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Modeling and analyzing of conformity behavior: A fuzzy logic approach
Optik 125 (2014) 6594–6598
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Modeling and analyzing of conformity behavior: A fuzzy logic approach GuiPing Wang a , ShuYu Chen b,∗ , Xin Yang c , Jun Liu a a b c
College of Computer Science, Chongqing University, Chongqing 400044, China College of Software Engineering, Chongqing University, Chongqing 400044, China College of Automation, Chongqing University, Chongqing 400044, China
a r t i c l e
i n f o
Article history: Received 29 October 2013 Accepted 14 July 2014 Keywords: Fuzzy logic Quantitative and qualitative methods Conformity behavior Individual behavior Group
a b s t r a c t Modeling students’ classroom behaviors can help educators and researchers better understand these behaviors, and further guide students toward well behaviors. Conformity refers to the tendency to change individual behavior to match group behavior. Through observation and experience, educators have accumulated much linguistic knowledge for describing and understanding students’ conformity behavior and influence. This paper presents a fuzzy logic approach for modeling participants’ classroom behaviors. The simulation results about two observed college classes show that the constructed fuzzy logic system is congruent with the observed participants’ classroom behaviors. Existing findings, as well as new findings, are verified through further simulation and analysis. The proposed fuzzy logic system helps educators quantitatively analyze and understand students’ conformity behavior in classroom. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction Modeling helps people better understand real world systems. Understanding and guiding students’ classroom behavior is always the concern of educators and researchers. The researches in social psychology indicate that individual behavior is influenced by environment, other people, and group. Conformity is an important type of social influence. It refers to the tendency to change one’s belief or behavior to match the behavior of others [1]. In literature, conformity behavior is also referred to as herd behavior [2,3] or collective behavior [4]. Educators and researchers have long been interested in how students’ individual behavior in classroom is influenced by environment and group behavior. Through observation and experience, they have accumulated much linguistic knowledge for describing and understanding such influence, e.g., (a) if the group learn in earnest and the teacher teaches well, then each individual tends to learn in earnest; (b) if the group learn in earnest, but the teacher teaches averagely, then each individual still tends to learn in earnest. Among various modeling methods, fuzzy modeling is one of the most effective quantitative approaches for transforming human
∗ Corresponding author. E-mail address: [email protected] (S. Chen). http://dx.doi.org/10.1016/j.ijleo.2014.07.082 0030-4026/© 2014 Elsevier GmbH. All rights reserved.
linguistic data into mathematical formulas and vice versa. It offers a unique advantage, i.e., the close relationship between linguistic description and resulting mathematical model [5]. Therefore, this paper presents a fuzzy logic approach for modeling participants’ classroom behaviors. The constructed fuzzy logic system is simulated with MATLAB. Simulation results about two observed classes show that the fuzzy logic system is congruent with the observed participants’ classroom behaviors. Existing findings, as well as new findings, are verified through further simulation and analysis. This paper mainly makes the following contributions: (i) presenting a fuzzy logic approach for modeling participants’ classroom behaviors; (ii) providing a significant attempt to quantitatively analyze and understand students’ conformity behavior in classroom; and (iii) discovering several new findings based on simulation results.
2. Related work 2.1. Conformity research The research on conformity can be traced back to Sherif’s pioneering experiment: a guess in the dark [6]. Asch conducted a series of conformity experiments [7–9]. Throughout these experiments, he wanted to examine: (a) what extent do social forces alter
G. Wang et al. / Optik 125 (2014) 6594–6598
people’s opinions; (b) which aspect of the group influence is most important, the size of the majority or the unanimity. Social psychology researches on conformity indicate that the size of the group, the unanimity of the group opinions, and individual’s commitment to the group can all affect conformity [1]. Rosander and Eriksson [10] investigate conformity behavior in use of the Internet. Their research indicates that half the participants are subjected to conformity manipulations. The result shows the participants a clear conformity to erroneous majority alternatives. They also discuss underlying reasons for such conformity. Chen [2] refers to conformity as herd behavior. He claims that when people use the product evaluations of others to indicate product quality on the Internet, online herd behavior occurs. He presents four studies examining herd behavior of online book purchasing. In sum, there are many studies addressing conformity in use of Internet [10], online purchasing [2], financial market [3,11], etc. This paper attempts to study college students’ classroom behavior from conformity point of view. 2.2. Fuzzy logic and modeling Fuzzy logic is one of the most appropriate quantitative methods describing an observed system. The description and characterization is built on natural languages. Natural languages are undoubtedly the most convenient and effective expression means for human, since they undergo thousands of years of historical development. In 1965, professor Zadeh published his seminal work on fuzzy sets [12], in which he detailed the mathematics foundation of fuzzy set theory. In 1973, he proposed the theory of fuzzy logic [13]. Tron and Margaliot [5] utilize fuzzy modeling as a tool for assisting human observers in the difficult task of transforming their observations into mathematical models, which advocates a new application of fuzzy modeling. They demonstrate unique advantages of fuzzy modeling using an example of territorial behavior of fish. Chrysafiadi and Virvou [14] constitute a literature review on student modeling for the last decade. They review the prevailing student modeling approaches in designing computer-based educational software and tutoring systems. They notice that there is an increase in the adoption of fuzzy techniques and Bayesian networks in order to deal the uncertainty of student modeling. Compared with aforementioned research work [2,5,10], this paper presents a fuzzy logic approach for modeling students’ individual conformity behavior in college classroom. 3. A fuzzy logic approach for modeling participants’ behaviors in classroom The motivation of this paper is that an interesting conformity phenomenon is first discovered in college classroom by natural language. Therefore, a fuzzy logic system is constructed to describe participants’ classroom behaviors from conformity point of view, as well as to study the factors that influence students’ conformity behavior. 3.1. Phenomenon description and analysis An interesting phenomenon is discovered in a same course for two classes: (a) a large class containing 120 students, and (b) a small class containing 90 students. “These students are all sophomores. The academic performance of each class is almost at the same level. But the teaching effectiveness differs greatly. The large class is arranged in a big classroom
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Fig. 1. The fuzzy logic model of determining GB.
