SUBJECTIVE DECISION MAKING IN STUDENTS’

ASSESSMENT USING TYPE-2 FUZZY LOGIC ADVISOR

M. A Owais

Computer Science & Engineering Department, King Fahd University of Petroleum and Minerals

Hafr Al-Batin College, P.O Box# 1803, Hafr Al-Batin, 31991, Saudi Arabia

mowais@kfupm.edu.sa

Keywords: Student Evaluation, Fuzzy Logic, Uncertainty, Cooperative Training, Senior/Capstone Project, Type-2 FLA.

Abstract: In this paper, we present and compare two-stage type-2 fuzzy logic advisor (FLA) to evaluate the students’

performance in domains where subjective decisions are made. We test our proposed model for evaluating

students’ performance in Computer Science Department in two domains namely cooperating training and

senior project assessment where we find these FLAs very useful and promising. In our proposed model, the

assessment criteria for different components of cooperative training and senior project are transformed into

linguistic labels and evaluation information is extracted into the form of IF-THEN rules from the experts.

These rules are modelled using FLS, which then is used as a fuzzy logic advisor (FLA) to make decisions

about students’ grades. The evaluator’s input for the system can be either singleton or non-singleton. Both

type-1 and type-2 fuzzy logic based models are implemented and compared with individual expert’s

evaluation.

1 INTRODUCTION

A student’s learning performance is measured by

some evaluation means in all sorts of teachings. A

student’s evaluation is the process by which all

relevant data about a student’s work are collected

and transformed into information for decision

making (Cooley and Lohnes, 1976). In most of the

cases, testing provides a measure of progression and

success of a student’s learning. To evaluate a

student’s performance, it is worthwhile to use a

number of different ways rather than relying on a

single formal exam (Donald et al., 1985). There are

various formal and informal ways of evaluation

including homework assignments, quizzes, projects,

reports, formal exams, class participation, team

activities, interviews, attendance, punctuality etc.

Whatever the method, it is good to record fairly

often how students are performing in each area.

Another important aspect to note is that whatever

method be used, the evaluation process should help

students develop their proficiency in a subject.

At undergraduate or associate degree level,

cooperative training and/or senior project are two

most important mechanisms (tools) to develop the

skills of a student. Cooperative (coop) training

provides an opportunity for students to integrate and

apply their academic learning with some real work

experience in industry. While completing a senior

project, generally a student develops some industrial

project or solves some related industrial problem

based on the techniques he/she learnt during his

academic career. In both of the above cases, a

student is exposed to the profession of his/her

subject area by working in the field or solving a real

problem for the industry. Normally, such a student is

evaluated through different means e.g. submission of

progress and final reports, on-site observation,

assessing the proposed design, final presentation etc

and marks are assigned for each of these activities.

These partial marks (results) are weighed up in some

way (using numbers or percentage) in order to

decide the final grade of a student for coop training.

However, we feel that the assessment in such

domains (i.e. observing student’s attitude towards

work, quality of work output, initiative and

creativity, presenting his work in final report and

presentation etc) is quite subjective and mostly

based on perception of an evaluator. The

conventional methods for evaluation usually do not

take into account the uncertainties in usage of words

for assessment. This gives us the motivation for

type-2 fuzzy set be used to model a word as it covers

the word uncertainties by using the concept of

footprint of uncertainty.

In this paper, an interval type-2 fuzzy set based

Fuzzy Logic Advisor (FLA) is presented to decide

the final grade of a student’s coop training. We also

compare type-2 and type-1 fuzzy logic models for

evaluating coop training. This paper is organized as

follows; in section 2 we describe background details

about coop training and related work. In section 3

our fuzzy logic model for evaluation is explained.

Section 4 presents experiments and results. The

paper is concluded in section 5 mentioning the

future work also.

2 BACKGROUND

2.1 Importance of Selected Domain

For assessing and improving students’ learning,

coop training and senior project are very important

tools. Recent report (Peter, 2008) shows that the

employers hold high regard for evaluation of senior

projects and coop training because these enhance

students’ knowledge and develop their skills to work

in real-world environment. Most of the employers

advise universities/colleges to focus resources in

assessing these components for improving students’

learning.

