Integrating Analytic Hierarchy Process with TOPSIS Method for Performance Appraisal of Private Banks

Studies in System Science (SSS) Volume 1 Issue 4, December 2013

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Integrating Analytic Hierarchy Process with TOPSIS Method for Performance Appraisal of Private Banks under Fuzzy Environment Samantha Islam*1, Golam Kabir*2, Tahera Yesmin3 Department of Industrial & Production Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh, School of Engineering, University of British Columbia (UBC), Kelowna, BC, Canada, Department of Industrial & Production Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh samantha500030@yahoo.com; 2golam.kabir@ubc.ca; 3taherayesmin@ipe.buet.ac.bd

*1

Abstract There is no denial of the fact that preparing employee appraisal is a critical managerial attempt in any organization associated with numerous opinion and enormous criteria which confines the implication of any single objective model.

Therefore, multi-criteria decision making approach has been implemented for this framework. Although, the dimensions of this model were principally designed with Balance Score Card model, AHP (Analytical hierarchical process), conventional TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution method), traditional Fuzzy AHP or the combination of two of them, there were loads of flaws that resulted in controversy of that analysis. They came short of defining a set of quantitative indicators while they lacked in scoring system or sometimes they showed inconsistencies or lack of mathematical precision and so on.

However, in order to ensure the drawbacks of these models to be overcome, in this article the integration of modified Fuzzy AHP and Fuzzy TOPSIS has been used to establish a new approach for preparing bank employee appraisal. This methodology will bring the vital facets of the model to shorten and helps bridge the gap among staffs for accomplishing more ideal level of performance.

Keywords Analytic Hierarchy Process; Decision Makin; Fuzzy Set; Performance Appraisal; TOPSIS

Introduction The main objectives of an appraisal system are usually to review performance, potential and identify training and career planning needs. In addition the appraisal system may be used to determine whether employees should receive an element of financial reward for their performance. Performance reviews give managers and employees opportunities to discuss how employees

progress and to see what sort of improvements can be made or help given to build on their strengths and enable them to perform more effectively (ACAS, 2005).

Performance measurement is a systematic effort with the purpose of discovery to what extent the services meet the people needs, and to what extent it has the ability to meet the needs (Halachmi, 1999).

The purpose of performance evaluation of a management technique is to control the project's progress and to evaluate the efficiency and effectiveness resulting from performing the project (Akalu, 2003). This frequently has considerable impact on organizations' performances and achievements.

However, the problem is that the performance evaluation models in management literature assume, in an implicit way, that the tasks' criteria are distinct and standardized, while, in the majority of systems, specially professional and service work, the judgment requires allocating enough time for completing every task (Hopp, 2007) and also selecting the relevant criteria for its evaluation. In some cases appraisers may allow the rating they give to one characteristic to excessively influence their ratings on all subsequent factors. The appraiser who decides that the employee is good in one important aspect and gives him or her similarly high markings for all other aspects demonstrates the 'halo' effect (Adeak, 2009).

Alternatively, one serious fault can sometimes lead an appraiser to reduce markings in other areas (the 'horns' effect) (Management Study Guide).

TaHo and Wu (2006) conducted the performance evaluation of banks by using market stocks and through Grey Relation analysis (GRA). By studying industry and trade, they selected indicators and

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implemented those indicators to evaluate the relative performances of Australia's three large banks. On the other hand, the debate of selecting reliable indicators and judgment on their importance size possesses some ambiguities and contradictions that have originated from the human differences. Furthermore, in the typical performance evaluation models, indicators mainly have not been defined based on organizational strategies and objective, as a result, they entail some problems in practice. Rinalini and Noth (2006), in their study, evaluated the activities of investigation and development organizations, using a comparative approach. The study of Lee et al., (2008) on combining the fuzzy AHP and balance score card (BSC) approaches was a step towards solving the problem of judgment on the indicators. On contrary, Ardabili (2011) mentioned the use of FAHP and TOPSIS to evaluate employee performance. The relative weights of the selected evaluation indices were estimated using fuzzy analytic hierarchy process and SAW and TOPSIS were employed for performance ranking of staff departments.

However, in this paper, different kinds of appraisal system and their limitations were discussed concisely.

Making an appraisal is such a decision making process that is too complex to be understood quantitatively.

Many approaches like conventional manager evaluation, multi source feedback, staffing review and performance evaluation are used to determine it. Among all these methods performance measurement is the most popular and logical one. Nevertheless, this process corresponds to the use of multiple criteria and enormous alternatives. In addition to this, the process is carried out based on the verbal expression. In contrast, the performance evaluation is an objective approach that demands precise mathematical computation. However, people succeed by using knowledge that is imprecise rather than precise. Fuzzy set theory, originally introduced by Lotfi Zadeh in the 1960's, resembles human reasoning in its use of approximate information and uncertainty to generate decisions. It was specifically designed to mathematically represent uncertainty and vagueness and provide formalized tools for dealing with the imprecision intrinsic to many problems. In this article, a comprehensive model has been developed for preparing employee appraisal for Bank. Furthermore, a case study has been conducted to depict the rationale of this framework and so forth.

Conventional Manager Evaluations In most organizations, the performance appraisal 58

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process begins when a manager rates an employee on a series of attributes. For instance, in one business, managers rated their front-line employees on whether they "demonstrated positive energy by handling customer issues on the spot." In many cases, the ratings do not correlate in any meaningful way to measurable outcomes (Koning, 2004). Often, there is no correlation, or worse, a negative one. In some cases, employees with the highest performance levels received the lowest ratings, and as a result, the least rewards. The end result is that the system weeds out top performers while rewarding mediocre ones. This happens because manager ratings are inherently subjective and this subjectivity only increases when the appraisals are linked to financial incentives such as merit pay raises.

In one company, employees referred to the performance appraisal as "that form you need to fill out to give a person a raise (Gallup business Journal)."

Multisource Feedbacks Many organizations have introduced multisource feedback, such as 360-degree surveys, in which managers, peers, or subordinates rate an employee on a fairly extensive list of attributes. But here are a few common problems. Occasionally, employees get to choose the people who evaluate them. This self-selection inherently biases the approach, as many employees tend to nominate colleagues who like them or will give them good ratings. Companies usually don't train managers.

