Prioritization of Students Understanding in Rules of Differentiation using Fuzzy Soft Matrices and Lambda – max Method


  • Samsiah Abdul Razak Universiti Teknologi MARA (UiTM), 35400 Tapah, Perak, Malaysia.
  • Aslina Omar
  • Ainon Syazana Ab. Hamid
  • Izni Syamsina Saari



Derivative, Chain rule, Product rule, Quotient rule, Composite function, Rational function, Fuzzy soft set, Fuzzy soft matrix, Fuzzy analytic hierarchy process, Lambda – Max method


Calculus is one of the most important courses especially for undergraduate students in many fields of study. Some researchers have identified the causes of the high failure rate which includes lack of basic foundation of mathematics and basic concept of differentiation. Aside from that, the main problems that can be seen among students are the difficulty in identifying the type of function in differentiation and identifying the suitable method to solve a particular problem. There are three rules included in differentiation which are the Chain Rule, Product Rule and Quotient Rule. This study is conducted to examine the level of understanding of the students on the function and the derivative techniques after applying derivative game applications in this course. This paper is based on Fuzzy Analytic Hierarchy Process (Fuzzy AHP) which use fuzzy number in pair-wise comparison matrix. The prioritization of students’ understanding in differentiation rules will then be measured by Fuzzy AHP using Lambda-max method. The highest among the three rules in differentiation will considered as a result. The findings of this study indicated that the highest score with 0.4700 is the Chain Rule. This study can help lectures to know the level or understanding among three rules in differentiation and lecturer well prepared their teaching materials in the classroom as well as to reduce the failure rate among students in this course

Author Biography

Samsiah Abdul Razak, Universiti Teknologi MARA (UiTM), 35400 Tapah, Perak, Malaysia.



Samsiah.R, & Daud.M. 2012. An Application of Soft Matrices in Group Decision Making Problems (Aplikasi Matrik Lembut dalam Masalah Pembuatan Keputusan Secara Berkumpulan), Menemui Matematik (Discovering Mathematics). Vol. 34 No. 1, pp.33– 39.

Samsiah.R,& Daud.M. 2013. A Decision Making method using Fuzzy Soft Sets. Malaysian Journal of fundamental and Applied Sciences, Vol. 9, No.2 99-104

S.A.Razak, Daud.M, & Ini Imaina.A, 2017, A Group Decision Making Problem Using Hierarchical Based Fuzzy Soft Matrix International Journal of Advanced and Applied Sciences, 4(10), pp 26-3.

Natasa.P & Zivojin.P. 2017. Application of fuzzy AHP for ranking and selection of alternatives in construction project management. Journal of civil engineering and management , issn 1392-3730 / eissn 1822-3605,2017 volume 23(8): pp 1123–1135

Natasa.P & Zivojin.P. 2016 Application of fuzzy AHP method based on eigenvalues for decision making in construction industry. ISSN 1330-3651 (Print), ISSN 1848-6339 (Online)

Aspinwall, L., & Miller, L. D. 2013. 000f7c1be7987fea1fb5ca4dc2cbca59.pdf. Journal of Intructional Psychology.

Habre, S., & Abboud, M. 2006. Students’ conceptual understanding of a function and its derivative in an experimental calculus course. Journal of Mathematical Behavior, 25(1), 57–72.

Hensel, R., Lowery, A., & Sigler, J. R. 2008. Breaking the Cycle of Calculus Failure: Models of Early Math Intervention to Enhance Engineering Retention. ASEE Annual Conference and Exposition.

Parameswaran, R. 2007. On understanding the notion of limits and infinitesimal quantities. International Journal of Science and Mathematics Education.

Hart, B.G.; Holloman, T.l.; Oapos; Connor, C.A. A Calculus Retention Program for Students at Risk in Engineering. Frontiers in Education Conference, 1995. Proceedings, 1995.

Tsang, E., Halderson, C., Kallen, K. Work In Progress – Western Michigan University’s Effort to Increase Retention of First-Time, First-Year Engineering and Applied Sciences Students. 37th ASEE/IEEE Frontiers in Education Conference. October 10-13, 2007, Milwaukee, WI.

Ohland, M.W., Yuhasz, A.G., Sill, B.L. Indentifying and Removing a Calculus Prerequisite as a Bottleneck in Clemson’s General Engineering Curriculum. Journal of Engineering Education, July 2004. pp. 253-257.

Klingbeil, N., Rattan, K., Raymer, M., Reynolds, D., Mercer, R., Kukreti, A. and Randolph, B., "A National Model for EngineeringMathematics Education," Proceedings 2007 ASEE Annual Conference & Exposition, Honolulu, HI, 2007.

Koch, D. “Intervention Strategy for Improving Success Rates in Calculus. Seminar on Teaching Mathematics”. Department of Mathematics, University of Michigan. November 12, 2007.

Ahmad, N.A., Shafaruniza, M., Muhammad, Y.Y., Haslenda, Y., Mohammad, N.A., Chu. H.H.,”Factors Related to Students’ Performance in Calculus”. Journal of Applied Environmental and Biological Sciences, 2017. pp .51-56.

Robin, H., Andrew L., J.Ryan, S.,” Breaking the cycle of calculus failure: models of Early math intervention to enhance engineering retention” American Society for Engineering, 2008.