**7. Steps in designing and implementing fuzzy cognitive mapping**

As with many other interview techniques, it is helpful to produce systematic guidelines describing the single steps of FCM before starting with the interviewing. These interview guidelines should function as a guidance/inspiration for how to conduct the interviews, and how to create FCMs over the case study areas. In this section we summarize the practical steps needed to design and conduct a FCM exercise. At first, how to draw a FCM must be explained to the interviewee(s)/stakeholder(s) using a cognitive map and its related FCM as an example. Once the interviewees understood the process of constructing a fuzzy cognitive map, then they are able to draw their own map of the issue under investigation following the steps below:

*Step 1: Identification of factors.* 

Based on the guidelines, each one of the interviewee is asked to identify the main factors which come to his/her mind when he/she is asked about the topic been investigated, e.g. the future environmental risks in the Black Sea, seen as a system where humans, marine animals and plants are all living together. After the identification of the main factors affecting the environmental topic under investigation, each stakeholder is asked to describe the existence and type of the causal relationships among these factors and then assesses the strength of these causal relationships using a predetermined scale, capable to describe any kind of relationship between two factors, positive and negative. Thus, a FCM from each interviewee is established presenting the main factors/variables and the relationships among them and illustrating the individual's perceptions about the topic under investigation.

*Step 2: Clustering of individual issues in more general concepts.* 

After the individual perceptions are elicited by interviews, a number of individual maps are produced. It is essential that the original concepts-variables, as described by lay people from interview, be clustered in more generic or more specific concepts, because most of them present the same meaning with a different word. Using experts' judgement, the importance of the original factors is discussed and they are then clustered. This can also be done through the construction of an ontological tree. This process of condensation enables aggregation of variables into high-level concepts, which then feed into the construction of the collective FCM.

#### *Step 3: Estimation of causal link strengths in collective FCMs*

The individual maps are then turned into a representative, collective map. To achieve this, all the suggested strength relations by lay people are transferred into linguistic variables using the aggregation method of SUM to obtain an overall linguistic weight. Following this, defuzzification turns linguistic weights into numerical weights in the range of [-1,1]. This condensed map is analyzed using the established indicators of out-degree, in-degree, centrality, density, hierarchy as well as the transmitter, receiver, and ordinary variables. Through this analysis the collective map is explained demonstrating its usefulness for identifying policies vis-à-vis individual FCMs.

#### *Step 4: FCM simulations*

Next a number of simulations are performed using the inference process given by equations (2) and (5). The calculated output of the FCM model shows how the system reacts under the assumptions given by the stakeholders or related users. Usually, the calculated output is different from the expected one, thus presenting a potential added value of Fuzzy Cognitive Map as a decision support tool.

## **8. An application of FCM in the Black Sea**

436 International Perspectives on Global Environmental Change

As with many other interview techniques, it is helpful to produce systematic guidelines describing the single steps of FCM before starting with the interviewing. These interview guidelines should function as a guidance/inspiration for how to conduct the interviews, and how to create FCMs over the case study areas. In this section we summarize the practical steps needed to design and conduct a FCM exercise. At first, how to draw a FCM must be explained to the interviewee(s)/stakeholder(s) using a cognitive map and its related FCM as an example. Once the interviewees understood the process of constructing a fuzzy cognitive map, then they are able to draw their own map of the issue under investigation

Based on the guidelines, each one of the interviewee is asked to identify the main factors which come to his/her mind when he/she is asked about the topic been investigated, e.g. the future environmental risks in the Black Sea, seen as a system where humans, marine animals and plants are all living together. After the identification of the main factors affecting the environmental topic under investigation, each stakeholder is asked to describe the existence and type of the causal relationships among these factors and then assesses the strength of these causal relationships using a predetermined scale, capable to describe any kind of relationship between two factors, positive and negative. Thus, a FCM from each interviewee is established presenting the main factors/variables and the relationships among them and illustrating the

