Optimization of Language Learning with TOPSIS
Subject Areas : Numerical Analysis
ترانه
جوانبخت
1
(دانشگاه کبک در مونترال)
Keywords: fuzzy logic, Optimization, TOPSIS, language learning, automated decision-making,
Abstract :
The present study focuses on the application of fuzzy sets in the optimization of language learning with TOPSIS. The appropriate consideration of the candidates’ characteristics is an important issue which can affect their language learning. Motivation, learner strategies, perseverance and age are the factors that affect language learning. The hypothesis in this paper was that the difference in the consideration of these factors can affect the individuals’ language learning. In this study, for the first time, the analysis of the candidates’ characteristics of two age categories was performed for the investigation of their impact on language learning. The purpose of this work was to analyze the candidates’ characteristics on the individuals’ language learning. The analysis with a decision making algorithm, TOPSIS, revealed the efficiency of this method. One of the advantages of this study was that the effect of different characteristics of the category members on the categories confusion has made the prediction for the optimization of language learning possible. Another advantage was that the modification of the TOPSIS method with the application of fuzzy disjunction has been efficient to provide an automated decision-making tool for this analysis. The results presented in this paper could be used for the development of algorithms and linguistic tools for the optimization of language learning with artificial intelligence.
Optimization of Language Learning with TOPSIS
Abstract
The present study focuses on the application of fuzzy sets in the optimization of language learning with TOPSIS. The appropriate consideration of the candidates’ characteristics is an important issue which can affect their language learning. Motivation, learner strategies, perseverance and age are the factors that affect language learning. The hypothesis in this paper was that the difference in the consideration of these factors can affect the individuals’ language learning. In this study, for the first time, the analysis of the candidates’ characteristics of two age categories was performed for the investigation of their impact on language learning. The purpose of this work was to analyze the candidates’ characteristics on the individuals’ language learning. The analysis with a decision making algorithm, TOPSIS, revealed the efficiency of this method. One of the advantages of this study was that the effect of different characteristics of the category members on the categories confusion has made the prediction for the optimization of language learning possible. Another advantage was that the modification of the TOPSIS method with the application of fuzzy disjunction has been efficient to provide an automated decision-making tool for this analysis. The results presented in this paper could be used for the development of algorithms and linguistic tools for the optimization of language learning with artificial intelligence.
Keywords automated decision-making, fuzzy logic, TOPSIS, optimization, language learning
1 Introduction
Language learning is a cognitive process in which memory is involved and requires improved performance and expericence. The capacity of manipulating information and relating it to long-term storage are important in this process [1]. Perception, short term memory and long term memory as well as working memory with a distinguishable construct and higher cognitive function that is an interface between these memories are involved in information processing, which in turn is applied in language learning [2–4]. Motivation, learner strategies, perseverance and age are the factors that have impact on language learning [5-9].
Decision-making is an important process that is applied for prediction and optimization in artificial intelligence. The automatic decision-making has been in development during recent years. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a method that has been developed by Hwang and Yoon in order to determine solutions from a finite set of alternatives [10]. The ranking of candidates is performed by this method according to their distances from their ideal solutions. This requires the calculations with the consideration of their profit and cost criteria [11–16].
Fuzzy sets that represent the classes of members are considered in fuzzy logic ; a non-classical logic with diverse applications in science and engineering. This logic has been used with TOPSIS for multi-criteria decision making problems [12–17]. TOPSIS has been widely used for the optimization of the properties of materials as well as the predication of the traits of human beings [18–22]. It has also been used for the characteristics prediction of manufactured devices and instruments. [23–32]
The analysis of language learning using TOPSIS and fuzzy disjunction has not been reported, yet. The results of this paper can be used in order to develop linguistic tools and more applications of this method for the optimization of language learning.
In order to investigate the optimization of language learning with the TOPSIS method, the remainder of this paper is structured as follows. Section 2 presents the preliminaries including the information on the definitions that are used in fuzzy logic. Section 3 presents the methods including the description of the TOPSIS method and its modification. The ananlysis results and discussion are presented in the following section. Finally, the conclusions including the information on the perspectives of this work are presented at the end of the paper.
