster represents a different performance level. In the second part, the clusters are labeled according to the cluster centers in a descending order. Regarding the fifteen evaluation criteria in the existing evaluation form, DMs rated company's 43 white collar employees according the seven-point-Likert scale as shown in Table 3.

Table 3. Seven-point Likert scale

POINT STATUE 1 Strongly disagree 2 Disagree 3 Disagree somewhat 4 Undecided 5 Agree somewhat 6 Agree 7 Strongly agree

The DMs unanimously assigned only one score to each employee for each criterion. Table 4 shows the assigned values for each evaluation criteria. The above-described FCM algorithm is executed using the data given in Table 4. The necessary inputs of the FCM algorithm for this case are determined:

• data objects to be clustered: they are given in Table 4,

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• number of clusters (c) = 4, (In this case, number of clusters is selected as 4 to make a comparison between FCM and present method in the company)

• threshold value = 2, • clustering error (error_ rate) is assigned as 0.01 and, • the maximum number of iteration (max_iteration) = 100

Table 4. Forty three employees and their degrees according to fifteen criteria

Cr1 Cr2 Cr3 Cr4 Cr5 … Cr11 Cr12 Cr13 Cr14 Cr15

Emp1 3 5 2 3 3 … 5 5 6 7 7 Emp2 5 5 5 5 6 … 6 5 7 3 1 Emp3 1 1 2 5 1 … 3 1 4 1 3 Emp4 4 4 3 4 5 … 4 1 3 3 3 Emp5 6 7 7 1 7 … 5 4 6 6 6 Emp6 6 2 6 5 7 … 3 6 7 6 5 Emp7 7 7 7 7 7 … 5 4 5 5 6 Emp8 7 6 7 7 6 … 6 7 7 7 7

…

Emp38 7 6 7 7 5 … 5 7 7 7 7 Emp39 5 2 3 4 2 … 2 4 2 1 4 Emp40 7 4 7 5 7 … 1 1 7 6 5 Emp41 2 7 6 6 2 … 3 4 5 6 5 Emp42 5 6 6 7 7 … 3 2 6 6 5 Emp43 5 5 5 5 7 … 1 1 3 5 5

Provided performance data are evaluated through FCM algorithm as defined in Section 3.1. The algorithm stops when it reaches to error_ rate or max_iteration. FCM algorithm builds four performance clusters as prescribed and, calculates membership degrees for each employee to these clusters. Calculation results are given in Table 5.

Table 5. Membership degrees of employees to clusters.

C1 C2 C3 C4

Emp1 0.21443633 0.333054928 0.331642207 0.120866535 Emp2 0.171293877 0.332097333 0.33287785 0.16373094 Emp3 0.044678208 0.102174467 0.102756383 0.750390942 Emp4 0.079157642 0.359219516 0.363810579 0.197812262 Emp5 0.281263461 0.307020511 0.306057201 0.105658827 Emp6 0.37790524 0.27944337 0.277199301 0.065452089 Emp7 0.282133918 0.310063914 0.308234455 0.099567713 Emp8 0.816997851 0.079740624 0.079139493 0.024122033

…

Emp38 0.851186915 0.065566013 0.064997284 0.018249788 Emp39 0.049265973 0.122513799 0.123239926 0.704980302 Emp40 0.211488565 0.317279163 0.317811551 0.153420721 Emp41 0.182358008 0.359145491 0.357400589 0.101095913 Emp42 0.333832814 0.309370753 0.30306031 0.053736123 Emp43 0.123176258 0.392829103 0.394525496 0.089469143

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FCM algorithm determines for each employee the cluster membership, considering the highest membership degree. As seen in Table 5, each employee is attached to the most appropriate cluster. For instance, Emp1 is attached to the cluster 2 with 0.333054928 and Emp3 is attached to the cluster 4 with 0.750390942 membership degree. In machine learning approach, the clusters are represented by their centroids effectively. In Table 6 the “cluster center” column is another output of the FCM algorithm. After the algorithm is completed, the clusters are constituted and the cluster centers are calculated and, clusters are labeled.

Table 6. The classification of the employees by FCM algorithm into the four performance level

