Development of a complementary fuzzy decision support system for employees’ performance evaluation

This study aims to improve employee evaluation system in one of the leading automobile manufacturers in Iran by designing a fuzzy decision support system (F.D.S.S.). Since this manufacturer is a large-sized company with over 35,000 employees, the number of managers regularly evaluated requires too much capacity from the human resource team and hence increases the rate of possible misjudgements. However, the proposed F.D.S.S. can reduce the rate of unfair or inconsistent assessments by converting qualitative assessments of the panel to linguistic variables. This action increases the precision of assessment and improves the quality of evaluations. The proposed F.D.S.S. is compared with a fuzzy TOPSIS method to confirm its reliability and validity in which the results show consistency with fuzzy TOPSIS. As a result, the F.D.S.S. is implemented for evaluation of managers in this automobile company instead of the traditional method. ARTICLE HISTORY Received 12 May 2016 Accepted 22 May 2018


Introduction
Nowadays, organisations are more aware that an employee's capability, knowledge and skills play a significant role in their overall success (Neluheni, Pretorius, & Ukpere, 2014). Therefore, the significance of change plans regarding human resource topics such as employee evaluation is noticeably increased among strategic goals (Billsberry, 2007). Such change plans are implemented to optimise the quality of outcomes and productivity, and reduce the inefficiencies, costs and redundancies of organisational processes. Most of these plans end in new methods designed to replace traditional methods practised for many years in these organisations. As a result, it is not possible to implement such changes with ease. The initial step is critical to prove that the change both can work and make improvements.
Employee evaluation is one of the soft topics that play a chief role in the total efficiency of human resource management. In large-sized companies, the urgency to enhance employee evaluation is higher due to the substantial number of repetitions. Managerial level appraisals are also challenging in these organisations because the human resource team should assess a more comprehensive set of criteria for each person, making the evaluation process more time-consuming and sensitive. In contrast, for non-managerial jobs the criteria are few and mostly there is no need for evaluation sessions.
To solve the problem of personnel evaluation at the managerial level of one of the biggest companies in the automotive industry of the Middle East, i.e., IKCO (formerly called Iran National before the Islamic revolution), a new approach is designed and tested by using linguistic criteria to improve the evaluation of managers. IKCO was established in 1963 and is now Iran's largest motor vehicle producer and industrial conglomerate. The number of staff at IKCO is more than 35,000. Since IKCO is a large-sized company, it is proposed to this company to design a fuzzy decision support system (F.D.S.S.) to facilitate the process of manager evaluation and reduce the inaccuracies observed. This F.D.S.S. is developed in MATLAB software (Matrix Laboratory). In order to test the F.D.S.S., a comparative test with a fuzzy TOPSIS is run for three candidates in the middle managerial positions who are considered as well qualified for this test by the human resource department.

Employee evaluation
The fundamental specifics of any human resource management system include the principles of employee evaluation. These principles have a leading role in organisational development practice since they indirectly affect the other systems of human resources by introducing appraisal criteria for each layer of the organisation. The employees and managers consider improvements in their work based on these criteria. If the criteria are not comprehensive or well designed, the process of employee evaluation might harm the goals of human resource management. Also, even if the process is not consistent or fair, employees perceive the results as non-constrictive. All of which makes employee evaluation one of the most sensitive tasks in human resource management. Another application of employee evaluation is training or coaching. Organisations know the strategic value of employees; therefor they attempt to implement policies that improve their knowledge and skills. However, to design these policies they need to find the critical issues. Employee evaluation can help in this regard by showing the major weak spots of a group or team (Hennman & Schwab, 1985).
Thus, the human resource department must ensure that the results of employee evaluation are accurate, consistent and fair in the short and long term, because results of employee evaluation are not just an input for identifying the amount of salaries or benefits but rather an input for other parts of the human resource management system. Employee evaluation might look like a simple task at first. However, it is indeed a complicated matter that requires dynamic and constant planning and improvement (Hennman & Schwab, 1985).

