Using Fuzzy Cognitive Maps as a Decision Support System for Political Decisions: The Case of Turkey’s Integration into the European Union Athanasios K. Tsadiras1 and Ilias Kouskouvelis2 1 Department of Informatics, Technological Educational Institute of Thessaloniki, P.O.BOX 14561, 54101 Thessaloniki, Greece
[email protected] 2 Department of International & European, Economic & Political Studies, University of Macedonia, Egnatias 156, P.O.Box 1591Thessaloniki 54006, Greece
[email protected]
Abstract. In this paper we use Fuzzy Cognitive Maps (FCMs), a wellestablished Artificial Intelligence technique that incorporates ideas from Artificial Neural Networks and Fuzzy Logic, to create a dynamic model of Turkey’s course towards its integration into the European Union, after the decision of December 18, 2004, according to which in October 3, 2005, Turkey will start negotiating its access to the European Union. FCMs create models as collections of concepts and the various causal relations that exist between these concepts. The decision capabilities of the FCM structure are examined and presented using a model developed based on the beliefs of a domain expert in the political situation in Turkey & European Union. The model is examined both statically using graph theory techniques and dynamically through simulations. Scenarios are introduced and predictions are made by viewing dynamically the consequences of the corresponding actions.
1 Introduction to Fuzzy Cognitive Maps Decision Support Systems are defined as “interactive computer-based systems, which help decision makers utilize data and models to solve unstructured problems” [1]. Unstructured problems are defined as “fuzzy, complex problems for which there are no cut-and-dried solutions” [2]. In International Relations theory, negotiations and crisis management [3] are consider unstructured or semistructured areas where Decision Support Systems can assist by providing new potentials to the decision making process. Cognitive Map (CM) models were introduced by Axelrod in the late 1970s and were widely used for Political Analysis and Decision Making in International Relations [4]. The structural and decision potentials of such models were studied and the explanation and prediction capabilities were identified [4], [5]. The introduction P. Bozanis and E.N. Houstis (Eds.): PCI 2005, LNCS 3746, pp. 371 – 381, 2005. © Springer-Verlag Berlin Heidelberg 2005
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of Fuzzy Logic gave new representing capabilities to CMs and led to the development of Fuzzy Cognitive Maps (FCM) by Kosko in the late 1980s [6], [7]. FCMs models are created as collections of concepts and the various causal relationships that exist between these concepts. The concepts are represented by nodes and the causal relationships by directed arcs between the nodes. Each arc is accompanied by a weight that defines the degree of the causal relation between the two nodes. The sign of the weight determines the positive or negative causal relation between the two concepts-nodes. Certainty Neuron Fuzzy Cognitive Maps (CNFCMs) were introduced in 1997 [8], giving additional fuzzification to the FCM structure. CNFCMs allow the activation of each concept’s activation to be a number from the whole interval [-1,1] (or, as in our case, in the interval [0,1]) allowing the representation of both the sign of the activation and its degree, while on the contrary, FCM allows each concept to have a binary value (-1 or 1), representing a negative or a positive activation and not the degree of the activation. Furthermore in CNFCM, the aggregation of the influences that each concept receives from other concepts is handled by function f M () that was used in MYCIN Expert System [9], [10] for certainty factors’ handling. The dynamical behavior and the characteristics of this function are studied in [11]. The artificial neurons that use this function as their threshold function are defined as Certainty Neurons [12].