with 180 seats. During a lesson, the students are seated dispersedly. The classroom is very noisy, and the class discipline is bad. The status of students’ participating in the lesson makes the teacher’s mood very bad. The teaching effectiveness is poor. However, the small class is arranged in a small classroom with 100 seats. During a lesson, the students are seated concentratedly. The class discipline is good. Most students listen to the teacher and take notes carefully. The teacher is in well mood. Therefore, the teaching effectiveness is good.” Several factors cause the difference in teaching effectiveness. Firstly, a large classroom is really not suitable for a lesson. In a large classroom, if the students are seated dispersedly, it is not easy for the teacher to observe every student. Therefore, the teacher could not tune the teaching according to students’ reflection. While in a small classroom, it is relatively easy for the teacher to observe the whole class. Secondly, if a classroom contains so many students, the class tends to be noisy. It is not easy for the teacher to maintain class discipline. Therefore, an individual student is more vulnerable to be influenced by other students. Thirdly, in a class with poor discipline, the teacher’s mood is affected as well. The teacher feels not respected by students. The poor mood will naturally affect the teacher’s thinking and disturb his teaching process. 3.2. The constructed fuzzy logic system The above phenomenon can be identified as a phenomenon and behavior in social psychology, i.e., conformity behavior. This paper constructs a fuzzy logic system from the following two aspects: the environment, and the participants’ behaviors. The environment includes two factors: (a) Occupancy ratio (OR): the ratio of class size to classroom capacity, OR ∈ [0,1]. OR has three fuzzy variables: high, medium, and low. The corresponding membership functions are: f1 , f2 , and f3 , respectively. (b) Classroom organization (CO): the observed average organization level of the whole class, CO ∈ [0,1]. CO also has three fuzzy variables: good, medium, and bad. The corresponding membership functions are: f4 , f5 , and f6 , respectively. The participants’ behaviors include students’ group behavior (GB), the teacher’s teaching behavior (TB), and students’ individual behavior (IB). (a) GB: it represents the earnestness extent to which all students listen to the teacher in class as a whole, GB ∈ [0,10]. (b) TB: it is a comprehensive index, which includes the extent to which the teacher can concentrate on teaching, and the popular degree of teacher’s teaching, TB ∈ [0,10]. (c) IB: it represents the earnestness extent to which an individual student listen to the teacher in class, IB ∈ [0,10]. GB has three fuzzy variables: well, general, and bad. The corresponding membership functions are: f7 , f8 , and f9 , respectively. The factors which influence GB include CO and OR, as shown in Fig. 1. The fuzzy logic rules determining GB are listed as follows.
G. Wang et al. / Optik 125 (2014) 6594–6598
Fig. 2. The fuzzy logic model of determining TB.
membership degree (or frequency)
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1
trapmf(x, 6.1, 8.9, 10, 10)
0.8 0.6 0.4 0.2 0 5
Fig. 3. The fuzzy logic model of determining IB.
R1: If CO is good, and OR is high, then GB is well. R2: If CO is good, and OR is medium, then GB is well. R3: If CO is good, and OR is low, then GB is general. R4: If CO is medium, and OR is high, then GB is general. R5: If CO is medium, and OR is medium, then GB is general. R6: If CO is medium, and OR is low, then GB is bad. R7: If CO is bad, THEN GB is bad. TB has three fuzzy variables: well, general, and bad. The corresponding membership functions are: f10 , f11 , and f12 , respectively. The factors which influence TB include GB and OR, as shown in Fig. 2. The fuzzy logic rules determining TB are listed as follows. R8: If GB is well, and OR is high, then TB is well. R9: If GB is well, and OR is medium, then TB is general. R10: If GB is well, and OR is low, then TB is general. R11: If GB is general, and OR is high, then TB is well. R12: If GB is general, and OR is medium, then TB is general. R13: If GB is general, and OR is low, then TB is bad. R14: If GB is bad, and OR is high, then TB is general. R15: If GB is bad, and OR is medium, then TB is bad. R16: If GB is bad, and OR is low, then TB is bad. IB has three fuzzy variables: well, general, and bad. The corresponding membership functions are: f13 , f14 , and f15 , respectively. The factors which influence IB include GB and TB, as shown in Fig. 3. The fuzzy logic rules determining IB are listed as follows. R17: If GB is well, and TB is well, then IB is well. R18: If GB is well, and TB is general, then IB is well. R19: If GB is well, and TB is bad, then IB is general. R20: If GB is general, and TB is well, then IB is general. R21: If GB is general, and TB is general, then IB is general. R22: If GB is general, and TB is bad, then IB is bad. R23: If GB is bad, THEN IB is bad.