After the individual perceptions are elicited by interviews, a number of individual maps are produced. It is essential that the original concepts-variables, as described by lay people from interview, be clustered in more generic or more specific concepts, because most of them present the same meaning with a different word. Using experts' judgement, the importance of the original factors is discussed and they are then clustered. This can also be done through the construction of an ontological tree. This process of condensation enables aggregation of variables into high-level concepts, which then feed into the construction of

The individual maps are then turned into a representative, collective map. To achieve this, all the suggested strength relations by lay people are transferred into linguistic variables using the aggregation method of SUM to obtain an overall linguistic weight. Following this, defuzzification turns linguistic weights into numerical weights in the range of [-1,1]. This condensed map is analyzed using the established indicators of out-degree, in-degree, centrality, density, hierarchy as well as the transmitter, receiver, and ordinary variables. Through this analysis the collective map is explained demonstrating its usefulness for

Next a number of simulations are performed using the inference process given by equations (2) and (5). The calculated output of the FCM model shows how the system reacts under the assumptions given by the stakeholders or related users. Usually, the calculated output is different from the expected one, thus presenting a potential added value of Fuzzy Cognitive

**7. Steps in designing and implementing fuzzy cognitive mapping** 

individual's perceptions about the topic under investigation. *Step 2: Clustering of individual issues in more general concepts.* 

*Step 3: Estimation of causal link strengths in collective FCMs* 

identifying policies vis-à-vis individual FCMs.

following the steps below: *Step 1: Identification of factors.* 

the collective FCM.

*Step 4: FCM simulations* 

Map as a decision support tool.

In order to illustrate in brief the methods described so far, we present a FCM exercise designed and implemented in the Northern Black Sea with Ukrainian stakeholders (for details see Kontogianni et al., forthcoming). In this application we were interested in investigating how the citizens perceive the future prospects and risks of the Black Sea marine environment; creating and analyzing their FCMs this can be achieved. We employed 29 in-depth lay people interviews (see Appendix A). Based on specific guidelines, each interviewee was asked to identify at first the main factors which come to his/her mind when he/she is asked about the Black Sea as a system where humans, marine animals and plants are all living together. During the interviews participants developed thus a FCM of the critical variables (important considerations) by drawing and circling the considerations they believe are important for environmental health of marine state ecosystem in the Black Sea area.

After the identification of the main factors affecting the environmental health of the marine ecosystem in the Black Sea, each stakeholder was asked to describe the existence and type of the causal relationships among these factors and then, the strength of the causal relationships-influences that may exist between these factors. This phase was implemented 13 grades scale, numbering from -6 to + 6, capable to describe any kind of relationship between two factors, positive and negative (see Table 1).

Thus, a FCM from each interviewee was established presenting the main factors/variables and the relationships among them illustrating the individual's perceptions about the future prospects and the risks about the ecological health of the marine environment in the Black Sea. Figure 3 illustrates the produced FCM defined by an individual/stakeholder from Ukraine for further assessment.

The initial number of important factors identified by stakeholders was 52. Since it was decided to produce a collective FCM providing detail for future risks-related issues we limited the number of factors having the same meaning through clustering. Using marine experts' judgement, the importance of the original 52 factors was discussed and then clustered in a total of 26 concepts (Table A in Appendix). The mean number of variables in the individual cognitive maps of the Black Sea ecosystem drawn by the 29 respondents was 7.86 ± 1.7, with 11± 6.513 connections on average between the variables that they defined. There were a total of 26 variables with 145 connections in the collective cognitive map obtained by clustering and augmented the 29 individual FCMs.

The process of condensation enabled aggregation of variables into high-level concepts, which then feed into the construction of a collective FCM for Ukrainian stakeholders. The collective FCM (consisting of 26 concepts and 145 relationships among concepts) is thus obtained (see Figure 4 developed in pajek software [http://vlado.fmf.unilj.si/pub/networks/pajek/]).

The collective FCM was then coded as adjacency matrix *E*=[e*ij*] and its structure was analyzed using the indices derived from graph theory (see section 4). Due to the complexity of the collective FCM graph (as the number of nodes and connections is very large) Figure 5 illustrates the most central variables with their weighted connections.