2 Preliminaries
The definitions for the application of fuzzy sets are reviewed here from [33-39]:
A fuzzy set is characterized by a membership function which has the values in the interval [0,1] in the universe of discourse. The fuzzy set is convex if the condition below is respected:
The fuzzy subset in the unverse of disourse is a fuzzy number with an α-cut defined as below:
The α-cut also is in the interval [0.1].
The universe of discourse contains at least a non-empty bounded closed interval with lower and upper bounds that can be written as below:
A triple (n1, n2, n3) can define the triangular fuzzy number with a membership defined as below:
The distance between two triangular fuzzy numbers is defined as below:
If these triangular fuzzy numbers are real numbers with the conditions below:
m1=m2=m3=m
and
n1=n2=n3=n
then the distance between them is defined as below:
The TOPSIS method that we used is compatible to the fuzzy environment as the definitions above are applicable to the category members and the candidates that are optimized in this method.
3 Methods
3.1 TOPSIS method
The evaluation matrix of the TOPSIS method includes the entry values for the class of the candidates’ characteristics for the study of their languag learning. For each characteristic, triangular fuzzy values of membership degrees and their mean values are attributed according to these terms : low, medium and high. The mean values of fuzzy membership degrees are used in the TOPSIS method. The steps of this method have been described previously [22].
3.2 Modified TOPSIS
This line was added to the first step of the TOPSIS code as described previously [22]:
evaluation_matrix[row_size-3][column_size-1] = evaluation_matrix[row_size-3][column_size-1] + 0.8
With this modification, only the age as the last criterion of the first candidate would increase with 0.8 and the value 1.0 as its maximum value would appear in the output of TOPSIS. This modification was according to a model from cognitive science called the model of the tree including the Łukasiewicz fuzzy disjunction for creating an automated decision-making process. According to this model, the category members or candidates and their characteristics would be considered as fuzzy sets with different fuzzy membership degrees [40][41]. The inappropriate consideration of the crtiteria that would affect the candidates’ ranking with TOPSIS were due to the inconsistency in epistemic beliefs, which in turn resulted in the category confusion. Therefore, the application of this model with fuzzy disjunction could help a better understanding of the impact of the epistemic belief inconsistency and category confusion on language learning. The modification with fuzzy disjunction replaced the membership degree for the age of the first young and old candidates with the value 1.0 in the matrices of evaluation as these candidates would understimate the age as a cost criterion and consider it as a profit one. In other words, they would not consider that the increase of their age could reduce their language learning efficiency.
4 Results and discussion
The steps below include the results obtained with the TOPSIS method. First, we determined the mean values of the triangular fuzzy membership degrees of the candidates’ characteristics. Table 1 shows the terms, corresponding triangular fuzzy membership degrees of the candidates’ characteristics and their mean values, respectively. The information about three candidates in two categories of young and old individuals (C-1, C-2 and C-3) with their characteristics is presented in the table. The first three characteristics, motivation, learner strategies and perseverance, have a positive effect on the output of the candidates’ language learning. These are profit criteria. Age as the last characteristic can have positive or negative impact on their language learning. Young people learn languags more easily than old people as they use memory with a function that can be affected with age. However, the first group know that the increasing of age could reduce their language skills, but the second group could neglect this phenomenon. In other words, the young candidates consider the age as a negative criterion, whereas the old ones consider it as a positive criterion. Therefore, for young candidates, age is a negative characteristic and cost criterion and for old candidates, it is a positive characteristic and profit criterion.
Table 1 Terms, corresponding triangular fuzzy membership degrees of young candidates’ characteristics and their mean values
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | medium | medium | low | high |
C-2 | medium | high | low | high |
C-3 | low | low | high | high |
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | 0.4, 0.5, 0.6 | 0.4, 0.5, 0.6 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 |
C-2 | 0.4, 0.5, 0.6 | 0.7, 0.8, 0.9 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 |
C-3 | 0.1, 0.2, 0.3 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 | 0.7, 0.8, 0.9 |
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | 0.5 | 0.5 | 0.2 | 0.8 |
C-2 | 0.5 | 0.8 | 0.2 | 0.8 |
C-3 | 0.2 | 0.2 | 0.8 | 0.8 |
Terms, corresponding triangular fuzzy membership degrees of the old candidates’ characteristics and their mean values are presented below.
