Multi Input Single Output Fuzzy Model to Evaluate the Performance

of Distance Education Media

Wassan Adnan Hashim

1 a

, Faiz A. Mohammed Alawy

and Jawad Hamad Hameed

Information Technology Department, Qala University College, Erbil, Iraq

Promoting Sustainable Change Inc, Michigan, U.S.A

Department of Petroleum Systems Control Engineering, Tikrit University, SalahAldin, Iraq

Keywords: Distance Education, Media, Adaptive Neuro-Fuzzy Inference System, MATLAB.

Abstract: Distance learning is being the preferred mean for continuous learning at any educational center and there is

urgent need to adapt with the technological requirements for such open learning methods. A fuzzy logic

based model has been introduced in this work to estimate the overhaul efficiency of the distance education

media to meet specific training objective. This fuzzy model has been tested to simulate the Tony Bates

“ACTIONS” model (Bates, 1995). The performance of the model has been validated by comparing the

model results with actual examples which have been obtained by conducting practical survey. The fuzzy

ANFIS model has been trained using back-propagation and least-square methods.

https://orcid.org/0000-0001-8473-8595

1 INTRODUCTION

The impact of the rapid development in the fields of

telecommunication and digital technologies have

helped in delivering online and distant learning

which in turn has expanded the learning

opportunities; because of this rapid technology

development and the availability of different

educational tools, organizations are facing many

challenging decisions to enhance their educational

systems. Learning centres are working

seriously

meet the fast growing needs for continuous learning

by redefining their systems to be more attractive for

the new and old learners. Universities, schools, and

training centres are developing new contents and

medias to make it easy for any person to reach out to

the learning resources at any time, with minimum

cost and easy access throughout the world (Teixeira

and Bates, 2019; Kappel and Lehmann, 2002; Zhang

and Jiang).

There are very limited practical theories for

selecting the most suitable learning media for certain

systems and the most common practice is to have the

organization management or a special committee of

experts to decide the best technology tools for each

specific case. The ACTIONS model (Bates, 1995) is

the most famous model for selecting the optimal

learning media which was developed for campus-

based as well as distance education. More detailed

approaches are also available at more micro-level

when it comes to designing specific multimedia

educational materials (Holden and Westfall, 2007)

(Simonson and Zvacek, 2019).

A model for technology selection is very

important to help covering a wide variety of learning

contexts and suggests strategic and tactical

institutional and instructional plans on both of

educational and operational issues. The optimal

design of an educational model should accommodate

new technology development and create a cost

effective system. As an example, SECTIONS is

found to be one of the best models to provide the

required needs. SECTIONS stands for: Student,

Ease of use, Cost, Teaching function, Interaction,

Organizational issues, Networking, and Security &

privacy.

This work is introducing a new model which is

based on multi input signals; easiness to access the

teaching or learning, estimated costs, user-

friendliness & interactivity, organizational issues,

novelty, and speed of the required change. The

suggested model is designed by using Adaptive

Neuro-Fuzzy Inference System (ANFIS) method of

fuzzy based modelling.

2 ANFIS MODEL DEFINITION

Modelling any specific system by using

conventional mathematical tools can be a very

difficult process especially when dealing with ill-

defined or uncertain systems, a process of several

pages of decision-trees, which are completely

impractical to apply. While a fuzzy inference system

employing fuzzy if then rules is much easier to

human knowledge and reasoning processes without

employing precise quantitative analyses. This fuzzy

modeling is first explored by Takagi and Sugeno

(Mehran, 2008; Yulianto and Komariyah, 2017).

Generally, there is no standard method to transform

the human experience into the rule base of a fuzzy

inference system in addition to the need to design a

tuning method to define the membership functions in

order to optimize the criteria of the output error and

performance index

ANFIS is an adaptive network based fuzzy

inference system which can be used as a basis for

constructing a set of fuzzy if-then rules with

appropriate membership functions to state the

required initial input-output pairs.

The basics of fuzzy if-then rules, fuzzy inference

systems, the structures and learning rules of adaptive

networks are described in (Al-Hmouz and Shen,

2011). In using ANFIS, there are almost no

constraints on the network structure and node

functions, but the network should be of feed forward

type (Salleh and Talpur, 2017). Figure 1 below

shows a simple example of a two input – nine rules

ANFIS system structure. A more complicated

structure of six input ANFIS model is used in this

work to model the distance education media

selection system.

Figure 1: Simple example of ANFIS structure with two

input – nine rules ANFIS.

