Control Engineering Education Critical Success Factors Modeling via Fuzzy Cognitive Maps

Engin Yesil, Cihan Ozturk, M. Furkan Dodurka, Atakan Sahin Istanbul Technical University, Faculty of Electrical and Electronics Engineering,

Control and Automation Engineering Department, Maslak, TR-34469, Istanbul, Turkey {yesileng, ozturkci, dodurkam, sahinata}@itu.edu.tr

Abstract — This paper represents the practical use of Fuzzy Cognitive Maps (FCMs) in order to model the control engineering educational critical success factors. FCMs are fuzzy signed digraphs with feedbacks, and they can model the events, values, goals as a collection of concepts by forging a causal link between these concepts. In this study, the concepts of the FCM model is developed by the help of the academics, then the suggested FCMs of each academic is aggregated to build the final FCM to model the control engineering educational critical success factors. Afterwards the model is coded in Matlab to study four scenarios via different simulations. The results of the simulations show the effectiveness of FCMs to understand the success factors of educational organizations and programs.

Keywords- Fuzzy Cognitive Maps; Critical Success Factors; Control Engineering Education; ABET Engineering Criteria 2000.

I. INTRODUCTION Cognitive maps were presented for the first time by

Axelrod [1] in 1976 in order to express the binary cause-effect relationships of the elements of an environment. Fuzzy cognitive maps (FCM) are fuzzy signed digraphs with feedbacks, and they can model the events, values, goals as a collection of concepts by forging a causal link between these concepts [2]. High flexibility and fast adaptability can be stated as the main advantages of FCMs [3]. Generally, there are two types of FCMs named manual FCMs and automated FCMs. The only difference between them is their ways of creation. Manual FCMs are produced by experts manually and automated FCMs are produced by other information sources numerically. In many cases, even if there is one expert who knows the application domain well, manual FCM generating procedure should be followed.

As mentioned in [4], there is an enormous interest in FCMs and this interest on the part of researchers and industry is increasing, especially in the areas of control [5-7], business [8,9], medicine [10-13], robotics [14,15], environmental science [16-18] and information technology [19, 20]. In addition to above mentioned areas, FCMs have a remarkable number of applications on education. In the education domain, cognitive maps are usually called concept maps since cognitive maps include only concepts in them. The start point work is done by Novak which turns concept mapping out to be seen as a powerful tool for science education [21]. The use of concept maps for both course-level and program-level assessment in engineering education is proposed in [22]. A coherent and integrated framework serving various assessment functions for educational assessment purposes is presented in [23]. A review of concept mapping applications in engineering disciplines in

general and in Electrical and Computer Engineering is given in [24]. In [25], the utilization of critical success factors to FCM in order to develop the educational management model of the Thailand science-based technology school is introduced. Constructing augmented fuzzy cognitive map based for modeling critical success factors in learning management systems and tools is proposed in [26]. Also, in [27], an Engineering Education Assessment System is studied using FCMs.

Critical success factors (CSFs) were firstly studied by Rockhart [28] in 1979 and CSFs define key areas of performance that are essential for the organization to accomplish its mission. It was originally used in the discipline of data analysis and business analysis. This term is a critical factor or activity required for securing the success of a company or an organization.

In this study, fuzzy cognitive maps are used for control engineering education CSFs modeling. This proposed FCM model is used to illustrate the causal relations between the concepts that are affecting the program outcomes of control engineering. Since the educational program outcomes (EPOs) are directly related with the control engineering students’ success, this model would help the academics to understand the what-if scenarios of the program. Moreover, they can understand more precisely which critical success factor affects the other one in a positive or negative manner.

The outline of the paper is organized as follows: Section II introduces the formulation of FCMs briefly. Section III describes critical success factors in the context of education. Section IV represents fuzzy cognitive maps developing procedure and how group FCMs are aggregated to the final FCM. Section V presents the simulation examples, scenarios and the obtained results. Finally, Section VI provides the discussions, conclusions and the future work.

II. A BRIEF INTRODUCTION OF FUZZY COGNITIVE MAPS A fuzzy cognitive map F is a 4-tuple (N, W, C, f) [29]

where;

• N = {N1, N2, …, Nn} is the set of n concepts forming the nodes of a graph.

• W: (Ni, Nj) → wij is a function of N×N to K associating wij to a pair of concepts (Ni, Nj), with wij denoting a weight of directed edge from Ni to Nj, if i ≠ j and wij equal to zero if i = j. Thus W(N × N) = (wij ) ∈ Kn×n is a connection matrix.