2.2 Cooperative Training/ Internship

Cooperative (coop) training is a planned and

supervised on-site training. It helps students to gain

job-related work experience and skills that assists

them in achieving their career goals. There are

different student activities that are monitored during

and after the coop training. Based on this

monitoring, final grades are assigned according to

the student’s performance in each activity. In

universities/colleges coop students are evaluated

using different means. We use following four means

to evaluate coop students at our college:

1. A student submits a number of progress

reports to his/her internal supervisor during

the coop training period.

2. A student is evaluated by his supervisor

(external) at work. In addition, internal

supervisor may also visit the student to

monitor his/her performance in the field.

3. A student submits a final report to the

university/college about his training.

4. A student presents his/her work in a

presentation to internal and/or external

supervisors, faculty members and other

students.

2.3 Senior/Capstone Project

Senior project gives students the experience of

tackling a realistic problem. The intent is to show

how to input theoretical knowledge gained into

practical use by starting from a word description of a

problem and proceeding through various design

phases to end up with a practical solution. The

project supervisor(s) guides the student in

conducting a feasibility study, preparation of

specifications, and the methodology for the design.

Detailed design and implementation of the project

are carried out followed by testing, debugging, and

documentation. Similar to the coop training, we use

four different means for evaluating a student’s work

during completing senior project. Except for the

second point where supervisor assesses a student’s

performance by evaluating design methodology,

complexity, level of achievement, quality of results

etc of his/her project, the rest of the means are same

as discussed in section 2.2 for coop training. Note

that these evaluation criteria are flexible and

generally based on policies from university or

college (while in some cases evaluation depends on

each individual).

After a number of years’ experience, we feel that

a perception-based evaluation model is more

suitable for assessment of coop training and senior

projects. We believe that the judgment for students’

training at work, report writing (literary quality,

quality of subject matter, formatting, structure etc.)

and presenting the work during presentation

(communication skills, organization etc.) are mostly

subjective rather than objective. It is difficult to

apply the objective methods to evaluate these

student activities. Also we found that supervisors

feel more comfortable while giving their judgment

in terms of words (Excellent, Very Good, and Good

etc.) than in numbers. To solve this problem, we

propose the use of fuzzy logic to model the students’

evaluation.

2.4 Fuzzy Logic

Fuzzy logic was first proposed and coined by Lotfi

A. Zadeh in 1965 (Zadeh, 1965). The main

motivation behind fuzzy logic was the existence of

imprecision and uncertainty in the measurement

process. Later, Zadeh also proposed the

methodology of computing with words (CW) in

which words are used in place of numbers for

computing and reasoning (Zadeh, 1973; Zadeh

1996). The concept of CW is very important in

human decision making systems as they employ

mostly word in making decisions and judgments.

CW involves a combination of natural language and

computation with fuzzy variables. It mimics the

perception-based decision making done by humans

in an environment of imprecision, uncertainty and

partial truth (Zadeh 1996; Zadeh 1999). The next

subsections describe some of the important concepts

related to fuzzy logic.

2.4.1 Linguistic Variables, Values and

Terms

In fuzzy logic, linguistic variables accepts linguistic

values which are words (linguistic terms) with

associated degrees of membership in the set.

Therefore, instead of considering length as a

numerical variable that assumes a numerical value of

1.72 meters, it is treated as a linguistic variable that

may assume, for example, linguistic values of “high”

with a degree of membership of 0.92, "short” with a

degree of 0.06, or "medium” with a degree of 0.7.

Linguistic variables accept values defined in their

term set - their set of linguistic terms. Linguistic

terms are subjective categories for the linguistic

variable. For example, for linguistic variable age, the

term set T(age) may be defined as follows:

T(age) = { "young", "not young", "not so young",

"very young", ..., "middle aged", "not middle aged",

..., "old", "not old", "very old", "more or less old",

"quite old", ..., "not very young and not very old", ...

}

2.4.2 Fuzzy Sets and Membership Functions

Each linguistic term is associated with a fuzzy set,

each of which has a defined membership function

(MF). Formally, a fuzzy set A in U is expressed as a

set of ordered pairs:

}|))(,{( UinxxxA

A

μ

=

In the above definition )(x

A

μ

is the membership

function, which provides the degree of membership

of

x

. This indicates the degree to which

x

belongs

in set A, where U is the universe of discourse. Let’s

illustrate these concepts using an example. Consider

the “Literary Quality (LQ)” is a metric to measure

the how well a student writes his report in terms of

style, grammar, clarity etc. Figure 1 illustrates a

linguistic variable LQ with four associated linguistic

terms namely “Excellent”, “Good”, “Fair” and

“Poor”. Each of four linguistic terms is associated

with a fuzzy set defined by a corresponding

membership function.