It is observed from graph indices calculations that the density of collective FCM is high and a mentioned complexity is present. A relatively high complexity is considered in the cases where the receiver variables are more than the transmitter variables, and in our case, the complexity is equal to 1.5 (complexity>1 means relatively high complexity). The most

Using Fuzzy Cognitive Mapping in Environmental

Decision Making and Management: A Methodological Primer and an Application 439

Fig. 4. The collective fuzzy cognitive map of Ukrainian stakeholders.


frequently mentioned (> 3 times) variables that were recurrent in the 29 fuzzy cognitive maps are: 'Coastal Development', 'Biodiversity', 'Tourism', and 'Municipal Solid Waste'.

Table 1. Interpretation of lay people's strength connections among concepts to crisp weights in the range [-1,1].

Fig. 3. The individual FCM defined by an individual/stakeholder from Ukraine.

frequently mentioned (> 3 times) variables that were recurrent in the 29 fuzzy cognitive maps are: 'Coastal Development', 'Biodiversity', 'Tourism', and 'Municipal Solid Waste'.

Sign and Strength of relationship

Table 1. Interpretation of lay people's strength connections among concepts to crisp weights

Fig. 3. The individual FCM defined by an individual/stakeholder from Ukraine.

Interpreted crisp

weight

(Linguistic weight)

*-6* Negatively very very strong -1 -5 Negatively very strong -0.9 -4 Negatively strong -0.75 -3 Negatively medium -0.5 -2 Negatively weak -0.3 -1 Negatively very weak -0.1 0 Zero 0 1 Positively very weak 0.1 2 Positively weak 0.3 3 Positively medium 0.5 4 Positively strong 0.75 5 Positively very strong 0.9 6 Positively very very strong 1

Strength connection by lay

people

in the range [-1,1].

Fig. 4. The collective fuzzy cognitive map of Ukrainian stakeholders.

Using Fuzzy Cognitive Mapping in Environmental

mental structure of our sample.

respondents' cognitive reality.

Decision Making and Management: A Methodological Primer and an Application 441

matrix *E* of the collective map. Simulations were generated using the five steps described previously implemented in Matlab R2008a environment for Windows. At first, we determine the steady state condition of the system's convergence before we consider any management options. We are doing this in order to be able to see the perceived tendency of the Black Sea ecosystem based on the collective cognitive map and test for its internal coherence. For this purpose, we run the generic FCM model with 50 different random initial states for all variables between 0 and 1 drawn from a uniform distribution. In all of these nomanagement simulations, the system reached a steady state after 25-30 iterations, where some of the produced final steady states for each initial condition were different. By excluding a chaotic behavior, we accordingly confirm a dynamically stable and coherent

Then, we consider a number of assumptions for the concepts and risk factors, which affect the future state of the environmental health of marine ecosystem in the Black Sea to analyze the system performance and its decision-making capabilities. Initially, we considered a case where all concepts are set to zero. This means that all concepts are not activated for this specific consideration. After 23 iterations the FCM system reaches a final state where the concepts "Biodiversity" and "Ecological State" exhibit very high values and therefore increase the environmental health of marine ecosystem. This is an upper bound for the Black Sea ecosystem health, conditioned by the basic structure of respondents' cognitive reality. In a next step, we consider a case where all concepts are set to one, meaning that the 24 factors are fully activated under this assumption. After 20 iterations the system reaches a final state where "Biodiversity" and "Ecological State" respectively clamp to zero. This is a lower bound for the Black Sea ecosystem health, conditioned by the basic structure of

In-between these two extreme cases, we develop a number of policy scenarios, based on a number of ad hoc interventions for the Black Sea ecosystem conservation. In these interventions, individual concepts and groups of concepts consequently were considered to be activated and the final state of FCM system under these scenarios determined. Each simulation runs under two different versions where the activated concepts are set either one or 0.5. The rationale for this approach is to test the influence of uncertainty in the functioning of the other concepts. The value of 0.5 means there is uncertainty concerning the true state of the impact of the other concepts. The calculated output of the FCM model shows how the system reacts under the assumptions given by the stakeholders or related users. Usually, the calculated output is different from the expected one, thus presenting a