CLUSTER NUMBER CLUSTER MEMBERS

CLUSTER CENTER CLUSTER LABEL

1 6, 8, 16, 22, 28, 38, 42 6.103838

Outstanding employee

2 1, 5, 7, 9, 10, 11, 12, 14, 17, 18, 19, 20, 23, 24, 26, 27, 31, 41 4.473125

Successful employee

3 2, 4, 13, 21, 29, 30, 32, 33, 34, 35, 40, 43 4.454098

Successful but development required in

certain criteria

4 3, 15, 25, 36, 37, 39 2.521343 Development required in many criteria

As seen in Table 6, the proposed method clustered the employees 6, 8, 16, 22, 28, 38 and 42 as cluster 1 that takes the highest performance measure (6.103838) and, is labeled as “outstanding employee”. An outstanding employee will be awarded by the top management. This cluster involves the highest performance employees according to FCM. The employees included in cluster 2 will be encouraged and motivated for the award in the future. At cluster 3, the deficiencies of the employees should be eliminated by training. 3, 15, 25, 36, 37 and 39th employees are clustered as cluster 4. They belong to the class of “development required in many criteria”. This cluster with the smallest center value (2.521343) includes the most inappropriate employees for awarding within 43 employees. While reviewing these clusters detailed, the membership degrees should be examined. For instance in cluster 4, 3rd employee’s membership degree is 0.75039; the 36th one’s is 0.6180; the 39th one’s is 0.7049. Between these three employees, the 36th one has a better performance level then the other two. The 3rd employee has the worst performance level then 36th and 39th one. If the company wants to dismiss an employee, in this situation the 3rd employee must be chosen among these three employees. Likewise, if the company wants to award only one employee, the 16th employee with the 0.88948 membership degree to cluster 1 should be chosen. The classification of 43 based on TPP and FCM are shown comparatively in Table 7.

Table 7. Comparison the results of TPP (existing performance appraisal system) and FCM (proposed method)

EMPLOYEE

NUMBER TPP FCM

Point Group Cluster Number 1 70 2 2 2 66 2 3 3 31 4 4 4 55 3 3 5 79 2 2 6 82 1 1 7 80 1 2 8 100 1 1

…

38 98 1 1 39 39 4 4 40 69 2 3 41 69 2 2 42 82 1 1 43 66 2 3

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The results of TPP and FCM methods, which are shown in Table 7, point out two occurring cases: the 2nd, 40th and 43rd employees are in the second group with the points 66, 69, and 66, respectively, according to the TPP; however, these employees are in the 3rd cluster according to FCM. Similarly, according to TPP, the 7th employee is in the first group, but FCM classifies the same employee as a “successful employee.” In brief, the conventional method classifies the 2nd, 7th, 40th, and 43rd employees different than FCM. In another case, although the 40th and 41st employees have the same TPP value (69), FCM assigns them to different clusters. This is probably due to the fact that the accumulated TPP value in the conventional method can cause the loss of the separate effects of the fifteen criteria.

5. DISCUSSION AND CONCLUSION Performance appraisal problems have been solved by several methods. The most commonly used one in practice is ranking and paired comparison ranking. In this process, as a multi criteria decision making problem, the raters always express their preferences on alternatives or on the attributes of employees, which can be used to help rank and categorize the employees or select the most appropriate one(s). While the performance appraisal method covers an important requirement, it is well known that traditional techniques have several weaknesses. Therefore, in this study, FCM algorithm is proposed as an alternative to conventional methods for performance appraisal problem and successful results are obtained. The proposed method makes some significant and remarkable contributions to strengthen the weaknesses of the conventional methods. Moreover, the proposed method enables the managers to group their employees with respect to several criteria. Thus, managers can determine the most appropriate employee(s), in case of promotion, salary determination, etc. In addition, in need of personal education, they will know which employee(s) requires training using the proposed method. FCM evaluates the employees according to their criteria values separately. This is the first contribution of the algorithm. On the other hand, using the current practice, the employees are sorted in a descending order with respect to the total scores based on evaluation criteria and grouped according to the predetermined thresholds. In addition, although, all evaluation criteria are rated separately, the classification of employees is done according to an aggregated value. The aggregated TPP value can cause a loss of separated effects of fifteen criteria. Divergently in FCM, the employees having the same total score can be assigned to different clusters. It means that different employees having the same total score can be dissimilar. Furthermore, in this paper, employees are categorized in four classes instead of sorting. Thus, a performance improvement can be done if necessary. The next contribution is about the determination of the clusters. Using the present practice of the company, the clusters are predetermined based on some thresholds to form the groups. However, only the cluster number and clustering error are necessary for FCM algorithm and the clusters and cluster bounds are formed automatically. Another contribution of the algorithm is about the membership degrees of the employees to the clusters. In the conventional method, an employee is strictly a member of a specific group or not. However, in FCM, each data point belongs to a cluster to some degree specified by a membership degree. The membership degrees of each employee to all clusters are computed using FCM. In this manner, prioritization can be done using these membership degrees in a certain cluster. The soft clustering ability of FCM is another advantage benefited in this paper. This allows managers to make final decision better. Namely, if the membership degrees of an employee to more than one cluster are closer to each other, the decision maker can assign this employee to the with higher membership degree In this paper, FCM is used for the first time as an effective solution method for performance appraisal problem. FCM algorithm not only selects the most appropriate employee(s), but also clusters all of them according to their membership degrees. Consequently, all sectors and all enterprises can use FCM for performance appraisal easily and efficiently due to its flexibility and fast computation time.

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