2 Development of FCM Model for the Case of Turkey’s Integration into European Union The reliability of an FCM model depends on whether its construction method follows rules that ensure its reliability. Since the model is created by the personal opinions and points of view of the expert(s) on the specific topic, the reliability of the model is heavily depended on the level of expertise of the domain expert(s). There are two main methods for the construction of FCMs : a) The Documentary Coding method [13], which involves the systematic encoding of documents that present the assertions of a specific person for the specific topic. b) The Questionnaire method [14], [15], which involves interviews and filling in of questionnaires by domain experts. In our case we used the second method, discussing, interviewing, analysing and also supplying with questionnaires a domain expert. The domain expert (a faculty member of the Department of International & European, Economic & Political Studies of the University of Macedonia) provided the international context, the actors and factors, the possible alternative scenarios, as well as the analysis of the findings. 2.1 The Case of Turkey’s Integration into the European Union: Important Actors/Concepts After the European Union’s European Council at Helsinki, the speed of Turkey’s course towards its integration into the Union has been increased. This course led to
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the decision of December 18, 2004, according to which in October 3, 2005, Turkey will start negotiating its access to the EU. This was not an easy decision to make and, yet, it is just the beginning of another road for Turkey and definitely not the end, as provided by the decision itself. The decision was not easy to make given the large variety of the EU’s member states interests, the opposition by large parts of their public opinion, the moderate progress of Turkey in fulfilling the EU’s enlargement criteria and the consistent support of Turkey from the United States government. And the decision to start negotiations is not the end, because the final integration of Turkey depends on a large variety of factors and actors. Through extensive interviews with the domain expert, the actors involved and considered important for the case, were identified as the following: The United States of America, The European Union, Greece, Cyprus, The European Union public opinion, The Turkish Government, The Turkish Armed Forces, The Turkish public opinion. It is a common place that the European future of Turkey depends not only on the willingness or the wishes of the various actors, but to a great extent from the fulfillment of the EU criteria. Fulfilling the criteria will be translated, perceived and advertised as a positive course for all those who more or less sincerely support Turkey’s European drive; the opposite will happen for those opposing Turkey’s entry into the Union. As indicators of a Turkish successful drive, the domain expert suggested five areas: Economy, Human Rights, The Turkish Armed Forces, The Greek – Turkish Relations, The Cyprus invasion problem. According the above, the list of the concepts that were identified as playing important role in our case and should appear in the FCM model, are the following: Concept 1. Concept 2. Concept 3. Concept 4. Concept 5. Concept 6. Concept 7. Concept 8. Concept 9.
USA Position European Union Position Greek Position Cypriot Position European Public Opinion Turkish Government Position Turkish Army Position Turkish Public Opinion Improvement of Turkish Economy
Concept 10. Improvement of Human Rights in Turkey Concept 11. Improvement of the Democratic Role of Turkish Army Concept 12. Improvement to Greek Turkish Relations Concept 13. Improvement to Cypriot Turkish Relations
2.2 Identification of Causal Relations Between Actors/Concepts A number of questionnaires were presented to the domain expert, in order to define the causal relationships that exist between the identified concepts of the case. Moreover, in these relationships, the degree to which a concept influences each other concept was extracted. The format of the questionnaire is given in figure 1. The expert had to fill in with + or – whether he believed that there is a positive or negative causal relationship between the concepts. The degree of these causal relationships was captured by allowing the expert to fill in the sign in one of the fields “Very Big”,
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What is influence of the USA position on this case, will influence and to what degree to the following The European Union Position European Public Opinion Position Turkish Army Position …… Numerical weights
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Fig. 1. Part of questionnaire concerning the case of Turkey’s Integration into European Union
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C7 Turkish Army Position
USA Position
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C4 Cypriot Position
C9 Improvement of Turkish Economy
C3 Greek Position
C10 Improvements of Human Rights in Turkey
C2 European Union Position
C11 Improvement of the Democratic Role of Turkish Army
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European Public Opinion
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C8 Turkish Public Opinion
Improvements to Greek-Turkish Relations
Fig. 2. FCM model for the case of Turkey’s Integration into European Union
“Big”, “Moderate”, “Small”, “Very Small”. These linguistic values could be transformed into numerical weights by assigning weights from the interval [0,1] according to the way that is shown in figure 1. To justify his opinion, additional questionnaires were presented to the expert. After studying the questionnaires and taking the weights identified by expert, the model presented in figure 2 was developed. In figure 2, only the signs of the arcscausal relationships are shown. The weights of the arcs are given in Appendix A.
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3 Static Analysis The static analysis of the model is based on studying the characteristics of the weighted directed graph that represent the model, using graph theory techniques. The first way to examine statically the model’s graph is by calculating its density [5]. The density d is defined as m d= n(n − 1) where m is the number of arcs in the model and n is the number of concepts of the model. Product n(n-1) is equal to the maximum number of arcs that a graph of n nodes can have. Density gives an indication of the complexity of the model. High density indicates increased complexity in the model and respectively to the problem that the model represents. Typical values of density are in the interval [0.05, 0.3]. The density of the graph in figure 2 is 69/(13x12) = 0.44 which is extremely high, and gives an indication of the great complexity of the problem that it represents. Graph Theory provides also the notion of node’s importance [4] that assists the static analysis of FCM models. Node’s importance (or cognitive/conceptual centrality as it is called by others [16], [17]) gives an indication of the importance that the node/concept have for the model, by measuring the degree to which the node is central to the graph. The importance of a node i is evaluated as imp(i ) = in(i ) + out (i )
where in(i) is the number of incoming arcs of node i and out(i) is the number of outcoming arcs of node i. According to this definition, the importance of the nodes of the FCM model for “Turkey’s Integration into European Union” is given in Table 1. Table 1. Importance of nodes In Out Imp
C1 8 5 13
C2 6 9 15
C3 6 7 13
C4 4 6 10
C5 1 4 5
C6 8 5 13
C7 6 3 9
C8 1 7 8
C9 4 6 10
C10 5 5 10
C11 10 2 12
C12 4 5 9
C13 6 5 11
It is found that the most central/important concepts were C2: “European Union Position”, C1: “USA Position”, C6: “Turkish Government Position” and C3: “Greek Position”.