Besides, 360 surveys can be quite time consuming, it takes skill to sort through and analyze the plethora of data and give employees clear and actionable feedback.

Most 360 reports do not measure performance; they measure style. Unless they are validated against the actual business outcomes required for success in a role, the reports may be a better reflection of a desired work style rather than desired results.

The natural tendency when using 360 degree survey is to fixate on the employee's problem areas while overlooking their strengths. Yet Gallup's research indicates that this is a backward approach, because a person's greatest opportunities for development are in his or her areas of strengths, not weaknesses. This means that a person's biggest opportunity for development has been completely overlooked. (“The Four Disciplines of Sustainable Growth, Gallup business journal�)

Staffing Review Staffing reviews are management team meetings in which managers rank, evaluate, and discuss the

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employees in the organization. Prior to the staffing review session, each participating manager lists the names of the employees he or she supervises. As objectively as possible -- and using a good balance of valid performance measures -- the managers then group those employees into three categories: top, middle, and bottom performers. (Sometimes a fourth category is included for employees who are new to their positions.)

To be sure, this forced-ranking evaluation method is controversial. Forcing the identification of a given proportion of bottom performers-even in topperforming teams-can alienate some employees and impede their development. But forcing a fixed proportion of employees into performance categories may not be necessary.

Performance Measurements Using a measurement-based performance appraisal process is the most objective approach to evaluate employees. One of its significant advantages is that it makes the process predictable for employees; they'll know just what they need to do to earn rewards.

Clearly, the challenge is to measure the right outcomes and to balance them properly for each role. Every measure has a downside, so a balanced approach usually provides a more accurate way to quantify an employee's performance. Various methods used in this approach are discussed below: Balance Score Card Balanced scorecard, is a widely-used performance measurement tool, aiming at planning and controlling organization activities to achieve organization objectives (Davis & Albright, 2004; Lawrie & Cobbold, 2004; Pinero, 2002). Robert Kaplan and David Norton, two professors of business department in Harvard University, by publishing an article in the journal of Business Review Harvard in 1992, introduced the model. This method turns mission and strategy into targets and criteria which can be classified into four different perspectives, including: learning and growth, internal business processes, financial and customer perspectives (Kaplan & Norton, 1992).

The incremental use of BSC around the world has made its weak and strong points appear, and entailed conduction of numerous studies on the issue (Nilsson, and Kald, 2002). The evidence obtained from these studies has confirmed the efficacy of BSC in private and public sectors, for instance two surveys results have revealed dissatisfaction of organization branch

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managers with BSC. Moreover, 48% of respondents have disagreed with fairness of BSC performance evaluation. It could be concluded that BSC might not lead us to the achievement of strategic and organizational objectives (Kaplan & Norton, 1992) Some reported shortcomings for BSC are: i) Firstly, significant contradiction among managers in implementing partial patterns because of impreciseness, subjectivity and verbal of the indicators in defining reinforcing quantitative indicators (Norreklit, 2003). ii) It could be of use that the organization under study is defined in terms of strategy and vision. iii) And it comes short of defining a set of quantitative indicators to stabilize performance values, either at an individual level (i.e. performance indicator) or integrate indicators. In contrast, BSC's results are integrated subjectively by users (Sue et al., 2003). iv) It has no scoring system.

Analytical Hierarchy Process According to Thomas Saaty (1991), the creator of the AHP, the theory of this multi-criteria method reflects the functioning of the human mind, that is, the natural way in which the mind deals with a large quantity of information, characteristic of complex situations. To facilitate understanding, the mind sorts elements with common properties into groups. The repetition of the model permits the aggregation of new elements into subgroups, at different levels of the system. This dynamic permits the structuring of a hierarchy, where the maximum level is composed of a single element, in which the objective of the decision is making process.

The purpose of the stratification is to verify the weight with which the elements of the level immediately below influence the level above and, consequently, the impact that each of these elements exercises on the main objective. The weights are attributed through a sequence of pair comparisons of dominance of the lowest factors in relation to the objective (Saaty, 1977).

Nevertheless one cannot ignore that the AHP has been the object of serious criticism since its appearance in the literature in the eighties. Some of the main criticisms are(i) Decision agents using verbal comparisons will have their judgments automatically converted to a numerical scale; however, the correspondence between these two scales is generally based on non tested hypotheses. (ii) Using the scale from 1 to 9 may cause inconsistencies; In this approach crisp values are taken 59

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which cannot be a measurement of verbal expressions. (iii) Weights are obtained with no reference to the scales on which attributes are measured; this may lead to different understandings of the questions, which is a potential source of errors. (iv) New alternatives may revert the initial ranking of alternatives: this has been raised by various authors such as Belton & Gear (1982), Dyer & Ravinder (1983) and Lootsoma. (v) The number of pair wise comparisons required may be considered too large which may lead to errors by fatigue. (vi) Dyer (1990) pointed out that the axioms of the AHP are not founded on descriptions of rational behavior that can be tested; Harker & Vargas (1987) have presented strong objections to this sixth criticism though. However, it was Bana e Costa & Vansnick (2001) that presented one of the most bruising criticisms to the AHP. These two authors identified a problem that occurs in the computation of the vector of priorities, particularly in the scales derived from the method, from a reciprocal positive matrix filled by questioning the decision agent. That problem has implications in the way priorities are quantified and not in the order of priorities. A quite serious aspect also raised by Bana e Costa & Vansnick (2001) is that the coefficient of inconsistency proposed by Saaty is not able to detect such flaw of the AHP. Therefore, conventional AHP seems inadequate to capture decision maker’s requirements explicitly (Kabir & Hasin, 2011a; 2011b). Since the fuzzy linguistic approach can take the optimism/pessimism rating attitude of decision-makers into account, linguistic values, whose membership functions are usually characterized by triangular fuzzy numbers, are recommended to assess preference ratings instead of conventional numerical equivalence method (Kabir & Hasin, 2012a).