6 7 8 9 x (or teacher's teaching behavior) Fig. 4. The membership function of well TB.
selected. Since U is continuous, it is divided into 100 equivalent subintervals. The frequency of each subinterval is counted and plotted in Fig. 4. The membership function, trapmf(x, 6.1, 8.9, 10, 10), is also plotted on the same figure. It is found that this function is a good estimation of the membership degree of well TB. Accordingly, all the aforementioned membership functions are determined as follows. OR: the membership functions of high, medium, and low OR are f1 = sigmf(x, 35, 0.68), f2 = gaussmf(x, 0.11, 0.57), and f3 = zmf(x, 0.25, 0.65), respectively. CO: the membership functions of good, medium, and bad CO are f4 = sigmf(x, 37, 0.76), f5 = trapmf(x, 0.3, 0.42, 0.7, 0.82), and f6 = zmf(x, 0.23, 0.51), respectively. GB: the membership functions of well, general, and bad GB are f7 = trapmf(x, 6.3, 9.5, 10, 10), f8 = gauss2mf(x, 0.8, 5.2, 1.1, 6.5), and f9 = trapmf(x, 0, 0, 3.2, 5.5), respectively. TB: the membership functions of well, general, and bad TB are f10 = trapmf(x, 6.1, 8.9, 10, 10), f11 = gauss2mf(x, 0.7, 5.0, 0.75, 6.6), and f12 = trapmf(x, 0, 0, 3.1, 5.2), respectively. IB: the membership functions of well, general, and bad IB are f13 = trapmf(x, 5.7, 9.2, 10, 10), f14 = gauss2mf(x, 0.75, 4.8, 0.78, 6.8), and f15 = trapmf(x, 0, 0, 2.9, 4.9), respectively. The sigmoidally shaped membership function sigmf(x, [a c]) is defined as: f (x, a, c) =
1 1 + e−a(x−c)
.
(1)
The Z-shaped membership function zmf(x, [a b]), (a ≤ b), is defined as:
f (x, a, b) =
⎧ 1 x≤a ⎪ ⎪ ⎪ 1 − 2[(x − a)/(b − a)]2 a ≤ x ≤ (a + b)/2 ⎨ 2 ⎪ (a + b)/2 ≤ x ≤ b 1 − 2[(b − x)/(b − a)] ⎪ ⎪ ⎩
(2)
The trapezoidal membership function trapmf(x, [a b c d]), (a ≤ b ≤ c ≤ d) is defined as:
4. Simulation and analysis 4.1. Membership functions This paper adopts fuzzy statistics to estimate above 15 membership functions. For example, in order to estimate the membership function of well TB, a sampling survey is made. Given the domain, U = [0,10], 257 students are asked to write down the most appropriate interval that describe well TB. 100 answers are then randomly
.
x≥b
0
The above three fuzzy logic models (Figs. 1–3) and rules R1–R23 constitute the established fuzzy system.
10
f (x, a, b, c, d) =
⎧ 0 x≤a ⎪ ⎪ ⎪ x−a ⎪ a≤x≤b ⎪ ⎪ ⎪ ⎨ b−a 1
b≤x≤c .
0
x≥d
⎪ ⎪ d−x ⎪ ⎪ c≤x≤d ⎪ ⎪ d−c ⎪ ⎩
(3)
G. Wang et al. / Optik 125 (2014) 6594–6598
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10 students' group behavior
students' individual behavior
The teacher's teaching behavior is fixed at 6.6. 8 6 4
10
2 0 0
0.2
0.4 0.6 0.8 students' group behavior
8 6 4 2 1
0.8
0.6
0.2 occupancy ratio
1
0.6
0.4
0 0
0.8
1
0.4 0.2 classroom organization
Fig. 6. Relation between GB and environment. Fig. 5. Relation between IB and GB.
10
as: 2
f (x, , c) = e−(((x−c)
)/2 2 )
.