Multi-criteria decision-making
In order to enhance the employee evaluation process, new techniques are implemented. Most of these techniques use multi-criteria decision-making (M.C.D.M.) due to the multi-dimensional advantages that they bring to managerial decision-making. For example, they can increase the speed and precision of assessment. Also, they can provide a full span of options to make sure that each company can find the best choice concerning the circumstance of its operation.
By definition, the problem of measuring according to a set of criteria is known as M.C.D.M.. Different authors have introduced various areas of applications for M.C.D.M. These methods can be used at national, organisational and project levels (Yousefi et al., 2018;Zavadskas et al., 2014). Most of these methods seek to find how to make the best decisions in terms of productivity (Sivilevi cius, . In managerial decisions also M.C.D.M. methods can be made by taking into account the priorities and objectives of different stakeholder's groups. In the hiring process or personnel evaluation at companies, decision makers can use most methods of M.C.D.M.. For instance, Ker sulien_ e and Turskis (2014) focused on a fuzzy M.C.D.M. algorithm, which integrates the principles of fusion of fuzzy information such as additive ratio assessment method with fuzzy numbers (A.R.A.S.), fuzzy weighted-product model and analytic hierarchy process (A.H.P.). The proposed method is appropriate to manage information assessed using both linguistic and numerical scales in a decision-making problem with a group of information sources. In another example, Karabasevic, Zavadskas, Turskis and Stanujkic (2016) designed a framework for the selection of candidates during the process of the recruitment and selection of personnel based on the stepwise weight assessment ratio analysis (S.W.A.R.A.) and A.R.A.S. methods under uncertainties (Ker sulien_ e & Turskis, 2012).
An appropriate mechanism concerning supporting personnel management practices can contribute to value over scope, time and total investment ( Saparauskas, Kazimieras Zavadskas, & Turskis, 2011). A high number of works applying M.C.D.M. techniques for assessment problems are published recently. Hybrid M.C.D.M. approaches, due to their abilities in integrating different techniques assist in handling miscellaneous information taking into account stakeholder's preferences when making decisions in management (Zavadskas, Govindan, Antucheviciene, & Turskis, 2016, Turskis, Zavadskas, Antucheviciene, & Kosareva, 2015.
Selection among alternatives like employee evaluation depends on a set of different conflicting criteria that have different optimisation directions.

Criteria for employee evaluation
In this paper, we design an F.D.S.S. to improve evaluation process. Then we use fuzzy TOPSIS to test our proposed F.D.S.S. With the comparison of two mentioned methods, we approve the reliability and validity of F.D.S.S. The steps of this research are shown in Table 1.
The framework of the current paper is based on the criteria of employee evaluation used in IKCO, as shown in Tables 2 and 3. The human resource team has developed this pool through many years of experience and constant improvements by their experts at the time. Based on the pool, 51 different items are categorised into eight different main skills.
The 51 sub-criteria constrain us to design a questionnaire for pairwise comparison in order to reduce the number of sub-criteria and solve this problem. The main goal of this reduction is to remove those factors that have a shared meaning and are making the ranking ambiguous. Reducing the criteria helps decision makers to more wisely evaluate the candidates since afterwards they only need to consider a few factors.
To make a pairwise comparison, a panel of experts are called including 40 professionals and academics from different deputies of human resources from all branches of IKCO. The questionnaire for this test is confirmed and distributed among the panel. Friedman test is applied to rank the results, which is a non-parametric statistical test used when the dependent variable is ordinal. The results of reduction are shown in Table 4, which categorises 12 sub-criteria in five main criteria.

Fuzzy numbers
In this part, some primal definitions of fuzzy sets, fuzzy numbers and linguistic variables are explained based on Klir and Yuan (1995), Kaufmann and Gupta (1991), Negi (1989), Buckley (1985) and Zadeh (1975). The basic definitions and notations mentioned below are used throughout this paper until otherwise stated.
Definition 1. A fuzzy setÃ in a universe of discourse X is characterised by a membership function mÃ(x) which associates with each element x in X a real number in the interval [0,1]. The function value mÃ(x) is termed the grade of membership of x inÃ. Step 1 Constructing decision model hierarchy (determining criteria and sub-criteria) Step 2 Computing significant sub-criteria deducted from Friedman test Step 3 Applying fuzzy TOPSIS for ranking Step 4 Designing a fuzzy decision support system (F.D.S.S.) for employee evaluation Step 5 Comparing results to confirm the validity and reliability of proposed F.D.S.S.