4 Dynamical Behavior of CNFCM Model The model of the case of “Turkey’s Integration into European Union” was simulated using the CNFCM technique that was mentioned in section 1. Various scenarios can be imposed, after inserting to the CNFCM simulation program we developed, the 13 concepts of the model and the causal relationships that exist among these concepts. The “what-if” scenarios that were tested were chosen in order to show the decision making capabilities of the method presented to the paper. The scenarios are shown in Table 2.
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A.K. Tsadiras and I. Kouskouvelis Table 2. “What –if” Scenarios Scenario
#1 #2
#3 #4 #5
Description All concepts are free to interact. Activation of C1: “USA Position” is initialized to +0.7 and C6: “Turkish Government Position” is initialized to +0.9 All concepts are free to interact. Activation of C1: “USA Position” is initialized to -0.5 and C6: “Turkish Government Position” is initialized to -0.5 (moderate negative) Activation of C1: “USA Position” is set & kept to -0.4. All other concepts are free to interact. Activation of C1: “USA Position” is set & kept to -0.7. All other concepts are free to interact. Activation of C3: “Greek Position” is set & kept to -0.8. All other concepts are free to interact.
4.1 Scenarios with All Concepts to Be Free to Interact
In the first two scenarios (#1 & #2), all 13 concepts of the model are free to interact. In scenario #1, the initial activations of the 13 concepts are those imposed by the domain expert, representing the activations of the current state of our case. The activation of C1: “USA Position” is initialized to +0.7 and C6: “Turkish Government Position” is initialized to +0.9, representing the strong willingness of USA & Turkish Government in the course of Turkey’s Integration into European Union. The system is set free to evolve dynamically. The dynamical behavior of the model is shown in figure 3 where we can see that reaches equilibrium at a fixed point. The equilibrium point is interpreted in the following way: The strong willingness of the Turkish Government and the USA towards Turkey’s Integration into European Union, influences a lot all other concepts of the system, leading gradually to high
Fig. 3. Simulation of CNFCM Model of “the case of Turkey’s Integration into European Union”. Transition phase to equilibrium for scenario #1.
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positive activation of all concepts, meaning that the road of Turkey’s Integration into European Union is open, according the current political state. Applying other scenarios to the system, with the activation of either of C1: “USA Position” or C6: “Turkish Government Position” to be initialized to a positive value and the other to a negative value, show similar dynamical behaviour (equilibrium to high positive values for the concepts). This means that even if one of these concepts (“USA Position” or “Turkish Government Position”) changed to a negative position towards the Turkey’s integration into European Union, the other is strong enough, together with the other concepts of the model, to lead the first one from a negative position to a positive position towards Turkey’s integration into European Union and so finally Turkey’s integration will be successful. In scenario #2, both concepts “Turkish Government Position” and “USA Position” are initialized to a moderate negative value (-0.5 and -0.5). This means that they both do not believe in Turkey’s Integration into European Union. The dynamical behavior of the model for this scenario is shown in figure 4 where we can see that reaches equilibrium at a high negative fixed point position. This equilibrium point is interpreted in the following way: The negative position of the Turkish government and the USA towards Turkey’s integration into the European Union, influences crucially all other concepts of the system, leading gradually to high negative activation of all concepts. The position of all factors becomes negative. It can be concluded that in this case, Turkey did not manage to integrate into the EU.
Fig. 4. Simulation of CNFCM Model of “the case of Turkey’s integration into European Union”. Transition phase to equilibrium for scenario #2.