As a result, the fuzzy-AHP should be more appropriate and effective than conventional AHP in real practice where an uncertain pairwise comparison environment exists (Sen & Cinar, 2010; Kutlu & Ekmekçioglu, 2012; Parsaei et al., 2012; Kabir & Hasin, 2012b). Decisionmakers usually find that it is more confident to give interval judgments than fixed value judgments. This is because usually he/she is unable to explicit about his/her preferences due to the fuzzy nature of the comparison process (Kahraman et al., 2003).

Proposed Model Performance appraisal is formed by performance evaluation of the employees. The managerial people 60

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who are in charge of performing employee appraisal by various methods. However, a proper evaluation process is necessary that would be precise and logical.

This is because it is not only motivational for the employees but also very much beneficial for the company to judge people in the right way. To do so the inherent quality of people needs to be judged in a quantified method. Besides, the verbal opinion and complement of managers are used to justify employees. Therefore there is vagueness in between these two steps.

Fuzzy logic is an effective tool for operating linguistic data. Fuzzy operation can be conducted by introducing this type of information to computer. For this, the most valid methodology is fuzzy set, logic and systems. The base of fuzzy system is used in decision making process for inputs built linguistic variables from membership function. These variables match with each other by linguistic IF-THEN rules’ preconditions. The result of each rule is determined by obtaining numerical value with defuzzified method from the membership values of input.

The verbal information is collected from the operators which are used to determine the membership function according to Fuzzy logic system. In this study the triangular membership function is used to determine the linguistic variables. After that, Fuzzy comparison matrices are formed for the defined evaluation criteria and sub-criteria. Then Fuzzy AHP method is applied on them to compute their weights. Finally, Fuzzy TOPSIS analysis is conducted on them by taking the employees as alternatives and evaluates them to prepare a final ranking.

Modified Fuzzy AHP There are the several procedures to attain the priorities in FAHP. The fuzzy least square method (Xu, 2000), method based on the fuzzy modification of the LLSM (Boender et al., 1989), geometric mean method (Buckley, 1985), the direct fuzzification of the method of Csutora and Buckley (2001), synthetic extend analysis (Chang, 1996), Mikhailov’s fuzzy preference programming (Mikhailov, 2003) and two-stage logarithmic programming (Wang et al., 2005) are some of these methods. Chang’s extent analysis is utilized in this research to evaluate the focusing problem. Chang (1996) develops a new approach for handling fuzzy AHP, using triangular fuzzy numbers for the pair wise comparison scale of fuzzy AHP, and using the extent analysis method for the synthetic extent values of the pair wise comparisons. A TFN denoted as M = (l, m, u)

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where l<m<u, has the following triangular type membership function:

synthetic extent with respect to the criterion x, denoted as S x = (lx, mx, ux), can be obtained via Eq. (3):

(1)

(3)

In this methodology, decision makers were asked to indicate the relative importance of two evaluation criteria in the same level. The scores of pair wise comparison are treated as linguistic variables, which are represented by positive TFNs as illustrated in Table 1

Where n is the size of the fuzzy judgment matrix A. To obtain

, perform the fuzzy addition

operation such that (4)

TABLE 1 LINGUISTIC TERM AND CORRESPONDING TRIANGULAR FUZZY NUMBERS (KABIR, 2012)

Linguistic term Extreme unimportance Intermediate values between 7-1 and 9-1 Very unimportance Intermediate values between 5-1 and 7-1 Essential unimportance Intermediate values between 3-1 and 5-1 Moderate unimportance Intermediate values between 1 and 3-1 Equally importance Intermediate values between 1 and 3 Moderate importance Intermediate values between 3 and 5 Essential importance Intermediate values between 5 and 7 Very vital importance Intermediate values between 7 and 9 Extreme unimportance

Fuzzy Number 9-1 8-1 7-1 6-1 5-1 4-1 3-1 2-1 1 2 3 4 5 6 7 8 9

Triangular scale 1/9,1/9,1/9 1/9,1/8,1/7 1/8,1/7,1/6 1/7,1/6,1/5 1/6,1/5,1/4 1/5,1/4,1/3 1/4,1/3,1/2 1/3,1/2,1 1,1,1 1,2,3 2,3,4 3,4,5 4,5,6 5,6,7 6,7,8 7,8,9 9,9,9

and to obtain fuzzy addition operation of C

ky

, perform the values such that (5)

and then compute the inverse of the vector in Eq. (5) by using Eq. (6): (6) According to Wang et al. (2007), Eq. (6) can be corrected as Eq. (7) (7)

The second step is to derive fuzzy ranking value of S x.

In this step, S x is compared to other synthetic extent After obtaining the fuzzy judgment matrices, Fuzzy values of A, S y = (ly, my, uy). According to Chang pair wise comparisons can be combined by use of the (1996), the degree of possibility of S x ≥ S y is obtained following algorithm (Büyüközkam and Feyziog  lu,by the following equation: 2004; Chang et al., 2009): (8)

(2) where (lijk, mijk, uijk) is the fuzzy evaluation of sample members k (k = 1,2, …., K).

The extent analysis method and the principle of TFNs comparison are used to derive the importance weights of criteria from pair wise comparisons. Let W be the normalized weight vector of triangular fuzzy comparison matrix A, which includes the importance weights of criteria in the crisp form. The steps for calculating this vector are as follows.

The first step is to calculate the fuzzy synthetic extent value of each pair wise comparison. Linguistic pair wise comparisons are transformed to corresponding TFNs illustrated in Table 1. Denote C  xy as the TFN related to the pair wise comparison of criterion x over criterion y, which is represented as (lxy, mxy, uxy).

According to Chang (1996), the value of fuzzy

where d is the ordinate of the highest intersection point D between

and

. To compare S.x and S.y,

we need both the values of V(S.y ≥ S.x) and V(S.x ≥ S.y).

However, according to Wang et al. (2007), the degree of possibility defined by the extent analysis method is an index for comparing two triangular fuzzy numbers rather than an index for calculating their relative importance. Therefore, normalized degrees of possibility can only show to what degree a triangular fuzzy number is greater than all the others, but cannot be used to represent their relative importance (Kabir & Sumi, 2013a). This problem can be well resolved by using the total integral value with index of optimism developed by Liou and Wang (1992), which derives the priorities of the synthetic extent values of A by the

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where α is index of optimism which represents degree of optimism for decision makers. If α approaches 0 in [0, 1], the decision makers are more pessimistic and otherwise they are more optimistic (Sen & Cinar, 2010; Kabir, 2012; Kabir & Sumi, 2012; 2013b).

numbers. Ratings of alternatives versus criteria and the importance weights of criteria are normalized before multiplication. The membership function of each fuzzy weighted rating can be developed by interval arithmetic of fuzzy numbers. A ranking method can then be applied easily to develop positive and negative idea solutions in order to complete the fuzzy TOPSIS model.

