UPSI Digital Repository (UDRep)



Abstract : Universiti Pendidikan Sultan Idris 
The conjoint method, which is based on fuzzy sets of numbers, is widely used to describe linguistic values for
human preference in an uncertain environment. However, the fuzzy sets used to describe the membership function
of linguistic value do not realistically represent the physical world, so the conjoint method can fill the gap and
produce more meaningful results. The fuzzy numbers conjoint method is used in this paper to analyze the
achievement goals of undergraduates in the learning of calculus. One hundred and seven selected Bachelor of
Science (Hons) Mathematics and Bachelor of Science (Hons) Actuarial Science students from one public
university in Klang Valley, Selangor, participated in this study. The data for this study, which was distributed via
Google form, was based on a previous study's Achievement Goals Questionnaire. The fuzzy number conjoint
method with similarity measure based on geometric distance, ambiguity, value, area, left and right height were
used to calculate and analyze the data gathered from respondents' opinions of attributes for each linguistic value.
The priority of the degree of agreement among undergraduates on the achievement goals in the learning of calculus
is worrying as they may not learn all that they possibly could in this subject 11 (A ) , getting better grades than most
other students 1 (A ) , followed by avoiding performing poorly compared to other students in this subject 2 (A ) , and
doing better than other students 12 (A ) with an overall ranking as follows
11 1 2 12 5 8 14 13 9 6 3 15 7 10 4 A A A A A A A A A A A A A A A .. The findings of this
study can be used to assist and guide academicians and mathematics educators in enhancing students' achievement
goals for calculus learning. 
References 
Abdullah, L., & Osman, A. (2011). Fuzzy Set Conjoint Model in describing students’ perceptions on Computer Algebra System learning environment. International Journal of Computer Science Issues, 8(2), 92–97. Ames, C. A. (1990). Motivation: What teachers need to know. Teachers College Record, 91(3), 409–421. Chen, C. T., Lin, C. T., & Huang, S. F. (2006). A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, 102(2), 289–301. Cross, V. V., & Sudkamp, T. A. (2002). Similarity and compatibility in Fuzzy Set Theory (Vol. 93). Springer. Chutia, R., & Gogoi, M. K. (2018). Fuzzy risk analysis in poultry farming using a new similarity measure on generalized fuzzy numbers. Computers & Industrial Engineering, 115, 543558. Dom, R. M., Hasan, H., Shahidin, A. M., & Apandi, N. A. (2019). Fuzzy TOPSIS ranking of academic programs’ competitiveness. International Journal of Academic Research in Business and Social Sciences, 9(13), 319–328. Gao, S., Zhang, Z., & Cao, C. (2009). Multiplication operation on fuzzy numbers. Journal of Software, 4(4), 331338. Gopal, K., Salim, N., & Ayub, A.F, M. (2019). Perceptions of learning Mathematics among Lower Secondary Students in Malaysia: Study on students’ engagement using Fuzzy Conjoint Analysis. Malaysian Journal of Mathematical Sciences, 13(2), 165. Khorshidi, H. A., & Nikfalazar, S. (2017). An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis. Applied Soft Computing Journal, 52, 478–486. Lazim, M. A., & Abu Osman, M. T. (2009). Measuring teachers’ beliefs about mathematics: A fuzzy set approach. World Academy of Science, Engineering and Technology 33, 1098–1102. Liang, Su. (2009). Validating the instrument: Students' perceptions on learning Calculus. NERA Conference Proceedings, 21. Osman, R., Hilmi, Z.A.G., Ramli,N., & Abdullah, N.H.M.(2020). Metaphors and images of mathematics among secondary school students. Academic Science Journal, 13,17. Sarala, N., & Kavitha, R. (2017). Fuzzy conjoint model in measuring students’ expectation and teachers’ belief on learning mathematics. International Journal of Advanced Trends in Engineering, Science and Technology, 2(2), 6–10. Sulaiman, N. S., Mohammad, D., Mohd Shariff, J., Sayed Ahmad, S. A.& Abdullah, K. (2017). Extended FTOPSIS with Distance and set Theoretic–Based Similarity Measure. Indonesian Journal of Electrical Engineering and Computer Science, 9(2), 387394. Sundre, D., Barry, C., Gynnild, V., & Ostgard, E. T. (2012). Motivation for achievement and attitudes toward mathematics instruction in a required Calculus Course at the Norwegian University of Science and Technology. Numeracy, 5(1), 118. Suparlan, A., Shohaimay, F., Haron, N, Zainal Abidin, S., Dasman, A., & Mokhtar@Mother, M. (2019). Evaluation of students’ perceptions of gamebased mathematics classroom using fuzzy conjoint analysis. Gading Journal of Science and Technology, 2(2), 54–63. Osman, R., Ramli, N., Badarudin, Z., Ujang, S., Ayub, H., & Asri, S. N. F. (2019). Fuzzy number conjoint method to analyse students’ perceptions on the learning of calculus. Journal of Physics: Conference Series, 1366, 012117. Patra, K., & Mondal, S. K. (2015). Fuzzy risk analysis using area and heightbased similarity measure on generalized trapezoidal fuzzy numbers and its application. Applied Soft Computing Journal, 28, 276–284. Journal of Science and Mathematics Letters, Vol 10, Issue 1, 2022 (1021) ISSN 24622052, eISSN 26008718 Ramli, N., & Mohamad, D. (2009). A centroidbased performance evaluation using aggregated fuzzy numbers. Applied Mathematical Sciences, 3(48), 23692381. Wang, W. (1997). New similarity measures on fuzzy sets and on elements. Fuzzy Sets and Systems, 85(3), 305309. Xu, Z., Shang, S., Qian, W., & Shu, W. (2010). A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers. Expert Systems with Applications, 37(3), 1920–1927.

This material may be protected under Copyright Act which governs the making of photocopies or reproductions of copyrighted materials. You may use the digitized material for private study, scholarship, or research. 