4.2 Scenarios with Selected Concepts to Be Set Steady to a Level
In the following two scenarios, concept “USA position” will be set steady to a level and will not change even if affected by other concepts (this is the case where USA government is strongly determined to follow its own position and not be influenced
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Fig. 5. Simulation of CNFCM Model of “the case of Turkey’s Integration into European Union”. Transition phase to equilibrium for scenario #3 (USA Position” is set to -0.4).
by other factors). In scenario #3 the USA position is moderate negative (-0.4). The initial activations of other concepts are those of scenario #1 (current political position according to our domain expert). The dynamical behavior of the model for this scenario is shown in figure 5 where we can see that reaches equilibrium at a high positive fixed point position. The equilibrium point of scenario #3 is interpreted in the following way: The moderate negative position USA towards Turkey’s integration into European Union, does not influence crucially other concepts of the system. This leads other concepts to carry on their transition towards to a positive activation level. It can be concluded that in this case Turkey manage to integrate into Europe. In scenario #4, the USA position is highly negative (-0.7, towards -0.4 of scenario #3). Having the initial activations of other concepts as those of scenario #1 (current political position according to our domain expert), the dynamical behavior of the model for this scenario is shown in figure 6. The system reaches equilibrium at a high negative fixed point position.Taking into consideration the transition phase of this case, as shown in figure 6, the equilibrium point of scenario #4 can interpreted in the following way: The highly negative position of the USA towards Turkey’s integration into the European Union, leads gradually the Turkish Army Position to change from positive to negative. This, together with the strong negative position of the USA, leads also to the change a) first of the position of Turkish Government, and then b) of the position of Turkish Public Opinion (both from positive to negative). After these, all concepts move towards high negative positions. It can be concluded that in this scenario Turkey does not manage to integrate into the European Union (even if its initial will is to integrate into European Union). In the final scenario, concept “Greek Position” will be set steady to a level and will not change even if affected by other concepts (this is the case where the Greek Government is strongly determined to follow its own position no matter the influences of other factors). So, in scenario #5 the Greek Government is strongly
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Fig. 6. Simulation of CNFCM Model of “the case of Turkey’s integration into the European Union”. Transition phase to equilibrium for scenario #4 (“USA Position” is set to -0.7).
Fig. 7. Simulation of CNFCM Model of “the case of Turkey’s Integration into European Union”. Transition phase to equilibrium for scenario #5 (“Greek Government Position” is set to -0.8).
negative towards Turkey’s integration into European Union (its activation set to -0.8), without exercising its veto power. The initial activations of other concepts are those of scenario #1 (current political position according to our domain expert). The dynamical behavior of the model for this scenario is shown in figure 7. It can be seen that system reaches equilibrium at a high positive fixed point position. Equilibrium point of scenario #5 can be interpreted in the following way: The initial positive position of the other concepts of the model, leads the system to a positive fixed point, even with Greek Government to have an opposite opinion. It can be concluded that Turkey manages to integrate into Europe, even with Greek Government to have a steady opposite position.
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5 Summary – Conclusions Using the FCM method, a model was created for the case of Turkey’s integration into European Union, based on the opinion of a domain expert. The model was first examined statically. The density of model’s graph was calculated and found extremely high, indicating the complexity of the case. The conceptual centralities of the concepts that exist in the model were also calculated and the most central, and consequently the most important concepts of the model were found. The model was then simulated in a computer and it was predicted that a) According to the current political state and if this situation is maintained (rebus sic standibus), Turkey can successfully move towards its integration into European Union. b) An occasional/initial change of position of the Turkish government (towards a negative position) can lead to the failure of the Turkey’s integration into the European Union, only if this is accompanied by a corresponding negative position of the USA on the matter. c) A determined moderate negative position of USA on Turkey’s integration into European Union cannot stop Turkey’s successful move towards its integration into European Union. d) On the contrary, a determined highly negative position of the USA on Turkey’s integration into the European Union can stop Turkey’s successful move towards its integration into the Union. e) A determined highly negative position of Greece on Turkey’s integration into European Union (without the exercise of the veto power and not accompanied with changes of other actors towards a negative position) cannot stop Turkey’s successful move towards its integration into the Union. Through the above static and dynamic studies of the FCM model, the CNFCM system was identified as an important and useful Decision Support System, since it is capable to provide support to decision makers, by making predictions on various scenarios that are imposed to the model that CNFCM creates. Conclusions on these scenarios are not drawn only from the final equilibrium that the system reaches, but also by studying the transition phase of the FCM system to equilibrium. The decision maker can test his decisions, by applying them to the CNFCM system and see the consequences to the other concepts of the model.
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Appendix A – Weights of Causal Relationships between Concepts Concepts / Weights C1: USA Position C2: European Union Position C3: Greek Position C4: Cypriot Position C5: European Public Opinion C6: Turkish Government Position C7: Turkish Army Position C8: Turkish Public Opinion C9: Improvement of Turkish Economy C10: Improvement of Human Rights in Turkey C11: Improvement of the Democratic Role of Turkish Army C12: Improvement to Greek - Turkish Relations C13: Improvement to Cypriot - Turkish Relations
C1
C2
C3
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C8
C9
C10 C11 C12 C13
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