There are many types of membership functions.

Some of the more common ones are triangular MFs,

trapezoidal MFs and Gaussian MFs.

2.4.3 Fuzzy Logic System

Fuzzy logic system is a system which has a direct

relationship with fuzzy concepts (such as fuzzy sets,

linguistic variables and so on) and fuzzy logic. The

most popular fuzzy logic systems in the literature

can be classified into three types: pure fuzzy logic

systems, Takagi and Sugeno’s fuzzy system, and

fuzzy logic system with fuzzifier and defuzzifier

(Wang, 1994).

Figure 1: Membership Functions for Literary Quality.

Since most of the engineering applications produce

crisp data as input and expects crisp data as output,

the last type is the most widely used one. Figure 2

shows the basic configuration of a fuzzy logic

system with fuzzifier and defuzzifier.

This type of fuzzy logic system was first

proposed by Mamdani (Mamdani, 1975). It has been

successfully applied to a variety of industrial

processes and consumer products (Mamdani, 1974).

The main fours components’ functions are as

follows.

Fuzzifier: It converts a crisp input to a fuzzy set.

Fuzzy Rule Base: Fuzzy logic systems use fuzzy

IF-THEN rules. A fuzzy IF-THEN rule is of the

form "IF X1 = A1 and X2 = A2 ... and Xn = An

THEN Y = B” where Xi and Y are linguistic

variables and Ai and B are linguistic terms. The ‘IF’

part is the antecedent or premise, while the ‘THEN’

part is the consequence or conclusion. An example

of a fuzzy IF-THEN rule is "IF Marks = Low THEN

Grade =Poor". In a fuzzy logic system, the collection

of fuzzy IF-THEN rules is stored in the fuzzy rule

base, which is known as the inference engine.

Fuzzy Inference Engine: Once all crisp input

values are fuzzified into their respective linguistic

values, the inference engine accesses the fuzzy rule

base to derive linguistic values for the intermediate

and the output linguistic variables. The inference

engine performs two main operations: aggregation

and composition. Aggregation is the process of

computing for the values of the IF (antecedent) part

of the rules while composition is the process of

computing for the values of the THEN (conclusion)

part of the rules.

Defuzzifier: It converts fuzzy output into crisp

output.

The details of the above four components can be

found in (Wang, 1994).

Figure 2: FLS with Fuzzifier and Defuzzifier.

Imprecise perception-based data can be best

modeled by using type-2 fuzzy logic (John and

Coupland, 2007). Mendel proposed using type-2

fuzzy sets and type-2 fuzzy logic systems to deal

with the different types of uncertainties (Mendel,

2001). Type-2 fuzzy sets help us to deal with the

uncertainty about the meaning of the words and

uncertainties about the consequent used in a rule.

Type-1 fuzzy sets cannot deal with this type of

uncertainty because the degree of membership is

considered as certain in type-1 fuzzy sets. Figure 3

shows footprint of uncertainty (FOU) for a Gaussian

membership function having a fixed standard

deviation, σ, and an uncertain mean that takes on

values in [m1, m2]. The example shown in Figure 3

depicts a case where the FOU is uniformly shaded. It

means that at each point in the FOU, the

membership degree is one. This type of membership

functions is known as interval type-2 membership

function.

A fuzzy logic system is considered to be type-2

as long as any one of its antecedent or consequent

sets is type-2. A detailed description of all the

components of Figure 4 and uncertain rule based

fuzzy logic (type-1 and type-2) system is provided

by Mendel (Mendel, 2001).

2.5 Related Work

Fuzzy theory has vast applications in different

disciplines from controls to machine learning to

decision making. It has also been applied in the

field of education (Ahmad, 2001; Kavcic et al.

2003). In (Montero et al., 2005), fuzzy logic based

evaluation system, to decide critical students’ final

marks, is presented. They used type-1 fuzzy logic

for evaluation purpose.

Figure 3: FOU for Gaussian Membership Function.

Figure 4: Type-2 Fuzzy Logic System.