Finally, define the normalized importance weight vector W = (w1, w2,…., wn)T of the fuzzy judgment matrix A by using following equation:

In this section, a TOPSIS-based model is presented. It is used to fined the rank of the alternative employees as follows:

following equation: (9)

(10) where wx is a non-fuzzy number.

After comparison is made, it is necessary to check the consistency ratio of the comparison. To do so, the graded mean integration approach is utilized for defuzzifying the matrix. According to the graded mean integration approach, a fuzzy number L x = (l, m, u) can be transformed into a crisp number by employing the below equation: (11) After the defuzzification of each value in the matrix, ‘consistency ratio’ (CR) of the matrix can easily be calculated and checked whether CR is smaller than 0.10 or not (Kutlu & Ekmekçioglu, 2012; Kabir & Sumi, 2013a; 2013b).

Step 1: Construct normalized decision matrix.

This step transforms various attribute dimensions into non-dimensional attributes, which allows comparisons across criteria. Normalize scores or data as follows: (10) Step 2: Construct the weighted normalized decision matrix.

Assume a set of weights for each criteria is wj for j = 1,…, n. Multiply each column of the normalized decision matrix by its associated weight. An element of the new matrix is: vij = wj rij , for i = 1, …, m; j = 1, …, n

(11)

Step 3: Determine the positive ideal and negative ideal solutions.

Positive Ideal solution:

TOPSIS Method

A*={ v1* , …, vn*},where vj* ={max(vij)if j∈J;min(vij)if j∈J'(12)

TOPSIS is one of the useful Multi Attribute Decision Making techniques. It is used when the user prefers a simpler weighting approach. TOPSIS method was firstly proposed by Hwang and Yoon (1981).

According to this technique, the best alternative would be the one that is nearest to the positive ideal solution and farthest from the negative ideal solution (Benitez et al., 2007; Kabir and Hasin, 2012b; Kabir and Sumi, 2012). The positive ideal solution is a solution that maximizes the benefit criteria and minimizes the cost criteria, whereas the negative ideal solution maximizes the cost criteria and minimizes the benefit criteria (Wang and Chang, 2007; Wang and Elhag, 2006; Wang and Lee, 2007; Lin et al., 2008). But in normal Fuzzy approach, linguistic variables result in crisp value that may create vagueness and imprecise transformation of verbal expression.

Negative ideal solution:

In fuzzy TOPSIS model, the ratings of alternatives under criteria and importance weights of criteria are assessed in linguistic values represented by fuzzy 62

A'={v1' , …, vn'},where v'={min(vij)if j∈J;max(vij)if j∈J'}(13) Step 4: Calculate the separation measures for each alternative, using the n-dimensional Euclidean distance.

The separation from the ideal alternative is: (14) Similarly, the separation from the negative ideal alternative is: (15) Step 5: Calculate the relative closeness to the ideal solution Ci*. The relative looseness of the alternative Ai with respect to A* is defined as (16) Since

≥ 0 and

≥ 0, then clearly

є [0,1]

Step 6: By comparing Ci* values, the ranking of alternatives are determined.

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For ranking alternatives using this index, alternatives can be ranked in decreasing order. The basic principle of the TOPSIS method is that the chosen alternative should have the “shortest distance” from the positive ideal solution and the “farthest distance” from the negative ideal solution.

Case Study The Standard Bank Limited has been taken as a sample to be considered. Three decision makers were interviewed and their views and illustration was taken.

They were the assistant bank branch manager, Human resource manager and Deputy managing director.

They prepare appraisal on the basis of 5 criteria: Job knowledge, Communication, Interpersonal skill, Quality, Technical & Technological knowledge which is given in Table 2.

Having job Knowledge means Possessing skills and knowledge to perform the job competently. In contrast, Communication skill needs Organizing and expressing

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ideas and information clearly, using appropriate and efficient methods of conveying the information. The Interpersonal Skills consists of sensitive to the needs, feelings and capabilities of others, approaching others in a non-threatening and pleasant manner and treats them with respect. The criteria Quality stands for Completing high quality work according to specifications, thoroughly following standards and procedures, Keeping complete records, Paying attention to details and having a strong sense of quality. Good technical skill means having technical knowledge and experience in the related field. Standard Bank has decided a rating scale and judged an employee according to that scale. Their current appraisal form is given in the appendix. The criteria were enlisted and the corresponding sub-criteria were sorted out from these.

In this study, the employees of accounts department have taken as alternatives. FUZZY AHP has been implemented to get the weights of criteria and subcriteria. Finally, FUZZY TOPSIS has been applied to conquer the performance appraisal as follows:

TABLE 2 CRITERIA AND SUB-CRITERIA FOR PREPARING PERFORMANCE APPRAISAL FOR THE BANK EMPLOYEE

Competency

Sub-criteria

Job Knowledge (J)

Possesses skills and knowledge to perform the job competently (J1)Improve ideas to develop the work (J2)Understands and responds prompt to the internal or external clients needs (J3)

Communication (C)

Is able to communicate clearly and seeks alternative ways to express his/her ideas (C1)Ability to negotiate, using persuasion to convince the others of his/her ideas (C2)Is able to listen, making sure that his understanding is compatible with the other party’s speech (C3)

Interpersonal Skills (I) Quality(Q) Technical and technological knowledge (T)

Conflict Resolution (I1)Pleasant manner and treats people with respect (I2)Ethics (I3) Completes high quality work (Q1)Desire to Improve Quality (Q2)Self-motivated (Q3) Has technical knowledge and experience in the related field (T1)Handles working tolls (T2)Proficiency in English (T3) TABLE 3 FUZZY COMPARISON MATRIX FOR CRITERIA