One sample policy making scenario is presented. The five most central concepts- MSW (Municipal Solid Wastes), HA (Human Activities), Urban Sewage, IA (Industrial Activities), HAB (Harmful Algal Blooms)- are considered as the only de-activated concepts whereas all the other 21 concepts are considered as activated concepts that take values: (a) equal to 1 and (b) equal to 0.5, depicting strong activation or uncertainty state. Table 3 depicts the calculated values of all concepts in the final state for the considered scenarios (a) and (b), main observations being the high values of Biodiversity (Bd) and Ecological State of marine environment (ECOL). A significant increase to Biodiversity and ECOL state is a potential outcome of conservation policies regulating the input of those five most central concepts acting as risk factors. Thus the future state of the marine ecosystem could be improved if the

potential added-value of Fuzzy Cognitive Map as a policy making tool.

five most central concepts might decrease at a significant amount.

Fig. 5. The collective FCM with most central variables and strong connections.

Table 2 gathers the calculated graph theory indices for the collective map and the sum of the 29 individual maps.


Table 2. Average (± SD) graph theoretical indices of the individual FCMs and the indices of the collective FCM.

The collective FCM was then used for analyzing system behaviour and to run management simulations. Simulations were generated using both inference equations, eq. (2) and rescaled eq. (5), by taking the product of the vector of initial states of variables (**A0**) times the square

Fig. 5. The collective FCM with most central variables and strong connections.

Maps 29 1 Variables (N) 7.86 ± 1.574 26 Number of connections (W) 11± 6.513 145 No. of transmitter variables (T) 2.21 ± 1.544 2 No. of receiver variables (R ) 1.96 ±1.267 3 No. of ordinary variables (O) 3.21 ±1.445 21 Connection/Variable (W/N) 1.33 ±0.617 4.577778 Complexity (Receiver/Transmitter) 1.02 ±1.198 1.5 Density (D=W/N^2) 0.167 ± 0.065 0.101728 Hierarchy index (h) 0.017 ± 0.005 0.012944

29 individual maps.

the collective FCM.

Table 2 gathers the calculated graph theory indices for the collective map and the sum of the

**Indices Individual Maps Collective FCM** 

Table 2. Average (± SD) graph theoretical indices of the individual FCMs and the indices of

The collective FCM was then used for analyzing system behaviour and to run management simulations. Simulations were generated using both inference equations, eq. (2) and rescaled eq. (5), by taking the product of the vector of initial states of variables (**A0**) times the square matrix *E* of the collective map. Simulations were generated using the five steps described previously implemented in Matlab R2008a environment for Windows. At first, we determine the steady state condition of the system's convergence before we consider any management options. We are doing this in order to be able to see the perceived tendency of the Black Sea ecosystem based on the collective cognitive map and test for its internal coherence. For this purpose, we run the generic FCM model with 50 different random initial states for all variables between 0 and 1 drawn from a uniform distribution. In all of these nomanagement simulations, the system reached a steady state after 25-30 iterations, where some of the produced final steady states for each initial condition were different. By excluding a chaotic behavior, we accordingly confirm a dynamically stable and coherent mental structure of our sample.

Then, we consider a number of assumptions for the concepts and risk factors, which affect the future state of the environmental health of marine ecosystem in the Black Sea to analyze the system performance and its decision-making capabilities. Initially, we considered a case where all concepts are set to zero. This means that all concepts are not activated for this specific consideration. After 23 iterations the FCM system reaches a final state where the concepts "Biodiversity" and "Ecological State" exhibit very high values and therefore increase the environmental health of marine ecosystem. This is an upper bound for the Black Sea ecosystem health, conditioned by the basic structure of respondents' cognitive reality.

In a next step, we consider a case where all concepts are set to one, meaning that the 24 factors are fully activated under this assumption. After 20 iterations the system reaches a final state where "Biodiversity" and "Ecological State" respectively clamp to zero. This is a lower bound for the Black Sea ecosystem health, conditioned by the basic structure of respondents' cognitive reality.