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | medium | medium | low | low |
C-2 | medium | high | low | low |
C-3 | low | low | high | low |
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | 0.4, 0.5, 0.6 | 0.4, 0.5, 0.6 | 0.1, 0.2, 0.3 | 0.1, 0.2, 0.3 |
C-2 | 0.4, 0.5, 0.6 | 0.7, 0.8, 0.9 | 0.1, 0.2, 0.3 | 0.1, 0.2, 0.3 |
C-3 | 0.1, 0.2, 0.3 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 | 0.1, 0.2, 0.3 |
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | 0.5 | 0.5 | 0.2 | 0.2 |
C-2 | 0.5 | 0.8 | 0.2 | 0.2 |
C-3 | 0.2 | 0.2 | 0.8 | 0.2 |
The second steps concerns the determination of the weights of alternatives for each criterion. The weights for each criterion are presented in table 2.
Table 2 The weights for each criterion
Candidates / Values | motivation | learner strategies | perseverance | age |
C1-C3 | 0.5 | 0.5 | 0.5 | 0.5 |
In the next step, the criteria matrices for young and old candidates are determined. Table 3 shows the criteria matrix indicating true for the profit criteria and false for the cost criterion, respectively. Motivation, learner strategies and perseverance are profit criteria, whereas age is the cost criterion for the young candidates. Motivation, learner strategies, perseverance and age are all profit criteria for the old candidates.
Table 3 Criteria matrix for young candidates
Alternatives/Values | motivation | learner strategies | perseverance | age |
C1-C3 | True | True | True | False |
The criteria matrix for the old candidates was as follows.
Alternatives/Values | motivation | learner strategies | perseverance | age |
C1-C3 | True | True | True | True |
The normalization of fuzzy membership degrees and weights is the next step. The vector normalization of the fuzzy membership degrees of the candidates’ characteristics as well as the normalization of their weights are followed by their multiplication, which gives the weighted normalization matrix. The results of the normalized decision matrix and weighted normalized decision matrix are shown in Tables 4 and 5, respectively.
Table 4 The normalized decision matrix for young candidates
Candidates / criteria | motivation | learner strategies | perseverance | age |
C1 | 0.68041382 | 0.51847585 | 0.23570226 | 0.57735027 |
C2 | 0.68041382 | 0.82956136 | 0.23570226 | 0.57735027 |
C3 | 0.27216553 | 0.20739034 | 0.94280904 | 0.57735027 |
The normalized decision matrix for the old candidates was as follows.
Candidates / criteria | motivation | learner strategies | perseverance | age |
C1 | 0.68041382 | 0.51847585 | 0.23570226 | 0.57735027 |
C2 | 0.68041382 | 0.82956136 | 0.23570226 | 0.57735027 |
C3 | 0.27216553 | 0.20739034 | 0.94280904 | 0.57735027 |
Table 5 The weighted normalized decision matrix for young candidates
Candidates / criteria | motivation | learner strategies | perseverance | age |
C1 | 0.17010345 | 0.12961896 | 0.05892557 | 0.14433757 |
C2 | 0.17010345 | 0.20739034 | 0.05892557 | 0.14433757 |
C3 | 0.06804138 | 0.05184758 | 0.23570226 | 0.14433757 |
The weighted normalized decision matrix for the old candidates was as follows.
Candidates / criteria | motivation | learner strategies | perseverance | age |
C1 | 0.17010345 | 0.12961896 | 0.05892557 | 0.14433757 |
C2 | 0.17010345 | 0.20739034 | 0.05892557 | 0.14433757 |
C3 | 0.06804138 | 0.05184758 | 0.23570226 | 0.14433757 |
In the next step, the best alternative (A+) and the worst alternative (A-) are obtained. Table 6 shows the results of these alternatives.
Table 6 The best alternative (A+) and the worst alternative (A-) for young candidates
Candidates / criteria | motivation | learner strategies | perseverance | age |
A+ | 0.17010345 | 0.20739034 | 0.23570226 | 0.14433757 |
A- | 0.06804138 | 0.05184758 | 0.05892557 | 0.14433757 |
The best alternative (A+) and the worst alternative (A-) for the old candidates were as follows.