J

C

I

Q

T

DM 1 DM 2 DM 3 Group DM 1 DM 2 DM 3 Group DM 1 DM 2 DM 3 Group DM 1 DM 2 DM 3 Group DM 1 DM 2 DM 3 Group

J 1,1,1 1,1,1 1,1,1 1,1,1 1/6,1/5,1/4 1/5,1/4,1/3 1/4,1/3,1/2 0.17,0.26,0.5 1/7,1/6,1/5 1/6,1/5,1/4 1/6,1/5,1/4 0.14,0.19,0.25 0.25,0.44,1 1/3,1/2,1 1/3,1/2,1 0.25,0.44,1 1/9,1/8,1/7 1/8,1/7,1/6 1/9,1/8,1/7 0.11,0.13,0.17

C 4,5,6 3,4,5 2,3,4 2,3.91,6 1,1,1 1,1,1 1,1,1 1,1,1 1/4,1/3,1/2 1/4,1/3,1/2 1/3,1/2,1 0.25,0.38,1 2,3.63,5 3,4,5 3,4,5 2,3.63,5 1/6,1/5,1/4 1/5,1/4,1/3 1/5,1/4,1/3 0.17,0.23,0.33

I 5,6,7 4,5,6 4,5,6 4,5.31,7 2,3,4 2,3,4 1,2,3 1,2.62,4 1,1,1 1,1,1 1,1,1 1,1,1 3,4.64,6 4,5,6 4,5,6 3,4.64,6 1/5,1/4,1/3 1/4,1/3,1/2 1/4,1/3,1/2 0.2,0.3,0.5

Q 2,3,4 1,2,3 1,2,3 1,2.29,4 1/4,1/3,1/2 1/5,1/4,1/3 1/5,1/4,1/3 0.2,0.28,0.5 1/5,1/4,1/3 1/6,1/5,1/4 1/6,1/5,1/4 0.17,0.22,0.33 1,1,1 1,1,1 1,1,1 1,1,1 1/8,1/7,1/6 1/7,1/6,1/5 1/8,1/7,1/6 0.13,0.15,0.2

T 7,8,9 6,7,8 7,8,9 6,7.65,9 4,5,6 3,4,5 3,4,5 3,4.31,6 3,4,5 2,3,4 2,3,4 2,3.3,5 5,6.65,8 5,6,7 6,7,8 5,6.65,8 1,1,1 1,1,1 1,1,1 1,1,1

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TABLE 5 FUZZY COMPARISON MATRIX FOR SUB-CRITERIA WITH RESPECT

Results and Discussions

TO JOB KNOWLEDGE

The detail procedure and out come is discussed as follows: Fuzzy AHP At the beginning of the calculation, it is necessary to check the consistency ratio of the comparison matrix The largest Eigen value 位max of the table 4 matrix is = 5.22105. The random consistency index of a 5-factor matrix = 1.12 as provided in table, and therefore, the calculated Consistency Index=0.0552618, inconsistency ratio= 0.049. Clearly, as stated before, a Consistency ratio that is less than 10% is acceptable and the judgments are said to be consistent.

TABLE 4 DEFUZZYFICATION MATRIX

J C I Q T

J 1 0.29 0.19 0.5 0.13

C 3.94 1 0.46 3.59 0.24

I 5.37 2.58 1 4.59 0.32

Q 2.36 0.30 .23 1 0.16

T 7.6 4.37 3.37 6.6 1

SJ= (14, 20.16, 27.0) * [1/56.98, 1/48.89, 1/48.79]= 0.2457, 0.4124, 0.5523 Sc=(5.37, 8.47, 12.0)* [1/63.15, 1/48.89, 1/42.42]= 0.0850, 0.1732, 0.2829 SI=(3.56, 5.09, 7.58)* [1/65.76, 1/48.89, 1/39.81]= 0.0541, 0.1041, 0.1904 SQ=(11.25,13.36, 21)*[1/60.03, 1/48.89, 1/45.54]= 0.1874, 0.2732, 0.4611

Decision maker DM 1 DM 2 DM 3 DM 1 DM 2 DM 3 DM 1 DM 2 DM 3

J1

J2

J3

SJ3=(2.20, 3.64, 6.00)*[1/16.7, 1/13.13, 1/11.42] = 0.1317, 0.2772, 0.5254 The integral values of these values were calculated as below IJ1= 0.5687, IJ2= 0.1548, IJ3= 0.3029 After obtaining the total integral values the priority weights of each criterion over another WJ1= 0.5541, WJ2= 0.1508, WJ3=0.2951 Likewise the previous method all sub-criteria under criteria are compared to each other on the basis of decision of three decision makers and their global and local weights are shown in Table 6.

TABLE 6 GLOBAL AND LOCAL WEIGHT OF SUB-CRITERIA

Priority of Criteria

The integral values of these values were calculated as below

J

0.3918

C

0.1724

I

0.1093

Q

0.2884

T

0.0380

WJ=0.3918,WC=0.1724,WI=0.1093, WQ=0.2884, WT= 0.0380 Now, the comparison matrix for the sub-criteria and the calculated weights are calculated. The comparison matrix for sub criteria under Job knowledge is given below: The de-fuzzyfication is done as previous Table 4 and found that Consistency ratio =0.00891884. Consistency ratio CR = 0.0153. Clearly, as stated before, a CR ratio that is less than 10% is acceptable and the judgments are said to be consistent.