In (Suarez, 2003), type-1 fuzzy set (membership

function) has been used to manage students’

performance in computer adaptive testing (CAT)

administration process. In (Zhou, 2001), criterion

referenced assessment techniques using fuzzy sets

(type-1) are proposed for student project assessment.

To our knowledge, type-2 fuzzy logic has not yet

been used for students’ evaluation, particularly for

coop training evaluation.

3 PROPOSED FUZZY LOGIC

ADVISOR

3.1 Assessment Components

As described in section 2.1, assessment of coop

training and senior project is divided into different

components. Each of these parts has number of

criteria to be monitored and evaluated during and

after training/project. Table 1 shows the four

different parts (means) of coop training evaluation

and their respective criteria to be judged by the

evaluator. Assessment components and criteria for

assessment for senior project are shown in Table 2.

The final grade of a student is computed based on

the outputs of four assessment components.

Table 1: Assessment Components and Criteria for Coop

Training.

Assessment

Component

Criteria for Assessment

Final Report

(FR)

• Format and Structure

• Literary Quality

• Quality of Subject Matter

Progress Report

(PR)

• Task Description

• Format and Submission

Final Presentation

(FP)

• Content and Organization

• Speaking (Presentation) Skills

• Response to Questions

External Evaluation

(EE)

• Enthusiasm and Interest in Work

• Ability to Learn and Search for

Information

• Relations with Co-Workers

• Punctuality and Delivering Work on

Time

Table 2: Assessment Components and Criteria for Senior

Project.

Assessment

Component

Criteria for Assessment

Final Report

(FR)

• Format and Structure

• Literary Quality

• Quality of Subject Matter

Progress Report

(PR)

• Task Description

• Format and Submission

Final Presentation

(FP)

• Content and Organization

• Speaking (Presentation) Skills

• Response to Questions

Supervisor Evaluation

(SE)

• Quality of Design Methodology and

Interest in Work

• Level of Achievement

• Quality of Results

• Punctuality and Delivering Work on

Time

3.2 Evaluation Model

We propose students’ coop and senior project

evaluation model based on knowledge mining

(knowledge engineering) methodology described in

(Mendel, 2001). The evaluation information is

extracted in the form of IF-THEN rules from

evaluators (experts) and these rules are modelled

using FLS, which then is used as a fuzzy logic

advisor (FLA) to make decisions about students’

grades. We propose a two-stage FLA based on

interval type-2 fuzzy logic, where each assessment

component is evaluated using an independent FLA

and then the results of these FLAs are combined to

calculate the final grade of a student using a second-

stage FLA. Figure 5 represents a two-stage FLA

framework for coop training. A similar model can be

drawn for senior project evaluation. Each of these

FLA has internal structure as described in section

2.2.4 (figure 4).

3.3 Antecedent & Consequent Fuzzy

Sets

In building a FLA we divide the whole range of all

the input (criteria of assessment) and output

(evaluation) attributes into number of fuzzy sets. We

use four type-2 fuzzy sets namely Excellent, Good,

Fair and Poor to represent each criterion of

assessment and the output of assessment

components of stage-1.

For our proposed model, we obtain this fuzzy set

classification from experts. As we have already

mentioned, different experts may provide different

assessments, based on their experience, regarding a

particular fuzzy set (e.g., Excellent) range of a

specific input/output attribute. This causes

uncertainty, as to which definition is more

appropriate to consider when one wants to define

antecedents/consequents while developing FLS. This

observation led us to use type-2 fuzzy sets, which

enables us to model uncertainty, caused due to

different experts’ opinion as just discussed, in the

FLS by blurring the antecedents’/consequents’

boundaries and defining the footprint of uncertainty

(FOU). For our model, based on survey from a

group of evaluators (experts) a range for above

labels is chosen using a scale 0 through 10. Table 3

shows the mean and standard deviation values for

these range labels based on our survey.

We associate triangle membership function with

the labels Fair (F) and Good (G), and piecewise

linear membership functions with labels Poor (P)

and Excellent (E). The uncertainty about the words

used in antecedents and consequents of rules and

uncertainties about the rule consequents are captured

in type-2 fuzzy sets using FOUs.

Figure 5: Two-Stage Type-2 Fuzzy Logic Based Framework for Cooperative Training Evaluation.

Table 3: Survey Results for Labels of Fuzzy Sets.