Candidates / criteria | motivation | learner strategies | perseverance | age |
A+ | 0.17010345 | 0.20739034 | 0.23570226 | 0.14433757 |
A- | 0.06804138 | 0.05184758 | 0.05892557 | 0.14433757 |
In step 6, the distances from the best alternative (di*) and the worst alternative (di-) are determined. The results of the distances from the best alternative (di*) and the worst alternative (di-) for the candidates are shown in Table 7.
Table 7 The distances from the best alternative (di*) and the worst alternative (di-) for young candidates
Candidates | di* | di- |
C1 | 0.1931279 | 0.12831623 |
C2 | 0.1767767 | 0.18603821 |
C3 | 0.18603821 | 0.1767767 |
The distances from the best alternative (di*) and the worst alternative (di-) for the old candidates are presented in the table below.
Candidates | di* | di- |
C1 | 0.1931279 | 0.12831623 |
C2 | 0.1767767 | 0.18603821 |
C3 | 0.18603821 | 0.1767767 |
The next step was the determination of the similarity coefficients of the young and old candidates according to their worst similarity. Table 8 shows the similarity coefficients and the rankings of the candidates.
Table 8 The similarity coefficients (CCi) and the ranking of the young candidates according to the worst similarity
Candidates | CCi | ranking |
C1 | 0.39918671 | 2 |
C2 | 0.51276341 | 3 |
C3 | 0.48723659 | 1 |
The similarity coefficients (CCi) and the ranking of the old candidates according to the worst similarity are presented in the table below.
Candidates | CCi | ranking |
C1 | 0.39918671 | 2 |
C2 | 0.51276341 | 3 |
C3 | 0.48723659 | 1 |
The distances from the ideal solution and similarity coefficients of the young and old candidates are presented in Fig. 1 and Fig. 2, respectively.
Fig. 1 The distances from the ideal solution and similarity coefficients of the young candidates
Fig. 2 The distances from the ideal solution and similarity coefficients of the old candidates
The obtained results show that the candidates’ distances from the postivie and negative ideal solutions as well as their rankings are the same for young and old candidates and the difference in their consideration of age as a profit or cost criterion does not affect their rankings in both groups.
In another series of experiments, we analyzed the output of the modified TOPSIS for young and old candidates. The obtained results are presented in the tables below.
Table 9 Terms. corresponding triangular fuzzy membership degrees of young candidates’ characteristics and their mean values
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | medium | medium | low | high |
C-2 | medium | high | low | high |
C-3 | low | low | high | high |
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | 0.4, 0.5, 0.6 | 0.4, 0.5, 0.6 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 |
C-2 | 0.4, 0.5, 0.6 | 0.7, 0.8, 0.9 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 |
C-3 | 0.1, 0.2, 0.3 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 | 0.7, 0.8, 0.9 |
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | 0.5 | 0.5 | 0.2 | 1.0 |
C-2 | 0.5 | 0.8 | 0.2 | 0.8 |
C-3 | 0.2 | 0.2 | 0.8 | 0.8 |
Terms, corresponding triangular fuzzy membership degrees of the old candidates’ characteristics and their mean values are presented in the tables below.
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | medium | medium | low | high |
C-2 | medium | high | low | low |
C-3 | low | low | high | low |
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | 0.4, 0.5, 0.6 | 0.4, 0.5, 0.6 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 |
C-2 | 0.4, 0.5, 0.6 | 0.7, 0.8, 0.9 | 0.1, 0.2, 0.3 | 0.1, 0.2, 0.3 |
C-3 | 0.1, 0.2, 0.3 | 0.1, 0.2, 0.3 | 0.7, 0.8, 0.9 | 0.1, 0.2, 0.3 |
Candidates / Criteria | motivation | learner strategies | perseverance | age |
C-1 | 0.5 | 0.5 | 0.2 | 1.0 |
C-2 | 0.5 | 0.8 | 0.2 | 0.2 |
C-3 | 0.2 | 0.2 | 0.8 | 0.2 |
The second step concerns the determination of the weights of alternatives for each criterion. The weights for each criterion are presented in table 10.
Table 10 The weights for each criterion