64

J3 1,2,3 3,4,5 2,3,4 1/3,1/2,1 1/4,1/3,1/2 1/3,1/2,1 1,1,1 1,1,1 1,1,1

SJ2=(1.42, 1.70, 2.50)*[1/19.42,1/13.13, 1/8.70 ] = 0.0731, 0.1294, 0.2874

Criteria

After obtaining the total integral values the priority weights of each criterion over another

J2 2,3,4 4,5,6 3,4,5 1,1,1 1,1,1 1,1,1 1,2,3 2,3,4 1,2,3

SJ1=(4.00, 7.79, 12.0)*[1/12.5, 1/13.13, 1/15.62] = 0.3200, 0.5933, 0.7682

ST=(1.61, 1.81 ,2.20)* [1/69.19, 1/48.89, 1/36.38]= 0.0232, 0.0370, 0.0605

IJ=0.4057, Ic=0.1786, II=0.1132, IQ=0.2987, IT=0.0394

J1 1,1,1 1,1,1 1,1,1 1/4,1/3,1/2 1/6,1/5,1/4 1/5,1/4,1/3 1/3,1/2,1 1/5,1/4,1/3 1/4,1/3,1/2

SubCriteria J1 J2 J3 C1 C2 C3 I1 I2 I3 Q1 Q2 Q3 T1 T2 T3

Priority of SubCriteria 0.5541 0.1508 0.2951 0.3282 0.1689 0.5028 0.5496 0.1515 0.2989 0.5296 0.1579 0.3124 0.2731 0.4518 0.2751

Final Priority of SubCriteria 0.2171 0.0591 0.1156 0.0566 0.0291 0.0867 0.0601 0.0166 0.0326 0.1527 0.0455 0.0901 0.0104 0.0172 0.0105

Fuzzy TOPSIS Analysis Now a TOPSIS analysis is conducted for computing the rank of the employees on the basis of the previous evaluated weights of criteria and sub-criteria. A rating scale is used in standard Bank for employee

Studies in System Science (SSS) Volume 1 Issue 4, December 2013

evaluation. The dedicated fuzzy number for their rating and the scale are shown in Table 7.

TABLE 7 LINGUISTIC VARIABLE CORRESPONDING TRIANGULAR FUZZY NUMBER

Linguistic variable Exceptional Exceeds expectations Meets expectations Below expectations Needs Improvement

Fuzzy number 7,9,10 5,7,9 3,5,7 1,3,5 0,1,3

Definitions of the ratings are given below: Exceptional: Consistently exceeds all relevant performance standards. Provides leadership, fosters teamwork, is highly productive, innovative, responsive and generates top quality work. Active in industryrelated professional and/or community groups.

Exceeds Expectations: Consistently meets and often exceeds all relevant performance standards. Shows initiative and versatility, works collaboratively, has strong technical & interpersonal skills or has achieved significant improvement in these areas.

Meets Expectations: Meets all relevant performance standards. Seldom exceeds or falls short of desired results or objectives. Lacks appropriate level of skills or is inexperienced/still learning the scope of the job.

Below Expectations: Sometimes meets the performance standards. Seldom exceeds and often falls short of desired results. Performance has declined significantly, or employee has not sustained adequate improvement, as required since the last performance review or performance improvement plan.

Needs Improvement: Consistently falls short of performance standards.

TABLE 8 PERFORMANCE EVALUATION MATRIX FOR DECISION MAKER 1

J1 J2 J3 C1 C2 C3 I1 I2 I3 Q1 Q2 Q3 T1 T2 T3

ALT1 5,7,9 3,5,7 5,7,9 5,7,9 5,7,9 3,5,7 3,5,7 7,9,10 7,9,10 5,7,9 5,7,9 3,5,7 5,7,9 3,5,7 1,3,5

ALT2 5,7,9 3,5,7 1,3,5 1,3,5 3,5,7 3,5,7 3,5,7 5,7,9 5,7,9 3,5,7 5,7,9 5,7,9 3,5,7 1,3,5 5,7,9

ALT3 7,9,10 5,7,9 5,7,9 3,5,7 3,5,7 3,5,7 1,3,5 5,7,9 3,5,7 7,9,10 1,3,5 3,5,7 5,7,9 7,9,10 3,5,7

ALT4 3,5,7 5,7,9 5,7,9 1,3,5 0,1,3 1,3,5 3,5,7 1,3,5 3,5,7 3,5,7 1,3,5 5,7,9 3,5,7 3,5,7 1,3,5

ALT5 5,7,9 3,5,7 5,7,9 7,9,10 7,9,10 3,5,7 3,5,7 5,7,9 3,5,7 5,7,9 5,7,9 3,5,7 5,7,9 5,7,9 7,9,10

So, Decision matrix for performance evaluation are given in Table 8.

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Therefore the decision matrices for 2 and 3 are made as before and the overall decision matrix are given in Table 9. After that the normalized decision matrix are determined which is shown in Table 10. Weights obtained are assigned to rating according to Table 1 are calculated (Table 11).

TABLE 9 GROUP DECISION MATRIX FOR ALTERNATIVE

J1 J2 J3 C1 C2 C3 I1 I2 I3 Q1 Q2 Q3 T1 T2 T3

ALT1 5,7.6,10 3,5.6,9 5,7,9 1,5.3,9 5,7,9 3,5,7 3,5.6,9 5,8.3,10 3,6.8,10 5,7,9 5,7,9 1,4.2,7 5,7,9 3,5.6,9 1,4.2,7

ALT2 5,8.3,10 3,5.6,9 1,3.9,9 1,3.9,9 3,6.3,9 3,5,7 3,6.3,9 3,6.3, 5,7,9 3,5,7 5,7,9 5,7,9 1,4.2,7 1,3,5 5,7,9

ALT3 5,8.3,10 3,6.3,9 1,4.7,9 1,4.2,7 3,5.6,9 1,4.2,7 1,3.9,9 3,6.3,9 3,5.6,9 5,8.3,10 1,3,5 3,5,7 5,7,9 5,8.3,10 3,6.3,9

ALT4 3,5.6,9 3,6.3,9 3,6.3,9 1,3,5 0,1.7,7 1,3.6,7 3,5,7 1,3.9,9 3,5.6,9 3,5,7 1,3.9,9 5,7,9 1,4.2,7 1,4.2,7 1,3.6,7

ALT5 5,7,9 3,5,7 5,7,9 5,7.6,10 3,7.4,10 3,5.6,9 3,5.6,9 5,7.6,10 3,6.3,9 3,6.3,9 5,7,9 3,6.1,10 5,7.6,10 3,6.8,10 3,7.4,10

TABLE 10 NORMALIZED FUZZY DECISION MATRIX

J1 J2 J3 C1 C2 C3 I1 I2 I3 Q1 Q2 Q3 T1 T2 T3

ALT1 0.5,0.76,1 0.3,0.56,0.9 0.5,0.7,0.9 0.1,0.53,0.9 0.5,0.7,0.9 0.3,0.5,0.7 0.3,0.56,0.9 0.5,0.83,1 0.3,0.68,1 0.5,0.7,0.9 0.5,0.7,0.9 0.1,0.42,0.7 0.5,0.7,0.9 0.3,0.56,0.9 0.1,0.42,0.7