3 DISTANCE EDUCATION

MODEL

The objective of designed ANFIS model is to

evaluate and enhance the media selection process

and to avoid the associated problems facing the

universities or education centers. Also, this ANFIS

model is introduced to estimate the overhaul

efficiency of the appropriate media for any

suggested distance education system using the

designing the parameters of Bates model.

3.1 Model Structure

Numerical and statistical data-based methods can be

complemented by the human expertise and

knowledge to design the required set of fuzzy rules

for a certain system. The modeling of distance

education media selection is designed using ANFIS

modeling techniques with six input parameters and

single output parameter. The Adaptive Neuro-Fuzzy

inference system (ANFIS) is a hybrid technique

which is based on fuzzy and neural networks to

enhance the performance of the system accuracy for

modeling and simulating complex systems with

none linear characteristics (Ritika and Bhardwaj,

2020). The required membership function

parameters for the designed fuzzy inference system

are calculated by feeding the given information that

is embedded in relation among the

input/output

training data sets. The ANFIS embedded learning

capabilities makes it more efficient and works

similarly to neural networks. The membership

functions parameters are tuned by using a

combination of back propagation and least squares

error minimization learning technique. Throughout

the learning process, the suggested membership

functions will continue to evolve until reaching the

required target error value. The calculation of fuzzy

membership functions is interpolated by gradient

vector to provide a measure of how well the

implemented fuzzy inference system is capable of

modeling the input/output data for a given set of

variables. The optimization process is applied to

adjust the network weights and parameters to

continuously reduce a previously designed output

error measure. This system is based on Sugeno-type

system to simulate the required model and analyze

the mapping relation between the input and output

data values and to determine the optimal distribution

of membership function (Qun, 2015). It is mainly

based on the fuzzy “if-then” rules from the Takagi

and Sugeno type. The equivalent Takagi and Sugeno

ANFIS architecture is shown in Figure 2. It contains

five successive layers and each layer involves

several nodes, with different node function per layer.

Figure 2: The equivalent Takagi and Sugeno ANFIS

Architecture.

The output signals from each node in the

previous layer is fed to the input signals in the

present layer. Each node is firing its output value

depending on its embedded activation function and

accumulated input from the previous layer. The node

output will be fed to the nodes in the next layer.

The below bullet points describe the

designed

ANFIS model:

 Total number of network nodes: 30 + 5 + 1

 Total number of the network linear parameters:

932

 Total number of the network nonlinear

parameters: 28

 Total number of the model parameters: 6 inputs

+ 1 output

 The total number of the training data pairs: 500

 The total number of used fuzzy rules: 19

Any text or material outside the aforementioned

margins will not be printed.

3.2 Model Input/Output Parameters

The fuzzy logic part of the ANFIS based model is

initially determined by the fuzzy sets of input/output

values which represent the possible values of these

variables. Figure 3 shows the general three stages of

the suggested model to simulate the distance

learning media selection system. Figure 3 shows a

sequence of six inputs to generate target single

output as a measure of the selected distance learning

media performance. That means, it is a multi-input

single output ANFIS model with six input

parameters (accessibility, cost, teaching,

interactivity, organization, and speed) and one

output parameter to indicate the selected distance

learning system performance.

Figure 3: The schematic model of the distance learning

media selection.

For each suggested set on these six input parameters,

the resulted output value is considered as the

estimated goodness of the distance learning media

for this specific state of input.

3.3 Membership Function

The fuzzy theory is based on the overlapped

triangular membership logic with a predefined

suitable width and values. Each element accordingly

can belong to a particular set with partial

membership value to each set. Depending on the

addressed problem, it is possible to define a suitable

membership function with certain environment and

limitation for each of the required variables. Table 1

below shows the initial description of the fuzzy sets

for a system with six input variables and the related

fuzzy classification

3.4 Fuzzy Rules Characteristics

Each of the six inputs of the designed system is

assigned to different levels of linguistic variables.

These variables have been tuned to generate only

nineteen rules. Keeping in mind that there are many

rules might be classified as 'not applicable'

conditions and accordingly are not included in the

designed set of accepted rules.

This ANFIS model for Bate’s ACTIONS

parameters is designed and trained by using

MATLAB fuzzy toolbox. The membership functions

are generated by using clustering algorithm.

Table 1: The definition of the fuzzy input variables.

Input Cat.1 Cat.2 Cat.3 Cat.4

Accessibility

Simple

Simple Difficult

0-4 3-7 5-10

Cost

V. Cheap Cheap Expensive

Expensive

0-3 2.5-5 3-6 6-10

Teaching

ability

Bad Good V. Good

0-3 2-6 5-10

Interactivity

Not user

friendly

User

friendly

0-4 4-10

Organization

Bad Suitable V. Suitable

0-3 2.6-6 5-10

Speed

V. Slow Slow Fast V. Fast

0-2 1.8-4 3.5-6.7 6-10

Figure 4: The membership functions after the

ANFIS

training.