In-between these two extreme cases, we develop a number of policy scenarios, based on a number of ad hoc interventions for the Black Sea ecosystem conservation. In these interventions, individual concepts and groups of concepts consequently were considered to be activated and the final state of FCM system under these scenarios determined. Each simulation runs under two different versions where the activated concepts are set either one or 0.5. The rationale for this approach is to test the influence of uncertainty in the functioning of the other concepts. The value of 0.5 means there is uncertainty concerning the true state of the impact of the other concepts. The calculated output of the FCM model shows how the system reacts under the assumptions given by the stakeholders or related users. Usually, the calculated output is different from the expected one, thus presenting a potential added-value of Fuzzy Cognitive Map as a policy making tool.

One sample policy making scenario is presented. The five most central concepts- MSW (Municipal Solid Wastes), HA (Human Activities), Urban Sewage, IA (Industrial Activities), HAB (Harmful Algal Blooms)- are considered as the only de-activated concepts whereas all the other 21 concepts are considered as activated concepts that take values: (a) equal to 1 and (b) equal to 0.5, depicting strong activation or uncertainty state. Table 3 depicts the calculated values of all concepts in the final state for the considered scenarios (a) and (b), main observations being the high values of Biodiversity (Bd) and Ecological State of marine environment (ECOL). A significant increase to Biodiversity and ECOL state is a potential outcome of conservation policies regulating the input of those five most central concepts acting as risk factors. Thus the future state of the marine ecosystem could be improved if the five most central concepts might decrease at a significant amount.

Using Fuzzy Cognitive Mapping in Environmental

**9. Summary and conclusions**

the new parameters considered.

**10. Acknowledgment** 

**11. Appendix A**  Interview protocol

Stage (1): A Formal Introduction

empirical modalities.

Decision Making and Management: A Methodological Primer and an Application 443

In this chapter, the FCM methodology was presented and analyzed for the elicitation and understanding of individual and collective knowledge, preferences and beliefs. The aim was to present to the reader both a theoretical underpinning of FCMs as well as a grasp of their

A cognition model, like FCM, represents a system in a form that corresponds closely to the way humans perceive it. Therefore, the model is easily understandable, even by a nonprofessional audience and each parameter has a perceivable meaning. The model can be easily altered to incorporate new phenomena, and if its behavior is different than expected, it is usually easy to find which factor should be modified and how. In this sense, a FCM is a dynamic modeling tool in which the resolution of the system representation can be increased by applying a further mapping. The FCM methodology developed makes it possible, if the initial mapping of the risk factors and future prospects of marine ecosystem is incomplete or incorrect, to make further additions to the map, and to predict the effects of

FCMs have some specific advantageous characteristics over traditional mapping methods: they capture more information in the relationships between concepts, are dynamic, combinable, and tunable, and express hidden relationships (Kosko, 1986, 1992). The resulting fuzzy model can be used to analyze, simulate, and test the influence of parameters and predict the behavior of the system. Summarizing, FCM helps describe the schematic structure, represent the causal relationships among the elements of a given decision environment, and the inference can be computed by a numeric matrix operation. With FCM

To illustrate the FCM methodology, an empirical application for modelling lay people perceptions is presented. We describe the main features of a FCM exercise designed to elicit the Black Sea stakeholder views/ perceptions about the risks that the Black Sea may face in the future 20 years. A generic model for environmental management is constructed by augmenting the individual FCMs drawn by lay people-stakeholders from Ukraine. The graph theoretical indices were calculated out of the individual cognitive maps and the collective cognitive map produced by augmentation. A number of scenarios were run using the FCM inference process to enable us to understand the complex structure of the Black Sea problems and the risks mainly affecting its marine ecosystem. This knowledge is further used to design policies that contribute in environmental management. The results show its functionality and demonstrate that the use of FCMs is reliable and efficient for this task.

This research was carried out within the IP project SESAME funded by the EU under Framework Programme 6, Key Action "Global change, climate and biodiversity", Contract No. 2006-036949. We thank the Coordinator Dr. E. Papathanassiou for his encouragement to

apply early in 2008 Fuzzy Cognitive Mapping in marine governance.

it is usually easy to find which factor should be modified and in which way.


Table 3. Initial and final concepts' state after 25 iterations for Scenario (a) and (b).