978-1-4799-0086-2/13/$31.00 ©2013 IEEE

• C: Ni → Ci is a function that at each concept Ni associates the sequence of its activation degrees such as for t∈N, Ci(t)∈L given its activation degree at the moment t. C(0)∈Ln indicates the initial vector and specifies initial values of all concept nodes and C(t)∈Ln is a state vector at certain iteration t.

• f: R → L is a transformation function, which includes recurring relationship on t≥0 between C(t + 1) and C(t).

The sign of wij expresses whether the relation between the two concepts is direct or inverse. The direction of causality expresses whether the concept Ci causes the concept Cj or vice versa. Thus, there are three types of weights [30]:

• Wij > 0, indicates positive causality,

• Wij < 0, indicates negative causality,

• Wij = 0, indicates no relation.

The calculation rule that was initially introduced to calculate the value of each concept is based only on the influence of the interconnected concepts [2], [5]

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=+ ∑≠=

n

ji1i

ijij w)t(Cf)1t(C (1)

where n is the number of concepts, Cj(t+1) is the value of concept Cj at time step t+1, Ci(t) is the value of concept Ci at time step t, and wij is the weight of the causal interconnection from concept ith toward concept jth. A simple FCM with 5 concepts and 7 weights are given in Fig. 1.

Fig. 1. A simple FCM.

In general, there are two kinds of threshold functions used in the FCM framework. The first one is the unipolar sigmoid function, where λ > 0 decides the steepness of the continuous function f and transforms the content of the function in the interval [0,1].

xe11)x(f λ−+

= (2)

The other threshold function, hyperbolic tangent, that has been used and which transforms the content of the function is

in the interval [-1,1],

xx

xx

eeee)xtanh()x(f λ−λ

λ−λ

+−=λ= (3)

where λ is a parameter used to determine proper shape of the function. Both functions use λ as a constant for function slope.

III. EDUCATIONAL CRITICAL SUCCESS FACTORS Educational critical success factors can be thought as the

success factors of the educational organization. This organization can be a university or more specifically a faculty or a program (degree). In this work, as the case study, the Control Engineering Program (CEP) in Istanbul Technical University is studied and CEP is located in the Faculty of Electrical and Electronic Engineering. Besides, Control Engineering has been a department since 2008. The Department of Control Engineering in bachelor degree had been fully accredited by Accreditation Board for Engineering and Technology, Inc. (ABET) in 2010.

ABET which introduces itself as the worldwide leader in assuring quality and stimulating innovation in applied science, computing, engineering, and engineering technology education [31] was founded in 1932 as the Engineers' Council for Professional Development (ECPD) and evaluated its first engineering degree programs in 1936. ABET's international activities began in 1979 when ECPD signed its first Mutual Recognition Agreement with the Canadian Engineering Accreditation Board. In 1997, ABET presented Engineering Criteria 2000 (EC2000) [32], thought at the time a revolutionary approach to accreditation criteria. EC2000 focused on what is learned rather than what is taught. At its base was the call for a continuous improvement process informed by the specific mission and goals of individual institutions and programs [33].

ABET has accredited programs in 24 different countries including Turkey. There are 5 universities which are Bilkent University, Bogazici University, Eastern Mediterranean University, Istanbul Technical University and Middle East Technical University accredited with 47 programs in total. Istanbul Technical University with 23 programs including Control Engineering is leading the others. Moreover, Istanbul Technical University is the world’s leading university with the most number of fully accredited engineering programs.

Before going in details how the educational critical success factors are decided, it should be underlined that the success of the students is thought to be the reflection of the success of the organization, which is in this study Control Engineering Department, and the related program. In other words, if the critical success factors of Control Engineering Program are correctly settled and the actions are taken to improve them, this will lead to improve the success of the graduates without concentrating the critical success factors of the students themselves.

While the critical success factors of Control Engineering Program have been worked on, there are external and internal resources that have been used. As external resources, ABET Engineering Criteria (EC 2000) [32] and ABET Engineering

Technology Criteria [34] are taken into consideration at most. As internal resources, the ITU Control Engineering Program ABET Self-Study Report [35], the annual reports of the program and the feedback surveys of the students, are used as well.

Firstly, the stakeholders of the educational success have to be clarified. It can be said that there are 3 stakeholders of the educational success named the students, the academicians and the administrators of the university.

The students of all universities are selected with a Student Selection and Placement System Examination in Turkey. The Control Engineering Program accepts students with relatively high points on that exam. Since enrolled student profile has been changed year by year, student profile should be seen as one of the critical success factors. Besides, technical knowledge, skills and behavioral skills of the students are the critical success factors as well.