ALT2 0.5,0.83,1 0.3,0.56,0.9 0.1,0.39,0.9 0.1,0.39,0.9 0.3,0.63,0.9 0.3,0.5,0.7 0.3,0.63,0.9 0.3,0.63,0.9 0.5,0.7,0.9 0.3,0.5,0.7 0.5,0.7,0.9 0.5,0.7,0.9 0.1,0.42,0.7 0.1,0.3,0.5 0.5,0.7,0.9

ALT3 0.5,0.83,1 0.3,0.63,0.9 0.1,0.47,0.9 0.1,0.42,0.7 0.3,0.56,0.9 0.1,0.42,0.7 0.1,0.39,0.9 0.3,0.63,0.9 0.3,0.56,0.9 0.5,0.83,1 0.1,0.3,0.5 0.3,0.5,0.7 0.5,0.7,0.9 0.5,0.83,1 0.3,0.63,0.9

ALT4 0.33,0.62,1 0.33,0.7,1 0.33,0.7,1 0.11,0.33,0.56 0,0.19,0.78 0.11,0.4,0.78 0.33,0.56,0.78 0.11,0.43,1 0.33,0.62,1 0.33,0.56,0.78 0.11,0.43,1 0.56,0.78,1 0.11,0.47,0.78 0.11,0.47,0.78 0.11,0.4,0.78

ALT5 0.5,0.7,0.9 0.3,0.5,0.7 0.5,0.7,0.9 0.5,0.76,1 0.3,0.74,1 0.3,0.56,0.9 0.3,0.56,0.9 0.5,0.76,1 0.3,0.63,0.9 0.3,0.63,0.9 0.5,0.7,0.9 0.3,0.61,1 0.5,0.76,1 0.3,0.68,1 0.3,0.74,1

TABLE 11 WEIGHTS AND SCALE OF THE ENTIRE CRITERION

Sub criterion J1 J2 J3 C1 C2 C3 I1 I2 I3 Q1 Q2 Q3 T1 T2 T3

Normalized global weight 1 0.272 0.532 0.261 0.134 0.399 0.277 0.076 0.150 0.703 0.209 0.415 0.048 0.079 0.048

Fuzzy scale 1,1,1 1/4,1/3,1/2 1/3,1/2,1 1/4,1/3,1/2 1/8,1/7,1/6 1/3,1/2,1 1/4,1/3,1/2 1/9,1/9,1/9 1/9,1/8,1/7 1/3,1/2,1 1/5,1/4,1/3 1/3,1/2,1 1/9,1/9,1/9 1/9,1/9,1/9 1/9,1/9,1/9

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Studies in System Science (SSS) Volume 1 Issue 4, December 2013

TABLE 12 WEIGHTED NORMALIZED DECISION MATRIX

ALT1 0.5,0.76,1 0.075,0.187,0.45 0.167,0.35,0.9 0.025,0.177,0.45 0.063,0.1,0.15 0.1,0.25,0.7 0.075,0.187,0.45 0.056,0.092,0.11 0.033,0.085,0.14 0.167,0.35,0.9 0.1,0.175,0.3 0.033,0.21,0.7 0.56,0.78,1 0.033,0.062,0.08 0.011,0.047,0.08

J1 J2 J3 C1 C2 C3 I1 I2 I3 Q1 Q2 Q3 T1 T2 T3

ALT2 0.5,0.83,1 0.075,0.187,0.45 0.033,0.195,0.9 0.025,0.13,0.45 0.038,0.09,0.15 0.1,0.25,0.7 0.075,0.21,0.45 0.033,0.07,0.1 0.056,0.088,0.13 0.1,0.25,0.7 0.1,0.175,0.3 0.167,0.35,0.9 0.11,0.47,0.78 0.01,0.033,0.056 0.56,0.78,1

ALT3 0.5,0.83,1 0.075,0.187,0.45 0.033,0.235,0.9 0.025,0.14,0.35 0.038,0.08,0.15 0.033,0.21,0.7 0.025,0.13,0.45 0.033,0.07,0.1 0.033,0.075,0.129 0.167,0.415,1 0.02,0.075,0.167 0.1,0.25,0.7 0.56,0.78,1 0.056,0.092,0.11 0.033,0.07,0.078

So the Weighted normalized decision matrix is determined (Table 12).

Therefore, the distance of each alternative from FPIS and FNIS; close coefficient hence the rank are shown in Table 13.

TABLE 13 DISTANCE OF EACH ALTERNATIVE FROM FPIS AND FNIS & CLOSENESS COEFFICIENT AND RANK

Ci*

Rank

A1

10.89

4.03

0.27

3

A2

10.50

4.37

0.29

1

A3

11.17

3.91

0.26

4

A4

11.33

3.42

0.23

5

A5

10.88

4.14

0.28

2

The rank of the employees has been given as A2> A5>A1>A3>A4 Standard Bank uses the previous almost a heuristically.

In addition to this, they give the same priority to all the criteria. Nevertheless, all criterion is not of same importance and their priority is the prerequisite of the employeeâ&#x20AC;&#x2122;s performance evaluation. By applying the new method, the achieved outcome is much more mathematical and logical. In this study, we have considered bank employees, but this method can be successfully implemented to other organizations too.

This outcome can act as a factor of motivation for the betterment of employee performance as well as the progress of the company greatly.