(4)
The two-sided Gaussian membership function gauss 2mf = f(x, 1 , c1 , 2 , c2 ) is a combination of two Gaussian membership functions: f(x, 1 , c1 ), and f(x, 2 , c2 ). 4.2. Simulation results of aforementioned two classes For the aforementioned large class, the class size is 120 (students), the classroom capacity is 180 (seats). Therefore, OR is 0.67. The observed CO value is 0.75. The simulation results of the large class are: GB is 6.7; TB is 6.62; and IB is 5.97. For the aforementioned small class, the class size is 90 (students), the classroom capacity is 100 (seats). Therefore, OR is 0.9. The observed CO value is 0.85. The simulation results of the small class are: GB is 8.77; TB is 8.48; and IB is 7.92. From the above results, it is found that the IB value in the small class is higher than that one in the large class, which means that an individual student in the small class behaves better than that in the large class. The results are congruent with the linguistic description and analysis presented in Section 3.1. 4.3. Further discussion This section further examines the factors that influence IB. (1) IB and GB The relation between IB and GB is described by the curve shown in Fig. 5, where TB is fixed at a medium value, 6.6. From Fig. 5, it is found that IB is verifiably influenced by GB. If group behave well, each individual tends to behave well. If group behave badly, each individual tends to behave badly as well. In other words, each individual student tends to adhere to group norms. Similar conclusions can be found in literature [1,15]. (2) GB and environment The relation between GB and environment is described by the surface shown in Fig. 6. From Fig. 6, it is verified that both these two environmental factors (i.e., OR and CO) influence GB. In a classroom with high OR and good CO, students tend to behave well. While in a classroom with low OR and bad CO, students tend to behave badly. Moreover, the impact of CO on GB is greater than that of OR, since the surface in Fig. 6 slides down faster along the axis of CO. This finding suggests teachers pay more attention to CO. (3) IB and environment
students' individual behavior
The Gaussian membership function gaussmf(x, [ c]) is defined
8
occupancy ratio: classroom organization is fixed at 0.6. classroom organization: occupancy ratio is fixed at 0.57.
6
4
2 0
0.2 0.4 0.6 0.8 classroom organization or occupancy ratio
1
Fig. 7. The impact of CO and OR on IB, respectively.
Since GB is influenced by environment, IB is also influenced by those two environmental factors. The relation between IB and CO is described by the solid curve shown in Fig. 7, where OR is fixed at a medium value, 0.57. The relation between IB and OR is described by the dash curve shown, where CO is fixed at a medium value, 0.6. From these two curves, it is verified that IB is also influenced by environment. In a classroom environment with high OR or good CO, an individual student tends to behave well. Slightly different from existing researches [7,16,17], it is found that IB is not simply influenced by group size, as shown in Fig. 7. More exactly, it is influenced by OR, i.e., the ratio of class size to classroom capacity. The larger the size of OR, the better an individual student behaves. The underlying reason is that in a classroom with low OR, students tend to be seated dispersedly and form their own small community. In such a community, an individual student is more likely in whispered conversation with other students. Therefore, he always cannot concentrate on listening to the teacher. While in a classroom with high OR, it is relatively easy for the teacher to observe the whole class and tune the teaching according to students’ reflection. Therefore, an individual student is more likely concentrate on listening. 5. Conclusion This paper presents a fuzzy logic approach for quantitatively modeling participants’ classroom behaviors. The simulation results of the proposed fuzzy system and the behaviors observed in two classes are congruent. Several existing findings and new findings are verified through further simulation and analysis. This paper provides a significant attempt to deep understand participants’ classroom behavior from conformity point of view. It is expected to help teachers actively guide students’
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G. Wang et al. / Optik 125 (2014) 6594–6598
conformity behavior in classroom, introduce new teaching methods to stimulate students’ enthusiasm and initiative in learning, and thus improve quality of classroom teaching. Acknowledgment The work is partially supported by National Natural Science Foundation of China (Grant No. 61272399). References [1] S.E. Taylor, L.A. Peplau, D.O. Sears, Social Psychology, 12th ed., Pearson Education Hall, Upper Saddle River, New Jersey, USA, 2006. [2] Y.F. Chen, Herd behavior in purchasing books online, Comput. Hum. Behav. 24 (5) (2008) 1977–1992. [3] S. Wang, Z. Zhe, Y. Kang, H. Wang, X. Chen, An ontology for causal relationships between news and financial instruments, Expert Syst. Appl. 35 (3) (2008) 569–580. [4] V.V. Breer, Game-theoretic models of collective conformity behavior, Autom. Remote Control 73 (10) (2012) 1680–1692. [5] E. Tron, M. Margaliot, Mathematical modeling of observed natural behavior: a fuzzy logic approach, Fuzzy Sets Syst. 146 (3) (2004) 437–450.