The academicians have non-negligible effect on the program success. It can be said that the profile of the academicians in ITU Control Engineering Program is relatively high. The academicians should create a competitive environment in lectures that can boost the program success. Hence, excessive demand of academicians from the students is a significant risk on the program success.

The administrators of the universities are responsible for the facilities, resources and the campus life. Better environment in a university campus would surely be a keystone of the success of the university and the programs. Besides, the program curriculums which are prepared and organized by the administrators are thought to be one of the most important educational critical success factors.

IV. DEVELOPING FUZZY COGNITIVE MAP Development of Fuzzy Cognitive Maps models can be

carried out mainly with two different approaches; expert based or automated learning approaches. Expert-based approaches require human knowledge whereas automated learning approaches need values of concepts at each iteration namely historical data. Developing FCM with expert based approach can be resulted in erroneous FCM because it completely relies on subjective human knowledge. Moreover, as the number of concepts grows the problem of developing FCM becomes too problematical for a human to solve by him- or herself. In spite of deficiencies of expert based methods, FCM models were mostly developed with them. This is mainly why automated learning approaches were revealed recently [36] and being not possible to obtain historical data all time. In case of obtaining data for the concepts, a learning method from literature [37-43] can be used. In expert based approaches, because of the reliability of the FCM model, a group of experts can develop FCM. In this case, every expert first designs his/her own FCM model, and then these models are aggregated into a single FCM model.

As stated by Kosko and, Khan [2, 44] expert based development FCM involves three main steps. In the first step, important concepts are defined from all available concepts. Then, in the second step, relationships between concepts are identified with their directions resulting in a graph with nodes

and directed edges. In the development of FCM the most challenging task is the third step. In this step, the strength of relationship with nodes (weights) is determined. As stated by Kosko [2] weights can take values from the interval of [-1, 1]. Higher positive (promoting) or negative (inhibiting) weights represent stronger relationships whereas 0 means no relationship. Because of the experts’ capability of assigning values to each weight, and the difficulty of specifying precise weight values, a linguistic approach is proposed by Kosko and Khan [2, 44]. In these approaches the sign of each relationship is determined firstly, and each relationship is described by linguistic terms, e.g. weak, medium, and strong; then, finally, the linguistic terms are transformed to numerical values.

One of the powerful properties of the FCMs is the ability of aggregating several experts’ knowledge easily. By combining several experts’ FCM models, the final FCM models become more reliable since then the model doesn’t only rely on a single expert. In the design phase, sometimes, all of the experts may not decide to use all of the concepts. Therefore, the sizes of the experts’ weight matrix might be different. In such situations, the experts’ maps are firstly equalized to same size by adding missing concepts coming from other experts’ maps. Secondly, zeros should be added to the weight matrices for the extra rows and columns. So, if the total number of separate concepts is , then the size of combined weight matrices will be [44]. For combining multiple FCMs into single FCM, two main well-known procedures are proposed in literature. In the first procedure it is assumed that all credibility of experts is the same. So the simplest method is to calculate average of each weight across all experts, given in the following equation [45]: 1

(4)

where k is the total number of the experts and is the FCM model of ith expert’s. In the second procedure, experts’ credibility can be different; therefore, the expert’s higher credibility leads to a higher influence in the combined FCM as proposed in [46-48]. The formula in (4) can be transformed to provide credibility of ith experts’ weight as follows [36]: 1∑ (5)

TABLE I. CSFS OF CONTROL ENGINEERING PROGRAM SUCSESS

C1: Facilities / Resources of the university C2: Program Curriculum C3: Knowledge of mathematics, science, and engineering

principles C4: Experimental skills C5: Designing skills C6: Student profile C7: Academic staff profile C8: Analytical thinking C9: Ethical, professional responsibility C10: Working in multi-disciplinary environment C11: Competition between the students C12: Excessive stress C13: Academics excessive demand C14: Communication skills C15: Control Engineering program success

Fig. 2. Concepts and the relations of the final FCM model.

For this study, a list of possible concepts is prepared using the ITU Control Engineering Program ABET Self-Study Report [35], and the previous research studies from the literature. Then, this list is given to 8 academics from ITU Control Engineering Department, and they are asked to choose the most important concepts that affect the Control Engineering program success.

As a result of this first stage; the experts, in this case the academics, agreed on 15 concepts. Then a survey that consists

of questions about the relations between the concepts is prepared for the academics who attend this study. The list of all concepts is tabulated in Table 1.

