**Ranking Academic Performance Using Fuzzy Vikor: A Case of Secondary Schools At Perlis** Siti Nor Nadrah Muhamad\*, Rasyidah Abd Halim, Wan Nurshazelin Wan Shahidan Faculty of Computer & Mathematical Sciences Universiti Teknologi MARA Perlis Branch, Malaysia. Nordianah Jusoh Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Alor Gajah Branch, Malaysia. Saida Farhanah Sarkam Faculty of Business and Management, Universiti Teknologi MARA Alor Gajah Branch, Malaysia. , , *Abstract* *Ranking is the process of structuring alternatives in order of priority. It is based on the criteria determined for each alternative involved. In this study, the researcher analyzed the percentage of candidates who scored in the 2016 Malaysia secondary school national examination, Sijil Pelajaran Malaysia (SPM), in the state of Perlis. The schools represent an alternative, while the examination subjects as the criterion. The study used fuzzy VIKOR method to determine the priority rank for the performance of five schools. Fuzzy VIKOR method evaluates the criteria and compose composite index of each alternative for the purpose of arranging them in order of preference alternatives. The result showed that fuzzy VIKOR method is able to rank the data more fair and accurate than other conventional methods such as TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) and PROMETHEE (Preference Ranking Organization METHod for Enrichment Evaluations). By using the proposed approach, the ambiguity involved in the evaluation data can be effectively represented and processed to assure a more effective evaluation process. The accurate ranking of schools might benefit the Education Ministry at the district level as more resources could be provided to the least performed school.* *Keywords: Fuzzy, Fuzzy VIKOR Method, Defuzzification, School Ranking, Performance Evaluation, Multi criteria decision making (MDCM)* **Introduction** In the last few years, the evaluation of the education system with excellent schools ranks has become an increasingly popular benchmark of the education system (Musani & Jemain, 2015). This is because using school ranking as a school performance evaluating tool will provide a direct influence on the schools involved. While poor school rankings might demotivate the school administrators, but if it is seen in a positive way, the stated school might improve themselves to perform better in the examination for the following years. The good-ranked schools, too, will benefit from the ranking as it will not only bring pride to the teachers and administrators but also encourages parents to send their children to those school. Furthermore, the local authority might decide to allocate more resources to the low-performing schools so that they could be as good (Tierney, 2013). This ranking also can be used as reference for formulating strategies and taking corrective actions to enhance academic achievement. This study will help secondary schools to evaluate their performance as it has direct influence on schools involved. Besides that, it is important for school administration to increase the positive publics’ perception to the school. In addition, it also affects the expenses allocated for student recruitment and operations, as well as acting as a guide for the school strategic planning. Hence, it will identify the school’s needs of assistance in terms of infrastructure, financing, enhancement of teachers and also for the development of conducive teaching and learning environment. Away from conventional methods of doing multi criteria decision making (MDCM) evaluation, this study applies the fuzzy VIKOR method in order to rank the schools. The fuzzy VIKOR method provides accurate information for evaluating school performance using the quantitative and qualitative data. This study uses data to measure the school’s academic achievement in Sijil Pelajaran Malaysia (SPM) 2016 for the purpose of ranking. Based on these data, the issue of how the data containing different information for each school can be analyzed in a fair and accurate manner where the results can reflect the actual situation of the school as it can be addressed well. **Literature Review** 1. *VIKOR Method* VIKOR method is a multi-criteria optimization which can solve multi criteria decision making (MCDM) problem with conflicting and noncommensurable (different units) criteria. It assumes an acceptable compromise for conflict resolution as decision-makers want a solution that is closest to the ideal and the alternative is assessed according to the set of criteria. This method focuses on ranking and selecting from a set of alternatives and determining a compromise solution to the conflicting decision criteria and can help decision-makers to get the final solution and achieve a decisive decision (Opricovic & Tzeng, 2007). 