Label Mean Std. Deviation

Start End Start End

A b σ

a

σ

b

Poor

0 4.7389 0 0.4898

Fair

4.7056 6.8778 0.4978 0.4295

Good

6.6556 8.7222 0.4419 0.3153

Excellent

8.4889 10.0000 0.3296 0.0000

We obtain FOUs by specifying upper and lower

membership function for each fuzzy set. These

fuzzy sets are calculated based on procedure

described in (Mendel, 2001). Figure 6 shows the

FOUs for the four fuzzy sets for ρ=0.5 (50%

percent uncertainty), where ρ is the fraction of

uncertainty and

10 ≤≤

ρ

.

Similarly, for stage-2, the output of stage-1 will

be used as input in the form of type-2 fuzzy set

shown above. The output of stage-2 (Grade) is also

divided into nine different fuzzy sets namely

Exceptional, Excellent, Superior, Very Good,

Above Average, Good, High Pass, Pass, and Fail.

In our proposed model, the initialization of

membership functions is done through singleton

input.

The criteria of assessment (indicators of

assessment components) are represented by type-2

fuzzy sets as we believe that these criteria are

judged on the basis of perception of an evaluator.

Figure 6: FOUs for Linguistic Labels.

3.3 Fuzzy Rule Base and

Defuzzification

In the rules formulation we follow the approach

where all the possible combinations of antecedent

fuzzy sets are employed (Mendel 2001). The

consequents of rules are provided by the experts

(evaluators) through survey. Each rule has a

histogram of responses. Our proposed model is

composed of five FLAs and each one has its own

set of rules. The number of rules depends on the

number of inputs and fuzzy sets associated with

them.

Table 4: Partial Histogram of Survey Responses for Final Report Evaluation.

Consequent Type-1 Type-2

Rule

No.

Antec. 1 Antec. 2 Antec. 3

Exc. Good Fair Poor C

avg

C

l

avg

C

r

avg

1 Excellent Excellent Excellent 8 0 0 0 9.162 9.08 9.24

2 Excellent Excellent Good 6 2 0 0 8.783 8.69 8.87

3 Excellent Excellent Fair 4 3 1 0 8.17 8.06 8.28

4 Excellent Excellent Poor 0 5 2 1 6.533 6.4 6.67

5 Excellent Good Excellent 6 2 0 0 8.783 8.69 8.87

6 Excellent Good Good 3 4 1 0 7.98 7.87 8.09

7 Excellent Good Fair 0 5 3 0 6.943 6.81 7.08

8 Excellent Good Poor 0 4 3 1 6.298 6.16 6.44

9 Excellent Fair Excellent 2 5 1 0 7.791 7.67 7.91

10 Excellent Fair Good 0 6 2 0 7.178 7.04 7.31

11 Excellent Fair Fair 0 5 3 0 6.943 6.81 7.08

12 Excellent Fair Poor 0 2 5 1 5.829 5.69 5.97

13 Excellent Poor Excellent 0 3 4 1 6.064 5.92 6.2

14 Excellent Poor Good 0 3 4 1 6.064 5.92 6.2

15 Excellent Poor Fair 0 0 6 2 4.95 4.8 5.1

For example, for Progress Report FLA, the number

of rules will be 4x4=16.While for Final Report

FLA, there will be 64 rules. Maximum number of

rules will be for External Evaluation FLA and

Coop Evaluation FLA i.e. 256. An example rule

for Coop Evaluation FLA will be of following

form:

Rl: IF FR is

E

~

AND PR is G

~

AND FP F

~

is

AND EE is

E

~

THEN GRADE is

DGV

~

(VERY

GOOD)

For later calculations, we find weighted

average (

l

avg

C ) of the rule consequents of each

rule using following formula (Mendel, 2001):

[]

l

avg

l

avg

M

i

l

i

M

i

iG

l

i

l

avg

CC

w

Cw

C ≡=

∑

∑

=

=

1

1

~

(1)

In the above equation,

iG

C

~

is the centroid of

the ith consequent and

l

i

w

is the weight associated

with the ith consequent for the lth rule. The

centroid for type-2 fuzzy sets is calculated using

the iterative procedure of the Karnik-Mendel (KM)

algorithm (Karnik and Mendel, 2001). The

consequent of each rule is treated as type-1 fuzzy

set. Initially we did survey for small group of

experts due to large number of rules. A partial

histogram of final report evaluation FLA with

three antecedents and a consequent, and

corresponding weighted average response for both

type-1 and type-2 is shown in table 4.