Using the survey results, the FCM of each academic is developed. After that, these FCM models are aggregated into a single FCM model using (4) since it is a difficult situation in this study to grade the experts. The weight matrix of the final FCM model is obtained as follows:

0000000.5800.300.4900000

0.1900.250.060.2600.890.3100.540.4400.0900

0.030.9700.820.640.840.860.580.350.650.040.140.2200

0.920.840.2100.890.910.970.240.230.8100.460.340.050

0.621.000.770.7900.890.950.670.390.780.270.130.350.420

000000000000000

000000000000000

01.001.000.570.450.760.42000.2900.170.2500

00.530.1100.530.410.940.1000.600.740.960.530.310

0.880.790.470.550.830.850.790.490.4400.4300.290.540

0.020.4100.110.170.800.180.130.550.1000.430.7300

00.52000.350.810.850.050.190.140.9700.750.220

000000000000000

0.140.5400.0900.970.680.0500.640.560.210.3900

0.780.880.850.780.960.850.580.740.260.690.570.370.220.470

(6)

V. SIMULATION STUDIES The final FCM model of CSFs of Control Engineering

Program success (6) is used for various simulations to realize different possible scenarios. For the simulations, codes are written in Matlab and in the codes the transformation function in (2) is implemented since the values of the nodes may fall within the range [0, 1] and λ is chosen 0.425. In order to remove the spurious influence of inactive concepts (with Ci = 0) on other concepts, and to avoid the conflicts that emerge in cases where the initial values of concepts are 0 or 0.5, a modified FCM reasoning formalism is preferred. For this study, the following calculation rule is used [12]:

1 2 1 ∑ 2 1 . (7)

By this implementation change, the problem with the initial zero values of concepts which through the threshold function, at second iteration step, take the value of 0.5 is solved.

The input nodes that influence but are not influenced by other nodes of FCM are concept 6 (C6), concept 7 (C7) and concept 13 (C13) that are student profile, academic staff profile and academics excessive demand, respectively. The concept (C15) Control Engineering program success will be directly affected by the initial values of input concepts. The other 11 concepts will affect each other and naturally the output concept (C15).

In this study, four different scenarios are simulated. Since the input concepts are more operational on the output concept change, six different simulations based on input concept changes are studied. In the first scenario, each input concept is set to one in sequence and three simulation results are obtained in order to discover the importance of each input concept on CEP success. In the second scenario, all input concepts are set to one at the same time, which means high student profile, high academic staff profile and high academics excessive demand. As the third scenarios, the initial concept values of high student and academic staff profile concepts set to one, and academics excessive demand concept initial value to zero see the effect of C13 on CEP success. Then, finally, the initial concept values of the FCM model is randomly defined to study change of each concept by time.

Fig. 3. Results of the simulation 1.

Scenario – 1: In this scenario, three simulations are obtained by assuming

that there is only one high input concept effective on CEP success where the intermediary concepts are set to zero. The result of the first simulation is given in Fig. 3, where it is seen that if only the student profile is high C15 control engineering program success will be very low. This initial condition will not lead the output of the other concept not even more than 0.5, which means average. Table 2 shows the initial and the final values of each studied concept.

In the second simulation, the academic staff profile is kept high and the effect is inspected. The initial and the final values of the concepts for this simulation are tabulated in Table 3. Also, in Fig. 4 the change of the concepts by iteration is given.

Fig. 4. Results of the simulation 2.

As the third simulation, the effect of the academics excessive demand is studied. When there is a high excessive demand there is a very little improvement in the CEP success (C15). This result can be seen from Fig. 5 and Table 4.

Fig. 5. Results of the simulation 3.

As a result of the first scenario, it can be concluded that student profile (C6), academic staff profile (C7) and academics excessive demand (13) has positive effect on control engineering program success. Within these three input concepts it seems that the academic staff profile has the highest importance.

Scenario – 2: In the second scenario, it is assumed that all input concepts

has high value, which is one, and the other concepts are set to zero, which means very low. The simulation result of this scenario is given in Fig. 6 and the initial and the final concept values are given in Table 5. The results show that when the student and the academic staff profile are high and there is an excessive demand from the academics then the success of CEP (C15) is very high. Also, under these conditions, the values of the other concepts will be more than around 0.8 which means also high. Similarly, concept 1 (C1), which is “Facilities / Resources of the university” will increase but not as high as the other concepts and its final value will stay around 0.65.

Fig. 6. Results of the simulation 4.