The training parameters are: Influential radius (Rc)

is 0.5, Quash factor (η) is 1.5, Accept ratio (R

)

0.5, and the Reject ratio (R

Reject

) is 0.15. The

applicable rules formulated for the model and the

memberships are given in Figure 4 below. The core

of the proposed ANFIS system is designed by using

fuzzy linear model type Sugeno which converts a

fuzzy inference engine into an adaptive network that

learns the relationship between inputs. The designed

system is deﬁned by the Bate’s model input

parameters (accessibility, cost, teaching ability,

interactivity, organization, speed) while the single

output is deﬁned as the related performance of the

tested distance learning system (sp).

The six input/single output bate’s model is used

to improve the converge speed of the ANFIS hybrid

leaning algorithm. The available data set is

randomly partitioned into a training set and a

checking (testing) sets. The training sets are a

practical description of the desired input/output data

which is used during the training stage to train the

model by minimizing the target output error. While

the checking data sets are used for the testing phase

and to carry out the cross validation of the ANFIS

model.

The ﬁrst-order (linear) ANFIS is trained using

the hybrid algorithm of the back-propagation and

least-square methods available through the

MATLAB toolbox. The rule viewer is used to

generate the below example of value-relations for a

certain state of training parameters shown in Figure

Figure 5: ANFIS rules shown by rule viewer.

The designed rules along with membership function

are also shown in rule viewer of fuzzy model as

given in the above Figure 5. This Figure 5 clearly

shows the characteristic of the six input parameters

for a certain example to present their accumulated

effect on the output variable.

4 TRAINING RESULTS AND

DISCUSSIONS

The first phase of the system design is the

convergence to the final shape of the ANFIS model

to optimize the distance education media selection

system for certain set of input variables. Then,

SYSTEM

PERFORMANCE,

Parameters

BATE

MODEL

ANFIS

(sugeno)

Accessibility

Cost

Interactivity

Teaching

ability

Organization

Speed

verifying the accuracy of the model in the testing

phase to demonstrate the designed model

performance. Figure 6 below is partially showing the

cross-relations among the six input variables and the

related interdependency of the model output value

on each of these inputs. Eight interdependent

relations were selected

randomly

to show eight

examples of the output surface area changing in

response to the associated change in two of the input

variables as shown in figure 6. The Eight different

three- dimensional relations for the system

performance shown in this figure prove that each of

the six input variables is affecting the final value of

the model output in a different way depending on the

pre- learning phase and the weighted effect of this

input variable and its interdependent relations with

the other input variables

Figure 6: Input/output surface area interdependent

relations.

Figures (7a) and (7b) are showing the ANFIS model

training to simulate the performance of Bate’s

ACTIONS model which is carried out by using 600

epochs before converging to the minimum accepted

preset error value. Figure (7c), is showing the final

ANFIS model output performance (output accuracy)

during the validation or checking stage

Figure 7: (a) Decrease of error during training phase.

(b) Decrease of error during testing phase.

In this model a total of 50 input/output data sets are

used as practical examples to verify the model

accuracy. It was found that only two input data sets

were out of range and couldn’t meet the expected

target output value and the output error has exceeded

five percent. The rest of the validation data sets have

shown individual error less than three percent. Thus,

the overall average error for the model is about five

percent which means that the simulated fuzzy model

is giving an overall of 95 percent accuracy. It can be

concluded that the designed ANFIS model is very

accurate and there is a very small error percentage

which is acceptable compared to the huge efforts

required to carry out the process by using the tedious

conventional methods which depend on using

human calculations under different conditions.

5 CONCLUSION

The feasibility of using ANFIS model technique was

demonstrated to simulate a simple adaptive system

to estimate the optimal choice of distance education

media. A

multi-input

single output adaptive Neuro-

Fuzzy model was developed and the designed model

was validated by using pre-calculated experimental

results for given conditions. The demonstration

results proved that the designed fuzzy model

accurate enough to be used by the educational

organization who are planning to upgrade to new

learning systems. It has been concluded that the

model is about 95 percentage accurate. A model

with such accuracy can be used by the practicing

educational system designers who would like to get

quick answers by using this optimized simple

intelligent tool. This work has emphasized the fact

that ANFIS modeling technique can be used as a

viable alternative to carry out analysis without

conducting actual experiments which might be very

expensive and time consuming process. The system

was found to be very flexible and easy to use.

Modeling using ANFIS techniques was proved to be

very cost effective and practical alternative to the

conventional methods.

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