2. *Fuzzy VIKOR* The VIKOR method can obtain the gap between the ideal alternative and each alternative, the rank order of alternatives, and the priority of improving the weaknesses of each alternative (Kuo & Liang, 2012). Therefore, some studies extend the VIKOR method to solve the problems of uncertain conditions, as this method deals with clear-cut and uncertain data simultaneously. As a result, Opricovic and Tzeng (2003) proposed using fuzzy logic for the VIKOR method by applying some defuzzification techniques, simply by using fuzzy values to define the attributes’ ratings and their importance in the first phase of their study. Opricovic and Tzeng (2007) also extended VIKOR in fuzzy environment to solve the problem of uncertainty in the decision-making state priority where it makes the ranking list, gives weight and provides a compromise solution. Musani and Jemain (2013) have applied fuzzy VIKOR to evaluate school performance based on linguistic information. This study was improved by Musani and Jemain (2015), who proposed fuzzy VIKOR method to solve school ranking problem. Meanwhile, Wu et al. (2012) suggested hybrid MCDM model by using analytics hierarchy process (AHP) and VIKOR method to rank 12 private universities in Taiwan. Kuo and Liang (2012) postulated to use fuzzy VIKOR to evaluate the performance of three major intercity bus companies while Chang (2014) used the method in studying the medical and healthcare service quality performance. In Rezaie et al. (2014), the authors suggested fuzzy AHP and VIKOR method to evaluate the performance of cement firms. Fuzzy AHP method was used to determine the weight of criteria taking the subjective judgment of decision maker and VIKOR method was then applied to rank the firms. Other than that, fuzzy VIKOR was used by Girubha and Vinodh (2012) in selecting the best automotive component that can be used for instrument panel by considering environmental impact factors while Tzeng et al. (2002) applied fuzzy VIKOR in ranking a number of restaurant locations. Devi (2011) used VIKOR to develop a method for solving multiple-criteria decision making problems and applied it to solve a robot selection problem for material handling task. Chen and Wang (2009) proposed fuzzy VIKOR method to deal with suppliers or vendors selection problems in the delivery process efficiency. Opricovic and Tzeng (2007) compares extended VIKOR method with three multi criteria decision making methods namely TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) and ELECTRE (Elimination and (Et) Choice Translating Reality) method to deal with hydropower systems. **Research Methodology** The main objective of the study is to rank school performance based on academic achievement in SPM examination for year 2016 and the data was collected from Jabatan Pendidikan Negeri Perlis, Malaysia. This study ranked five selected schools (School DSA, School SA, School A, School SS and School TB) and to be evaluated by multiple conflict core subjects (Malay, English, History and Mathematics) using five grades for which are excellent (g5), honours (g4) , average (g3), pass (g2) and fail (g1). The schools selected were from the same rural area, based on similarities in the courses offered and the selection did not involve religious schools, science and vocational or technical school where intakes were based on a number of preconditions (Musani & Jemain, 2016). The Fuzzy VIKOR method is used in this study for the calculation of school ranking and to decide the best core subject. The data were analyzed using Microsoft Excel 2007. The modified Fuzzy VIKOR and the fuzzy set theory methods are shown in following steps: *Step 1: Identify appropriate linguistics variab**le and trapezoidal fuzzy number* In this method, the ranking of school performance are assessed in linguistics variable can be expressed in positive trapezoidal fuzzy number. It is suggested by Zadeh (1975) which provides a level of knowledge that is more suitable to be used in fuzzy linguistic variables. As an example, the achievements of students on the course outcome for SPM result level are labeled as fail, pass, average, honours and excellent. As previously stated, the linguistic variables and a trapezoidal fuzzy numbers for this study was practiced by Zadeh (1975) as shown in Table 1. A positive trapezoidal fuzzy number can be defined as (a1, a2, a3, a4). The membership function is given by defined as: > (1) The algebraic operation for the trapezoidal fuzzy number can be addition, multiplication and subtraction. Given any two positive trapezoidal fuzzy numbers, A =(a1, a2, a3, a4) B =(b1, b2, b3, b4) and a positive real number r, some main operations of fuzzy numbers A and B were practiced by Liu et al. (2012). > A + B = (a1+b1, a2+b2, a3+b3, a4+b4) > > A - B = (a1-b1, a2-b2, a3-b3, a4-b4) > > A x B ≈ (a1b1, a2b2, a3b3, a4b4) > > r x B ≈ (rb1, rb2, rb3, rb4) (2) Table 1: Linguistic variables for each level of achievement | Linguistic | Variable | Trapezoidal fuzzy number (TzFN) | | ---------- | -------- | ------------------------------- | | Excellent | g5 | (8,9,10,10) | | Honours | g4 | (6,7,8,9) | | Average | g3 | (3,4,5,7) | | Pass | g2 | (1,2,3,4) | | Fail | g1 | (0,0,0,2) | *Step 2: Construct a fuzzy decision matrix.