Source: authors.
Definition 2. A fuzzy setÃ in the universe of discourse X is convex if and only if: for all x1; x2 in X and all k ¾ [0, 1] where min denotes the minimum operator (Klir & Yuan, 1995).
Definition 3. The height of a fuzzy set is the largest membership grade attained by any element in that set. A fuzzy setÃ in the universe of discourse X is called normalised when the height ofÃ is equal to 1 (Klir & Yuan, 1995).  Definition 4. A fuzzy number is a fuzzy subset of the universe of discourse X that is both convex and normal. Figure 1 shows a fuzzy numberÑ in the universe of discourse X that conforms to this definition (Kaufmann & Gupta, 1991).
Definition 6. Trapezoid fuzzy numbers: let, n1 < n2 < n3 < n4 be a fuzzy set. It is called a fuzzy trapezoid number, if its membership function is (Kaufmann & Gupta, 1991) Definition 7. While variables in mathematics usually take numerical values, in fuzzy logic applications, the non-numeric linguistic variables are often used to facilitate the expression of rules and facts. A linguistic variable is a variable whose values are expressed in linguistic terms. The concept of a linguistic variable is very useful in dealing with situations which are too complex or not well defined to be reasonably described in conventional quantitative expressions.  Assume that a decision group has K decision makers and the fuzzy rating of each decision maker can be represented as a positive trapezoidal fuzzy number. Let the fuzzy ratings of all decision makers be trapezoidal fuzzy numbers: Uk ¼ (ak; bk; ck; dk), k ¼ 1; 2; … ; K. Then the aggregated fuzzy rating can be defined as:  From the practical point of view, there are many different membership functions available to choose, but the selection of membership function should be based on the expert's views because matching the data with a suitable membership function is extremely important. In general, the trapezoidal and triangular membership functions are the most used functions. It is believed the trapezoidal membership function generally works very well in different applications (Barua, Mudunuri, & Kosheleva, 2014). However, it is observed that the trapezoidal membership function is usually more effective than using a triangular membership function (Bouchon-Meunier, Dotoli, & Maione, 1996). The trapezoidal membership function is applied to develop the employee evaluation model as the initial model in this paper, and its development can be investigated and compared with other linear and nonlinear membership functions and if required replaced with more optimised ones. In order to describe the assessment status, the closeness coefficient is divided into five equal sub-intervals to cover 0 to 1. For each sub-interval, a linguistic variable is defined to divide the assessment status of candidates, as shown in Table 5.
In the following, every eight steps of fuzzy TOPSIS is delineated, and their related results are shown accordingly.
Step 1: The first step of fuzzy TOPSIS is to develop a hierarchical structure of the assessment problem, which is shown in Figure 1. After developing the hierarchy, decision makers have to determine the relative weights of each criterion and sub-criterion shown in Table 6. Weights are determined by using a pairwise comparison between each pair of criteria. Four decision makers are asked to make pairwise comparisons to determine relative weights, using a one to five preference scale based on the criteria shown in Table 6. All pairwise comparisons are made by four decision makers who based on the norms must attend all interview sessions held in an interactive face to face sessions. Tables 7 and 8 show the average weights of decision makers. The result of another pairwise comparison among sub-criteria is shown in Table 9.
In Tables 7 and 8, the geometric mean for each c1, c2, c3, c4 and c5 is calculated based on the following formula: ffiffiffiffiffiffi ffi x 1 n p x 2 :::x n After this step, the normal weight of each item is calculated based on its weight in the total geometric mean. The total normalised weight of each sub-criteria is shown Observing organisation rules C23 High criticism ability C32 Propagation of coworking culture C42 Attention to redesign job processes to make them better C52 Controlling employees' duties C24 Source: authors.
in the last column of Table 9. For example, C1 has two sub-criteria which have their own weights. Each of them is multiplied by the C1-weight, and the final results are inserted in the last column.
Step 2: The assessment of three candidates was done by four decision makers. This assessment was based on linguistic variables. Table 10 shows the fuzzy number which corresponds to each linguistic variable. For example, candidate A was assessed by D1 for C11 being reported as 'very good' hence the correspondent trapezoidal fuzzy number in Table 11 is '(8, 9, 9, and 10)'.
Step 3: The normalised weight of each sub-criterion is converted to the trapezoidal fuzzy number; Table 12 shows the fuzzy weight of each candidate.
Step 4: In this step, the decision matrix of fuzzy TOPSIS is confirmed and shown in Table 13.
Step 5: In this step, normalised decision matrix of fuzzy TOPSIS is shown in Table 14.
Step 6: Determining the F.P.I.S. (fuzzy positive ideal solution and F.N.I.S. (fuzzy negative ideal solution is done and shown in Table 15.
Step 7: Distances between A, B, C and A À and A þ with respect to each criterion are shown in Tables 16 and 17.
Step 8: The closeness coefficient (CC i ) is shown in Table 18. Based on Table 18 all candidates are approved, and candidate A stands as the best candidate for employee evaluation. Candidates C and B are respectively in the subsequent rankings.
In Table 10, to calculate the average trapezoidal fuzzy number we have used the following logic: For the first number the minimum is used. For the last number the maximum is used. For the two numbers in the middle the average is calculated then rounded.  We can calculate CC i by using the formula below; the results are shown in Table 18.
Based on the results shown in Table 18, candidate A is selected as best with the highest performance. Candidate C stands second, while candidate B has the worst performance.