[6] M. Sherif, The Psychology of Social Norms, Harper and Brothers, New York, 1936. [7] S.E. Asch, Effects of group pressure on the modification and distortion of judgments, in: H. Guetzkow (Ed.), Groups, Leadership and Men, Carnegie Press, Pittsburgh, PA, 1951, pp. 177–190. [8] S.E. Asch, Social Psychology, Prentice-Hall, Englewood Cliffs, NJ, 1952. [9] S.E. Asch, Studies of independence and conformity: I. A minority of one against a unanimous majority, Psychol. Monogr. 70 (9) (1956) 1–70. [10] M. Rosander, O. Eriksson, Conformity on the Internet – the role of task difficulty and gender differences, Comput. Hum. Behav. 28 (5) (2012) 1587–1595. [11] A.V. Banerjee, A simple model of herd behavior, Q. J. Econ. 107 (3) (1992) 797–817. [12] L.A. Zadeh, Fuzzy sets, Inf. Control 8 (1965) 338–353. [13] L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Syst. Man Cybern. 3 (1) (1973) 28–44. [14] K. Chrysafiadi, M. Virvou, Student modeling approaches: a literature review for the last decade, Expert Syst. Appl. 40 (11) (2013) 4715–4729. [15] R.B. Cialdini, N.J. Goldstein, Social influence: compliance and conformity, Annu. Rev. Psychol. 55 (2004) 591–621. [16] B. Latané, S. Wolf, The social impact of majorities and minorities, Psychol. Rev. 88 (5) (1981) 438–453. [17] R. Bond, Group size and conformity, Group Process. Intergroup Relat. 8 (4) (2005) 331–354.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Modeling and analyzing of conformity behavior: A fuzzy logic approach GuiPing Wang a , ShuYu Chen b,∗ , Xin Yang c , Jun Liu a a b c
College of Computer Science, Chongqing University, Chongqing 400044, China College of Software Engineering, Chongqing University, Chongqing 400044, China College of Automation, Chongqing University, Chongqing 400044, China
a r t i c l e
i n f o
Article history: Received 29 October 2013 Accepted 14 July 2014 Keywords: Fuzzy logic Quantitative and qualitative methods Conformity behavior Individual behavior Group
a b s t r a c t Modeling students’ classroom behaviors can help educators and researchers better understand these behaviors, and further guide students toward well behaviors. Conformity refers to the tendency to change individual behavior to match group behavior. Through observation and experience, educators have accumulated much linguistic knowledge for describing and understanding students’ conformity behavior and influence. This paper presents a fuzzy logic approach for modeling participants’ classroom behaviors. The simulation results about two observed college classes show that the constructed fuzzy logic system is congruent with the observed participants’ classroom behaviors. Existing findings, as well as new findings, are verified through further simulation and analysis. The proposed fuzzy logic system helps educators quantitatively analyze and understand students’ conformity behavior in classroom. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction Modeling helps people better understand real world systems. Understanding and guiding students’ classroom behavior is always the concern of educators and researchers. The researches in social psychology indicate that individual behavior is influenced by environment, other people, and group. Conformity is an important type of social influence. It refers to the tendency to change one’s belief or behavior to match the behavior of others [1]. In literature, conformity behavior is also referred to as herd behavior [2,3] or collective behavior [4]. Educators and researchers have long been interested in how students’ individual behavior in classroom is influenced by environment and group behavior. Through observation and experience, they have accumulated much linguistic knowledge for describing and understanding such influence, e.g., (a) if the group learn in earnest and the teacher teaches well, then each individual tends to learn in earnest; (b) if the group learn in earnest, but the teacher teaches averagely, then each individual still tends to learn in earnest. Among various modeling methods, fuzzy modeling is one of the most effective quantitative approaches for transforming human
∗ Corresponding author. E-mail address: [email protected] (S. Chen). http://dx.doi.org/10.1016/j.ijleo.2014.07.082 0030-4026/© 2014 Elsevier GmbH. All rights reserved.
linguistic data into mathematical formulas and vice versa. It offers a unique advantage, i.e., the close relationship between linguistic description and resulting mathematical model [5]. Therefore, this paper presents a fuzzy logic approach for modeling participants’ classroom behaviors. The constructed fuzzy logic system is simulated with MATLAB. Simulation results about two observed classes show that the fuzzy logic system is congruent with the observed participants’ classroom behaviors. Existing findings, as well as new findings, are verified through further simulation and analysis. This paper mainly makes the following contributions: (i) presenting a fuzzy logic approach for modeling participants’ classroom behaviors; (ii) providing a significant attempt to quantitatively analyze and understand students’ conformity behavior in classroom; and (iii) discovering several new findings based on simulation results.
