Page 1 of 13
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 05
May 2019
Available online: https://ejbss.org/ P a g e | 1766
Students’ Progress Reports Evaluation Based on Fuzzy
Hybrid Vector Similarity Measure
Shubhankar Saha
Guest Faculty, Dept. of Education, University of Kalyani
&
Dr. Arjun Chandra Das
Assistant Professor, Dept. of Education, University of Kalyani
Abstract:
Evaluation is the act of placing value on something. Evaluation may be said to be the process
by which value judgements of the educational status or achievement of students are formed.
Thus, to evaluate means to form judgement on the level of achievement and this presupposes
that there is a predetermined level available. In present time, progress report used in the
Govt.-aided secondary and primary schools in West Bengal has two parts: Summative
evaluation and formative evaluation. Generally, examiners use crisp numbers to evaluate
respective subjects in both types of evaluation. In formative evaluation, examiners are to
evaluate students’ traits and skills on the basis of some criteria. For example, they evaluate
students according to their participation, questioning and enquiry, explaining and ability of
application, empathy and co-operation, aesthetic and creative manifestation, etc. A more
realistic approach may be to use linguistic assessments instead of numerical values. Prefer to
use some linguistic terms such as very good, good, bad, etc. instead of crisp values. These
terms are the sources of impreciseness and involve a substantial amount of fuzziness.
Consequently, summative and formative evaluation needs to be modified to reflect the real
performance of the students.
Key words: Evaluation, Summative evaluation and formative evaluation, level of
achievement, crisp number, crisp values, fuzziness etc.
Introduction:
Student evaluation is the process of determining the performance levels of individual students
in relation to educational learning objectives. A high quality evaluation system certifies,
supports, and improves individual achievement and ensures that all students receive a fair
evaluation in order not to constrain students' present and future prospects. Thus, the system
should regularly be reviewed and improved to ensure that it is suitable, fair, impartial and
beneficial to all students. It is also desirable that the system is transparent and automation
measures should be embedded in the evaluation.
Evaluation is the act of placing value on something. Evaluation may be said to be the process
by which value judgements of the educational status or achievement of students are formed.
Thus, to evaluate means to form judgement on the level of achievement and this presupposes
that there is a predetermined level available.
In present time, progress report used in the Govt.-aided secondary and primary schools in
West Bengal has two parts:
Page 2 of 13
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 05
May 2019
Available online: https://ejbss.org/ P a g e | 1767
Summative evaluation
Formative evaluation
Generally, examiners use crisp numbers to evaluate respective subjects in both types of
evaluation.
In formative evaluation, examiners are to evaluate students’ traits and skills on the basis of
some criteria. For example, they evaluate students according to their
participation,
questioning and enquiry,
explaining and ability of application,
empathy and co-operation, aesthetic and creative manifestation, etc.
However, under many conditions, crisp data are inadequate to model real-life situations.
Human judgments are often imprecise and cannot assess his/her evaluation with an exact
numerical value. A more realistic approach may be to use linguistic assessments instead of
numerical values. Prefer to use some linguistic terms such as very good, good, bad, etc.
instead of crisp values. These terms are the sources of impreciseness and involve a substantial
amount of fuzziness. Consequently, summative and formative evaluation needs to be
modified to reflect the real performance of the students.
The specific objectives of the study are as follows:
To know the various definitions of Fuzzy numbers.
To use linguistic term in formative evaluation;
To utilize the linguistic terms in fuzzy environment;
To define the ideal evaluation of each subject in case of formative
evaluation;
To employ tangent similarity measure between the ideal evaluation and the
evaluation of each subject;
To demonstrate the proposed model with a real example.
Literature Review:
Zadeh (1965) proposed fuzzy set which can deal with imprecise or vague information quite
effectively.
Biswas (1995) presented a fuzzy evaluation method (fem) for applying fuzzy sets in students’
answer scripts evaluation.
Page 3 of 13
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 05
May 2019
Available online: https://ejbss.org/ P a g e | 1768
Cheng and Yang (1998) presented a method using fuzzy sets in education grading systems
to solve the subjective judging problems of teachers.
Wang and Chen (2008) presented two methods for evaluating students’ answer scripts using
fuzzy sets.
Chen and Li (2013) presented a method for Evaluating students’ answer scripts based on
interval-valued intuitionistic fuzzy sets.
Methodology of the Study:
This research has been done on the basis of descriptive method. For the educational research
many types of descriptive method had been used but in this research the case study method is
most suitable method. So the researcher used it.
Definitions of fuzzy numbers:
In the following, we briefly review some basic definitions of fuzzy sets, which will be used
throughout the presentation.
Definition 1.Fuzzy Set (Zadeh, 1965)
Let X be a universe of discourse. A fuzzy set A in X is given by
A = {< x, (μA
(x)) > x ε X,
Where μA
(x): X → [0,1] membership function of the element to the set x to A.
Definition 2.
A fuzzy set A in X is said to be convex if for any x1, x2 ε X ,
μA
(λx1 + (1 − λ)x2
) ≥ Min (μA
(x1), μA(x2)),
Where λ ε [0,1]
Definition 3.
A fuzzy set A in X is called normal fuzzy set if ∋ xiε X, μA
(xi
) = 1,
Definition 4.
A fuzzy number is a fuzzy subset of the universe of discourse X that is both convex and
normal. The following fuzzy number x in the universe of discourse X which is both convex
and normal.
Definition 5. Fuzzy Number ( Kaufmann & Gupta 1985)
A triangular fuzzy number ã can be defined by a triplet (a1, a2, a3) shown in figure-1. The
membership function μã(x) is defined as follows :
μã
(x) = 0 , x < a1