Proposed F.D.S.S. to evaluate employees
The F.D.S.S. is run to determine the validity and reliability of corresponding results. This step requires building fuzzy inference defined as the process of mapping from a given input to output using fuzzy logic. This mapping provides a basis from which decisions can be made, and patterns discerned. The process of fuzzy inference involves all of the pieces that are described in the previous sections: membership functions, logical operations and if-then rules. Two types of fuzzy inference systems are implemented in the toolbox of MATLAB: Mamdani-type and Sugeno-type. These two types of inference systems vary in the way their outputs are determined (Jang, Sun, & Mizutani, 1997).
Fuzzy inference systems have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems and computer vision. Due to their multidisciplinary nature, fuzzy inference systems are linked with other names such as fuzzy-rule-based-systems. One of the major applications of F.D.S.S. is to enhance qualitative decision-making. As was mentioned before, employee evaluation problems should be attached to linguistic area since the human judgements are not consistent when the numbers are too many.
which was introduced in 1985 (Sugeno, 1985). It is similar to the Mamdani method in many respects. The first two parts of the fuzzy inference process, fuzzifying the inputs and applying the fuzzy operator, are exactly the same. The main difference between Mamdani and Sugeno is that the Sugeno output membership functions are either linear or constant. A typical rule in a Sugeno fuzzy model has the formula like z ¼ ax þ by þ c. Based on mentioned method of fuzzy inference, we have used the Sugeno method. According to points of decision makers at IKCO company we have coded 12 sub-criteria with seven segments of fuzzy membership in MATLAB, we have used five main criteria with three segments of fuzzy membership.
Step 1: We have designed the decision matrix as the input of MATLAB software. The average fuzzy numbers are converted from linguistic variables which are obtained from four decision makers interviewing three candidates.
Step 2: We have to defuzzify Table 19 as the inputting of MATLAB software. There are lots of defuzzification methods. We have used Mean Value method for defuzzification. Table 19 shows the defuzzified matrix.  Step 3: We have coded fuzzy logic in MATLAB. It was based on three linguistic variables with sixteen rules which are determined by experts at IKCO company. We have defined the function of the Sugeno model. The weights in the function are obtained from the TOPSIS model.  Y ¼ 0:2 C 1 þ 0:15 C 2 þ 0:07 C 3 þ 0:39 C 4 þ 0:19 C 5 Step 4: We have run the software. Figure 2 shows the status of candidate A, Figure 3 shows the status of candidate C, and Figure 4 shows the status of candidate B. Based on software calculations the candidate A with value of 8.75 is the first priority in evaluation and candidates C and B are in other ranks with values of 7.53 and 7.21.

Conclusion
In this paper, a fuzzy decision support system (F.D.S.S.) is proposed for employee evaluation. The performance of the proposed method is compared with fuzzy TOPSIS, which confirms the reliability and validity of proposed F.D.S.S. VIKOR and fuzzy axiomatic design (Cevikcan, Cebi, & Kaya, 2009) or COPRAS  are examples of modern methods available that could also be used for comparative test. Nevertheless, we have compared our results with fuzzy TOPSIS for three middle managers to assure top managers that the proposed model not only matches with a similar method but also can enhance the process. As a result, this F.D.S.S. is implemented in IKCO as a replacement for the traditional method to solve the issues observed in evaluation of managers.    The main reason that F.D.S.S. is suggested in IKCO roots in the simplicity and the advantages of this method to other similar methods. Although other methods such as fuzzy A.H.P., fuzzy TOPSIS or fuzzy VIKOR are also possible, there is no reliable source to prove the advantage of one model over another in all conditions, which is the basic reason that many papers are published in order to compare different models in different problems. Given that the main aim of this paper is to develop an initial model, this study just shows the first step of the change plan implemented in IKCO by proving that F.D.S.S. is a valid and advanced tool in comparison with the traditional methods of employee evaluation.