2. Related work 2.1. Conformity research The research on conformity can be traced back to Sherif’s pioneering experiment: a guess in the dark [6]. Asch conducted a series of conformity experiments [7–9]. Throughout these experiments, he wanted to examine: (a) what extent do social forces alter
G. Wang et al. / Optik 125 (2014) 6594–6598
people’s opinions; (b) which aspect of the group influence is most important, the size of the majority or the unanimity. Social psychology researches on conformity indicate that the size of the group, the unanimity of the group opinions, and individual’s commitment to the group can all affect conformity [1]. Rosander and Eriksson [10] investigate conformity behavior in use of the Internet. Their research indicates that half the participants are subjected to conformity manipulations. The result shows the participants a clear conformity to erroneous majority alternatives. They also discuss underlying reasons for such conformity. Chen [2] refers to conformity as herd behavior. He claims that when people use the product evaluations of others to indicate product quality on the Internet, online herd behavior occurs. He presents four studies examining herd behavior of online book purchasing. In sum, there are many studies addressing conformity in use of Internet [10], online purchasing [2], financial market [3,11], etc. This paper attempts to study college students’ classroom behavior from conformity point of view. 2.2. Fuzzy logic and modeling Fuzzy logic is one of the most appropriate quantitative methods describing an observed system. The description and characterization is built on natural languages. Natural languages are undoubtedly the most convenient and effective expression means for human, since they undergo thousands of years of historical development. In 1965, professor Zadeh published his seminal work on fuzzy sets [12], in which he detailed the mathematics foundation of fuzzy set theory. In 1973, he proposed the theory of fuzzy logic [13]. Tron and Margaliot [5] utilize fuzzy modeling as a tool for assisting human observers in the difficult task of transforming their observations into mathematical models, which advocates a new application of fuzzy modeling. They demonstrate unique advantages of fuzzy modeling using an example of territorial behavior of fish. Chrysafiadi and Virvou [14] constitute a literature review on student modeling for the last decade. They review the prevailing student modeling approaches in designing computer-based educational software and tutoring systems. They notice that there is an increase in the adoption of fuzzy techniques and Bayesian networks in order to deal the uncertainty of student modeling. Compared with aforementioned research work [2,5,10], this paper presents a fuzzy logic approach for modeling students’ individual conformity behavior in college classroom. 3. A fuzzy logic approach for modeling participants’ behaviors in classroom The motivation of this paper is that an interesting conformity phenomenon is first discovered in college classroom by natural language. Therefore, a fuzzy logic system is constructed to describe participants’ classroom behaviors from conformity point of view, as well as to study the factors that influence students’ conformity behavior. 3.1. Phenomenon description and analysis An interesting phenomenon is discovered in a same course for two classes: (a) a large class containing 120 students, and (b) a small class containing 90 students. “These students are all sophomores. The academic performance of each class is almost at the same level. But the teaching effectiveness differs greatly. The large class is arranged in a big classroom
6595
Fig. 1. The fuzzy logic model of determining GB.
with 180 seats. During a lesson, the students are seated dispersedly. The classroom is very noisy, and the class discipline is bad. The status of students’ participating in the lesson makes the teacher’s mood very bad. The teaching effectiveness is poor. However, the small class is arranged in a small classroom with 100 seats. During a lesson, the students are seated concentratedly. The class discipline is good. Most students listen to the teacher and take notes carefully. The teacher is in well mood. Therefore, the teaching effectiveness is good.” Several factors cause the difference in teaching effectiveness. Firstly, a large classroom is really not suitable for a lesson. In a large classroom, if the students are seated dispersedly, it is not easy for the teacher to observe every student. Therefore, the teacher could not tune the teaching according to students’ reflection. While in a small classroom, it is relatively easy for the teacher to observe the whole class. Secondly, if a classroom contains so many students, the class tends to be noisy. It is not easy for the teacher to maintain class discipline. Therefore, an individual student is more vulnerable to be influenced by other students. Thirdly, in a class with poor discipline, the teacher’s mood is affected as well. The teacher feels not respected by students. The poor mood will naturally affect the teacher’s thinking and disturb his teaching process. 3.2. The constructed fuzzy logic system The above phenomenon can be identified as a phenomenon and behavior in social psychology, i.e., conformity behavior. This paper constructs a fuzzy logic system from the following two aspects: the environment, and the participants’ behaviors. The environment includes two factors: (a) Occupancy ratio (OR): the ratio of class size to classroom capacity, OR ∈ [0,1]. OR has three fuzzy variables: high, medium, and low. The corresponding membership functions are: f1 , f2 , and f3 , respectively. (b) Classroom organization (CO): the observed average organization level of the whole class, CO ∈ [0,1]. CO also has three fuzzy variables: good, medium, and bad. The corresponding membership functions are: f4 , f5 , and f6 , respectively. The participants’ behaviors include students’ group behavior (GB), the teacher’s teaching behavior (TB), and students’ individual behavior (IB). (a) GB: it represents the earnestness extent to which all students listen to the teacher in class as a whole, GB ∈ [0,10]. (b) TB: it is a comprehensive index, which includes the extent to which the teacher can concentrate on teaching, and the popular degree of teacher’s teaching, TB ∈ [0,10]. (c) IB: it represents the earnestness extent to which an individual student listen to the teacher in class, IB ∈ [0,10]. GB has three fuzzy variables: well, general, and bad. The corresponding membership functions are: f7 , f8 , and f9 , respectively. The factors which influence GB include CO and OR, as shown in Fig. 1. The fuzzy logic rules determining GB are listed as follows.
G. Wang et al. / Optik 125 (2014) 6594–6598
Fig. 2. The fuzzy logic model of determining TB.
membership degree (or frequency)
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1
trapmf(x, 6.1, 8.9, 10, 10)
0.8 0.6 0.4 0.2 0 5
Fig. 3. The fuzzy logic model of determining IB.