The final output of our proposed FLAs is a

type-reduce interval set, having the following

form:

[

]

rlTR

yyY ,

=

(2)

Where

l

y and

r

y are computed using

following two fuzzy basis function (FBF)

expansions (Mendel, 2001):

∑∑

∑∑

∑

∑

=+=

=+=

=

=

+

+

==

L

i

M

Li

i

i

L

i

M

Li

i

l

i

i

l

i

M

i

i

l

M

i

i

l

i

l

l

ff

yfyf

f

yf

y

11

11

1

1

(3)

∑∑

∑∑

∑

∑

=+=

=+=

=

=

+

+

==

R

i

M

Ri

i

i

R

i

M

Ri

i

r

i

i

r

i

M

i

i

r

M

i

i

r

i

r

r

ff

yfyf

f

yf

y

11

11

1

1

(4)

For a type-2 fuzzy set

F

~

, we calculate f and

f using following equations:

[

]

M

FFF

f

~

2

~

1

~

......,min

μ

μ

μ

=

(5)

[

]

M

FFF

f

~

2

~

1

~

......,min

μμμ

=

(6)

2

rl

yy

y

+

=

(7)

Finally, the defuzzified output of FLAs can be

found by using following equation:

4 EXPERIMENTS & RESULTS

We implemented type-1 and type-2 fuzzy logic

advisors (FLAs) using MATLAB fuzzy logic tool

box. We compared our FLA with the existing

coop/senior project evaluation system. In the

existing system, same assessment components are

used for coop evaluation but the usage of linguistic

labels with the range is fixed. Using these fixed

range assessment method, the overall performance

of a student is assessed by simply adding their

marks in different components. We implemented a

fuzzy logic advisor based on the inputs of experts

for range of different linguistic variables for

evaluation (shown in table 3). Our system uses the

rule-based fuzzy inference system to calculate the

overall grade of a student which provides more

accurate evaluation of a student as compared to

existing method. We found that the uncertainties in

the representation of criteria for assessment

(linguistic variables) can be well taken into

account by using type-2 fuzzy sets.

For verification of our model, we selected a

sample of students’ evaluation and compared the

outputs of the individual’s FLA with the output of

our proposed consensus type-1 and type-2 FLAs.

For this purpose same assessment components and

criteria were used. Figure 7 shows a comparison

for the outputs of individual and consensus type-1

FLAs for final report (FR) evaluation. This plot

shows that the outputs of individual and consensus

FLAs differ marginally for most of the students.

Figures 8 and 9 show the comparisons for

outputs of individual and consensus type-2 FLAs

for the same assessment component (FR) with 50%

and 100% uncertainty. These two plots depict that

the individual assessment lies in between the limits

of consensus assessment (left-hand and right-hand

curves) which reflects that type-2 based system

captures all those uncertainties which are there due

to words in surveys and consensus consequents.

Figure 7: Comparison for Individual and Type-1

Consensus.

Figure 8: Comparison for Individual and Type-2

Consensus FLAs (50% uncertainty).

Figure 9: Comparison for Individual and Type-2

Consensus FLAs (100% uncertainty).

5 CONCLUSIONS & FUTURE

WORK

This paper describes a rule-based fuzzy logic

advisor (FLA) to evaluate the cooperative training

and senior project of students at undergraduate and

associate degree level. We used the knowledge

mining (engineering) methodology to develop this

system where we gathered evaluation information

from experts. The system is initially tested for a

small group of students in computer science

department at our college and we found it very

useful for assessing students’ performance in their

cooperative training. Our type-2 fuzzy set model

has the potential to capture the uncertainties due to

words used in subjective evaluation of a student.

Future work involves further testing of the

system for large number of students from different

departments and investigating the use of the

system for other courses/situations e.g. assessing

group projects etc. Moreover, type-2 fuzzy sets

will also be tested for representing final grades.

There are some other issues which need to be

considered in future e.g. deciding the optimal

number of linguistic input/output variables for

assessment components, working with non-

singleton input from evaluators, and deciding the

appropriate number of experts for survey response

etc. In future these issues will be taken into

consideration for improving the overall

performance of the system.

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