Use of Fuzzy Numbers for Assessing Problem Solving Skills
الموضوعات : مجله بین المللی ریاضیات صنعتی
Michael Gr‎.‎ Voskoglou‎
1
(Department of Mathematical Sciences, School of Technological Applications, Graduate Technological Educational Institute (T. E. I.) of Western Greece, Patras, Greece.)
S. N. Mishra
2
(Department of Mathematics, National Institute of Technology Durgapur, West Bengal, India.)
الکلمات المفتاحية: Problem Solving Assessment, Fuzzy Logic (FL), Fuzzy Numbers (FNs), Triangular (TFNs) and Trapezoi, Centre of Gravity (COG) Defuzz,
ملخص المقالة :
The importance of Problem Solving (PS) has been realized for such a long time that in a direct or indirect way affects our daily lives in many ways. Assessment cases appear frequently for PS skills which involve a degree of uncertainty and (or) ambiguity. Fuzzy logic, due to its nature of characterizing such cases with multiple values, offers rich resources for dealing with them. On the other hand, Fuzzy Numbers (FNs) play a fundamental role in fuzzy mathematics, analogous to the role played by the ordinary numbers in classical mathematics. In the present paper we utilize the two simplest forms of them, i.e. the Triangular and Trapezoidal FNs, together with the Centre of Gravity (COG) defuzzification technique as assessment tools for PS skills. Our results are illustrated by three examples in which the assessment outcomes of FNs are validated through their comparison with the corresponding outcomes of assessment methods of the bi-valued and fuzzy logic already tested in author's earlier works.