R1: If CO is good, and OR is high, then GB is well. R2: If CO is good, and OR is medium, then GB is well. R3: If CO is good, and OR is low, then GB is general. R4: If CO is medium, and OR is high, then GB is general. R5: If CO is medium, and OR is medium, then GB is general. R6: If CO is medium, and OR is low, then GB is bad. R7: If CO is bad, THEN GB is bad. TB has three fuzzy variables: well, general, and bad. The corresponding membership functions are: f10 , f11 , and f12 , respectively. The factors which influence TB include GB and OR, as shown in Fig. 2. The fuzzy logic rules determining TB are listed as follows. R8: If GB is well, and OR is high, then TB is well. R9: If GB is well, and OR is medium, then TB is general. R10: If GB is well, and OR is low, then TB is general. R11: If GB is general, and OR is high, then TB is well. R12: If GB is general, and OR is medium, then TB is general. R13: If GB is general, and OR is low, then TB is bad. R14: If GB is bad, and OR is high, then TB is general. R15: If GB is bad, and OR is medium, then TB is bad. R16: If GB is bad, and OR is low, then TB is bad. IB has three fuzzy variables: well, general, and bad. The corresponding membership functions are: f13 , f14 , and f15 , respectively. The factors which influence IB include GB and TB, as shown in Fig. 3. The fuzzy logic rules determining IB are listed as follows. R17: If GB is well, and TB is well, then IB is well. R18: If GB is well, and TB is general, then IB is well. R19: If GB is well, and TB is bad, then IB is general. R20: If GB is general, and TB is well, then IB is general. R21: If GB is general, and TB is general, then IB is general. R22: If GB is general, and TB is bad, then IB is bad. R23: If GB is bad, THEN IB is bad.
6 7 8 9 x (or teacher's teaching behavior) Fig. 4. The membership function of well TB.
selected. Since U is continuous, it is divided into 100 equivalent subintervals. The frequency of each subinterval is counted and plotted in Fig. 4. The membership function, trapmf(x, 6.1, 8.9, 10, 10), is also plotted on the same figure. It is found that this function is a good estimation of the membership degree of well TB. Accordingly, all the aforementioned membership functions are determined as follows. OR: the membership functions of high, medium, and low OR are f1 = sigmf(x, 35, 0.68), f2 = gaussmf(x, 0.11, 0.57), and f3 = zmf(x, 0.25, 0.65), respectively. CO: the membership functions of good, medium, and bad CO are f4 = sigmf(x, 37, 0.76), f5 = trapmf(x, 0.3, 0.42, 0.7, 0.82), and f6 = zmf(x, 0.23, 0.51), respectively. GB: the membership functions of well, general, and bad GB are f7 = trapmf(x, 6.3, 9.5, 10, 10), f8 = gauss2mf(x, 0.8, 5.2, 1.1, 6.5), and f9 = trapmf(x, 0, 0, 3.2, 5.5), respectively. TB: the membership functions of well, general, and bad TB are f10 = trapmf(x, 6.1, 8.9, 10, 10), f11 = gauss2mf(x, 0.7, 5.0, 0.75, 6.6), and f12 = trapmf(x, 0, 0, 3.1, 5.2), respectively. IB: the membership functions of well, general, and bad IB are f13 = trapmf(x, 5.7, 9.2, 10, 10), f14 = gauss2mf(x, 0.75, 4.8, 0.78, 6.8), and f15 = trapmf(x, 0, 0, 2.9, 4.9), respectively. The sigmoidally shaped membership function sigmf(x, [a c]) is defined as: f (x, a, c) =
1 1 + e−a(x−c)
.
(1)
The Z-shaped membership function zmf(x, [a b]), (a ≤ b), is defined as:
f (x, a, b) =
⎧ 1 x≤a ⎪ ⎪ ⎪ 1 − 2[(x − a)/(b − a)]2 a ≤ x ≤ (a + b)/2 ⎨ 2 ⎪ (a + b)/2 ≤ x ≤ b 1 − 2[(b − x)/(b − a)] ⎪ ⎪ ⎩
(2)
The trapezoidal membership function trapmf(x, [a b c d]), (a ≤ b ≤ c ≤ d) is defined as:
4. Simulation and analysis 4.1. Membership functions This paper adopts fuzzy statistics to estimate above 15 membership functions. For example, in order to estimate the membership function of well TB, a sampling survey is made. Given the domain, U = [0,10], 257 students are asked to write down the most appropriate interval that describe well TB. 100 answers are then randomly
.
x≥b
0
The above three fuzzy logic models (Figs. 1–3) and rules R1–R23 constitute the established fuzzy system.
10
f (x, a, b, c, d) =
⎧ 0 x≤a ⎪ ⎪ ⎪ x−a ⎪ a≤x≤b ⎪ ⎪ ⎪ ⎨ b−a 1
b≤x≤c .
0
x≥d
⎪ ⎪ d−x ⎪ ⎪ c≤x≤d ⎪ ⎪ d−c ⎪ ⎩
(3)
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10 students' group behavior
students' individual behavior
The teacher's teaching behavior is fixed at 6.6. 8 6 4
10
2 0 0
0.2
0.4 0.6 0.8 students' group behavior
8 6 4 2 1
0.8
0.6
0.2 occupancy ratio
1
0.6
0.4
0 0
0.8
1
0.4 0.2 classroom organization
Fig. 6. Relation between GB and environment. Fig. 5. Relation between IB and GB.