Scenario – 3: In the third scenario, the effect of all of the input concepts

is considered. Sometimes, there is a belief of many academics, who think that the students only learn if they are highly demanded. In this scenario, the excessive demand (C13) is set to zero, which means a balanced demand is presupposed. Besides, the other two input concepts are kept high. Therefore, the aim of this scenario is to see the effect of academics excessive demand on the success of CEP. The initial and the final values of fifteen concepts are tabulated in Table 6, and the simulation result is given in Fig. 7. It can be determined that the effect of C13 is very low according to the FCM model developed by the experts.

Fig. 7. Results of the simulation 5.

TABLE II. INITIAL AND FINAL VALUES OF THE CONCEPTS FOR SIMULATION 1 (SCENARIO I)

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15

Initial Values 0 0 0 0 0 1.00 0 0 0 0 0 0 0 0 0

Final State Values 0.38 0.28 0.25 0.26 0.21 1.00 0 0.27 0.34 0.26 0.42 0.31 0 0.45 0.20

TABLE III. INITIAL AND FINAL VALUES OF THE CONCEPTS FOR SIMULATION 2 (SCENARIO I)

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15

Initial Values 0 0 0 0 0 0 1.00 0 0 0 0 0 0 0 0

Final State Values 0.57 0.56 0.44 0.46 0.42 0 1.00 0.35 0.55 0.45 0.34 0.37 0 0.45 0.37

TABLE IV. INITIAL AND FINAL VALUES OF THE CONCEPTS FOR SIMULATION 3 (SCENARIO I)

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15

Initial Values 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 0

Final State Values 0.35 0.25 0.11 0.12 0.08 0 0 0.19 0.2 0.08 0.37 0.47 1.00 0.20 0.06

TABLE V. INITIAL AND FINAL VALUES OF THE CONCEPTS FOR SIMULATION 4 (SCENARIO II)

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15

Initial Values 0 0 0 0 0 1.00 1.00 0 0 0 0 0 1.00 0 0

Final State Values 0.65 0.78 0.92 0.91 0.95 1.00 1.00 0.90 0.80 0.93 0.78 0.87 1.00 0.81 0.95

TABLE VI. INITIAL AND FINAL VALUES OF THE CONCEPTS FOR SIMULATION 5 (SCENARIO III)

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15

Initial Values 0 0 0 0 0 1.00 1.00 0 0 0 0 0 0 0 0

Final State Values 0.65 0.75 0.89 0.88 0.92 1.00 1.00 0.81 0.80 0.92 0.63 0.73 0 0.80 0.94

TABLE VII. INITIAL AND FINAL VALUES OF THE CONCEPTS FOR SIMULATION 6 (SCENARIO IV)

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15

Initial Values 0.24 0.87 0.53 0.91 0.97 0.59 0.12 0.93 0.60 0.88 0.42 0.61 0.07 0.92 0.64

Final State Values 0.38 0.27 0.18 0.19 0.14 0.59 0.12 0.20 0.29 0.17 0.35 0.25 0.07 0.34 0.12

Scenario – 4: As the last scenario, the initial values of each concept are

set to a value in interval [0, 1]. As seen in Table 7, input concepts C6, C7 and C13 have initial values as 0.59, 0.12 and 0.07, respectively. This can be stated as the student profile is a bit more than average, a bad academic profile and no excessive demand. Under these initial conditions, the result illustrated in Fig. 8 is obtained. In it is seen, C15 in the beginning is high but because of the low academic profile by iteration success of CEP decreases to 0.12 from 0.64. In addition, all the other intermediate concept values have drastic decreases except C1 since it is directly related with the academic profile. Here, C1value slightly increases but can only reach to 0.38, which is less than average.

Fig. 8. Results of the simulation 6.

VI. CONCLUSIONS In this study, the practical use of Fuzzy Cognitive Maps

(FCMs) in order to model the control engineering educational critical success factors is presented. For this purpose, eight academics from Istanbul Technical University Control and Automation Engineering Department shared their ideas to build FCM. Then these eight FCMs are aggregated to a final FCM, which represents the synthesis of all the academics. Matlab environment is used for developing FCM, and the necessary codes are generated for simulations to study four different scenarios. The results show under which conditions the concepts effects the success of control engineering education in Istanbul Technical University. Also, the developed FCM is used to understand the relational effects represented with fuzzy weights between the concepts and how to change these weights for improving the educational program outcomes. As future work, it is planned to increase the number of academics participated to this research and apply different FCM aggregation methods proposed in literature to obtain possible better models.

VII. ACKNOWLEDGMENT The authors thank to all academicians of Istanbul Technical

University Control and Automation Engineering Department for their support on this work.

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