Conclusion Appraisal, a great tool to connect employees, managers and trade unions to obtain their views and commitment can help improve employees' job performance by identifying strengths and weaknesses and determining how their strengths can be best utilized within the organization and weaknesses

66

ALT4 0.33,0.62, 0.083,0.233,0.5 0.11,0.35,1 0.028,0.11,0.5 0,0.027,0.13 0.0367,0.2,0.78 0.083,0.187,0.39 0.122,0.044,0.11 0.037,0.078,0.143 0.11,0.25,0.78 0.022,0.1,0.33 0.187,0.39,1 0.11,0.47,0.78 0.012,0.052,0.086 0.012,0.052,0.086

ALT5 0.5,0.7,0.9 0.075,0.167,0.35 0.167,0.35,0.9 0.125,0.253,0.35 0.038,0.108,0.16 0.1,0.28,0.9 0.075,0.187,0.45 0.056,0.084,0.11 0.033,0.078,0.129 0.1,0.315,0.9 0.1,0.175,0.3 0.1,0.305,1 0.56,0.84,0.11 0.033,0.075,0.11 0.033,0.082,0.11

overcome as well can help to reveal problems which may restrictin employeesâ&#x20AC;&#x2122; progress and cause inefficient work practices.

However, sometimes the mismatch in evaluation process can mislead a company to motivate people in the right way. This can be caused by various reasons.

Sometimes the basic criteria can not be identified for performance evaluation, where the illustration or subcriteria is not clear to the management or the requisite can be identified but can not be given proper importance while all the requirements are regarded as same weight. Besides, in some cases proper alignment among the multiple characteristics can not be established; sometimes accurate logical and mathematical process can not be obtained. Hence the outcome can be dissatisfactory In this article, an appraisal preparing method has been shown based on employee evaluation. In this process the subjective and objective aspects were assembled while trying to cover all the factors that could affect the performance of employees. This method tended to remove the limitations of previous methods to a large extent. However, it may experience some shortcomings in case considering the 360 degree approach. Here the opinions of some decision makers were taken. But it would be more worthwhile if the study would be conducted more thoroughly. Although, a 360 degree approach is really time consuming. Moreover, here the case study of the bank was performed on the basis of their previous performance measurement attributes.

But some additional attributes like performance in previous project or future commitment or goal orientation etc should be added to measure the performance of employees. It actually depended on the field over which the study was carried out. Whatever the criteria is, this frame work can be used greatly. Using smart

Studies in System Science (SSS) Volume 1 Issue 4, December 2013

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software like MATLAB for the simulation process can fuel this agenda to a great extent.

Journal of the Institute do Management Sciences, 36(3),

This study has been conducted by taking a sample of a bank’s accounts department employees. The bank can determine whether to give promotion, rewards or any other benefit by determining their employee’s performance by this method. This will be very fruitful and there is no chance of the induction of personal liking or disliking and it can be open to all. As a result employees can be inspired to better off their performance.

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Samantha Islam attained her Bachelor degree on Industrial & Production Engineering from Bangladesh University of Engineering & Technology (BUET), Dhaka. ‘Integrating Analytic Hierarchy Process with TOPSIS Method for Performance Appraisal of Private Banks under Fuzzy Environment’ is her first research oriented work. She is enthusiastic and keen on the area of Engineering management and ache for paving the way for the development of this field.

Golam Kabir is a PhD student in the School of Engineering at The University of British Columbia (UBC), Kelowna, British Columbia, Canada. He was also an Assistant Professor in the Department of Industrial and Production Engineering at Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh. He received his MSc and BSc in Industrial and Production Engineering from BUET in 2011 and 2009, respectively. His research interests include multi-criteria decision analysis under risk and uncertainty, infrastructure asset management and life cycle analysis. He has a large number of international journal publications in his credit.

Tahera Yesmin received her BSc and MSc in Industrial and Production Engineering from Bangladesh University of Engineering and Technology, Dhaka, Bangladesh. She is an Assistant Professor in the Department of Industrial and Production Engineering at Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh.

She has a good number of international journal and conference papers. Her research interests include safety analysis, human factors and project planning and management.

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Appendix TABLE: CURRENT APPRAISAL FORM OF STANDARD BANK LTD

Annual Performance Appraisal Form Of Standard Bank Limited Appraisal Score

Overall Score:

/ 5.0

EMPLOYEE INFORMATION

Name:

Job Title:

Manager Name:

Department:

Hire Date:

Last Appraisal Date:

Evaluated By: DEFINITION OF RATINGS EXCEPTIONAL (5): Consistently exceeds all relevant performance standards. Provides leadership, fosters teamwork, is highly productive, innovative, responsive and generates top quality work. Active in industryrelated professional and/or community groups.

EXCEEDS EXPECTATIONS (4): Consistently meets and often exceeds all relevant performance standards.

Shows initiative and versatility, works collaboratively, has strong technical & interpersonal skills or has achieved significant improvement in these areas.

MEETS EXPECTATIONS (3): Meets all relevant performance standards. Seldom exceeds or falls short of desired results or objectives. Lacks appropriate level of skills or is inexperienced/still learning the scope of the job.

BELOW EXPECTATIONS (2): Sometimes meets the performance standards. Seldom exceeds and often falls short of desired results. Performance has declined significantly, or employee has not sustained adequate improvement, as required since the last performance review or performance improvement plan.

NEEDS IMPROVEMENT (1): Consistently falls short of performance standards.

INSTRUCTIONS Describe the employee's contributions in each of the performance categories below. It is IMPERATIVE that you illustrate specific, detailed examples since the last performance evaluation. Ratings MUST support and be substantiated by narrative comments.

PERSONAL ATTRIBUTES (Matrix format) Score: / 5.0 % Ratings Score Competency Comments Scale /5.0  Quality Completes high quality work according to specifications.

Thoroughly follows standards and procedures. Keeps complete (0%) records. Pays attention to details. Has a strong sense of quality and knows how to achieve it.  Job Knowledge Possesses skills and knowledge to perform the job competently.

(0%)  Communication Organizes and expresses ideas and information clearly, using appropriate and efficient methods of conveying the information.

(0%)

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Studies in System Science (SSS) Volume 1 Issue 4, December 2013



Interpersonal Skills Is sensitive to the needs, feelings and capabilities of others.

Approaches others in a non-threatening and pleasant manner and treats them with respect.

Technical and technological knowledge Has technical knowledge and experience in the related field

(0%)  (0%)

SUMMARY SCORE PERSONAL ATTRIBUTES (Matrix format) Score : 0.0 Quality Job Knowledge Communication Interpersonal Skill Technical & Technological Knowledge EMPLOYEE COMMENTS

I agree with this evaluation I do not agree with this evaluation MANAGER COMMENTS Comments

70

1.3

2.5

3.8

5.0