10
as: 2
f (x, , c) = e−(((x−c)
)/2 2 )
.
(4)
The two-sided Gaussian membership function gauss 2mf = f(x, 1 , c1 , 2 , c2 ) is a combination of two Gaussian membership functions: f(x, 1 , c1 ), and f(x, 2 , c2 ). 4.2. Simulation results of aforementioned two classes For the aforementioned large class, the class size is 120 (students), the classroom capacity is 180 (seats). Therefore, OR is 0.67. The observed CO value is 0.75. The simulation results of the large class are: GB is 6.7; TB is 6.62; and IB is 5.97. For the aforementioned small class, the class size is 90 (students), the classroom capacity is 100 (seats). Therefore, OR is 0.9. The observed CO value is 0.85. The simulation results of the small class are: GB is 8.77; TB is 8.48; and IB is 7.92. From the above results, it is found that the IB value in the small class is higher than that one in the large class, which means that an individual student in the small class behaves better than that in the large class. The results are congruent with the linguistic description and analysis presented in Section 3.1. 4.3. Further discussion This section further examines the factors that influence IB. (1) IB and GB The relation between IB and GB is described by the curve shown in Fig. 5, where TB is fixed at a medium value, 6.6. From Fig. 5, it is found that IB is verifiably influenced by GB. If group behave well, each individual tends to behave well. If group behave badly, each individual tends to behave badly as well. In other words, each individual student tends to adhere to group norms. Similar conclusions can be found in literature [1,15]. (2) GB and environment The relation between GB and environment is described by the surface shown in Fig. 6. From Fig. 6, it is verified that both these two environmental factors (i.e., OR and CO) influence GB. In a classroom with high OR and good CO, students tend to behave well. While in a classroom with low OR and bad CO, students tend to behave badly. Moreover, the impact of CO on GB is greater than that of OR, since the surface in Fig. 6 slides down faster along the axis of CO. This finding suggests teachers pay more attention to CO. (3) IB and environment
students' individual behavior
The Gaussian membership function gaussmf(x, [ c]) is defined
8
occupancy ratio: classroom organization is fixed at 0.6. classroom organization: occupancy ratio is fixed at 0.57.
6
4
2 0
0.2 0.4 0.6 0.8 classroom organization or occupancy ratio
1
Fig. 7. The impact of CO and OR on IB, respectively.
Since GB is influenced by environment, IB is also influenced by those two environmental factors. The relation between IB and CO is described by the solid curve shown in Fig. 7, where OR is fixed at a medium value, 0.57. The relation between IB and OR is described by the dash curve shown, where CO is fixed at a medium value, 0.6. From these two curves, it is verified that IB is also influenced by environment. In a classroom environment with high OR or good CO, an individual student tends to behave well. Slightly different from existing researches [7,16,17], it is found that IB is not simply influenced by group size, as shown in Fig. 7. More exactly, it is influenced by OR, i.e., the ratio of class size to classroom capacity. The larger the size of OR, the better an individual student behaves. The underlying reason is that in a classroom with low OR, students tend to be seated dispersedly and form their own small community. In such a community, an individual student is more likely in whispered conversation with other students. Therefore, he always cannot concentrate on listening to the teacher. While in a classroom with high OR, it is relatively easy for the teacher to observe the whole class and tune the teaching according to students’ reflection. Therefore, an individual student is more likely concentrate on listening. 5. Conclusion This paper presents a fuzzy logic approach for quantitatively modeling participants’ classroom behaviors. The simulation results of the proposed fuzzy system and the behaviors observed in two classes are congruent. Several existing findings and new findings are verified through further simulation and analysis. This paper provides a significant attempt to deep understand participants’ classroom behavior from conformity point of view. It is expected to help teachers actively guide students’
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conformity behavior in classroom, introduce new teaching methods to stimulate students’ enthusiasm and initiative in learning, and thus improve quality of classroom teaching. Acknowledgment The work is partially supported by National Natural Science Foundation of China (Grant No. 61272399). References [1] S.E. Taylor, L.A. Peplau, D.O. Sears, Social Psychology, 12th ed., Pearson Education Hall, Upper Saddle River, New Jersey, USA, 2006. [2] Y.F. Chen, Herd behavior in purchasing books online, Comput. Hum. Behav. 24 (5) (2008) 1977–1992. [3] S. Wang, Z. Zhe, Y. Kang, H. Wang, X. Chen, An ontology for causal relationships between news and financial instruments, Expert Syst. Appl. 35 (3) (2008) 569–580. [4] V.V. Breer, Game-theoretic models of collective conformity behavior, Autom. Remote Control 73 (10) (2012) 1680–1692. [5] E. Tron, M. Margaliot, Mathematical modeling of observed natural behavior: a fuzzy logic approach, Fuzzy Sets Syst. 146 (3) (2004) 437–450.
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