* > (3) Xij and Wj are linguistic variables denoted by trapezoidal fuzzy number where Xij is the rating of alternative Ai with respect to Cj. Wj is the importance weight of the j th criterion. A trapezoidal fuzzy number can be defined as . *Step 3: Defuzzification of fuzzy decision matrix and fuzzy importance weight are determined.* \= \= (4) Where the following is fuzzy important weight can be calculated as: > , 0 (5) (6) M is the Total number of alternative, is standard deviation value for criteria , is the important weight of the criterion While, is mean of rating of the alternative with respect to and = total rating of the alternative with respect to . *Step 4: Determine the best value and worst value for all criteria using the equation bellow:* *Step 5: Compute the values of utility index, Si, and value of regret index, Ri, using the following equation practice from Opricovic and Tzeng (2003).* (7) (8) *Step 6: The index VIKOR, Qi is calculated by:* (9) Where, and Given the v is introduced as the weight of the strategy of the maximum group utility and usually v = 0.5. *Step 7: Rank the alternative by sorting each Si, Ri and Qi in ascending order.* *Step 8: Proposing compromise solution using two conditions.* Compromise solution is considered only if two conditions C1 and C2 are satisfied. C1: Acceptable advantage: Where, is the second position in the alternatives ranked by Q, is the first position in the alternatives ranked by Q, and M is total number of alternative. C2: Acceptable stability in decision making: Alternative, must also be the best ranked by S or/ and R. When one of the condition is not satisfied, a set of compromise solutions will be suggested below: 1) Alternative A1 and A2 if only C2 is not satisfied or 2) Alternative A1, A2, .…. Am if condition C1 is not satisfied. Am is calculated using the equation . **Results and Discussions** Based on the result of the fuzzy VIKOR analyses shown in Figure 1, the ascending rank suggested that DSA (SMK Dato’ Sheikh Ahmad) has the best criteria among the other five candidate schools. DSA has been selected as the best school by satisfying both condition (C1) and (C2) with validation using least VIKOR index value v = 0.5. DSA has the lowest VIKOR index, value which is 0.000. A (SMK Arau) was second in rank with 0.803 score, followed by SA (SMK Syed Ahmad) with 0.872 score, SS (SMK Syed Sirajuddin) is the second last with 0.892 score and TB (SMK Tengku Budriah) is last rank with the highest VIKOR index value which is 1.001. \[CHART\] **Conclusion** The case study proved the ability of the proposed fuzzy MCDM model to effectively solve school ranking problem under fuzzy environment. Using this method, the ranking of schools assessed in linguistics variable by trapezoidal fuzzy numbers and the importance weight of the criteria are evaluated in crisp value. The study used fuzzy VIKOR method to determine the priority rank for the performance of five secondary schools in Arau, Perlis. The result shows that SMK Dato’ Sheikh Ahmad is the best school because it has the lowest VIKOR index value which is 0.000. SMK Arau is second in ranking with 0.803 score, followed by SMK Syed Ahmad with 0.872 score, SMK Syed Sirajuddin as the second last with 0.892 score and lastly SMK Tengku Budriah with the highest VIKOR index value which is 1.001. By using the proposed approach, the ambiguity involved in the data evaluated can be effectively represented and processed to assure a more effective evaluation process. In addition, the results of this study serve as a reference point for schools and educational institutions in their efforts to improve performance and conduct assessments to form the basis of academic and education. **Recommendations** Future research is recommended to take place outside of Arau area which may utilized data obtain from boarding schools, religious schools and vocational or technical schools to reflect a more accurate performance of schools in Perlis. 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