FUZZY AGENTS: A HYBRID TOOL FOR EXPLORING
COASTAL ZONE SPATIAL PROCESSES

Rafael Medeiros Sperb, Rodrigo Becke Cabral, Rodrigo Zanato Tripodi

Universidade do Vale do Itajaí, (BR)

Introduction
The interaction dynamics amidst coastal user groups and the environment has increased to threaten natural resources availability. Overpopulation and loss of environmental resources are common predictions for coastal zones. Numerical models have been used to study human impacts in these zones, with limited capacity to handle user groups´ spatial perception and their consequent spatial distribution. This paper proposes a Fuzzy Agent-based Model (SPERB, 2002) simulation for analyzing land occupation scenarios from people's spatial perception and behavior. Both perception and behavior are explored through natural language (linguistic terms).

Fuzzy Agent-based Model and Coastal Zone Management
In general terms, environmental quality should not be seem as an abstraction of our need for a health environment, but a materialization of all beneficial functions that sustains life on earth. This approach considers the environment as a common property and, as such, it must be managed (JENTOFT, MCCAY & WISLON, 1998). It is undeniable that we live in a planet that is dominated by human beings, whose activities transform those functions. Hence, it is not admissible to believe that it is possible to manage the environment apart of human activities. They have expanded to a point that they affect virtually all ecosystems on earth (GREENS & KLOMP, 1998). Our society needs to preserve not only parks and reserves confined in isolated areas, but learn and incorporate the notion of preserving all beneficial functions in its daily relation to the environment (AGARDY, 1997).
These previous considerations emphasize the relation between environment, its functions and humans. Environmental quality is directly related to the existence of beneficial functions, even without humans' acknowledgment. Since we consider human activities to be the major source of environmental transformation, it seems prudent to comprehend how humans perceive and act upon environmental attributes before conducing any management effort.
Coastal Zone Management is well known for employing plans, programs and regulations to promote sustainable uses of coastal resources while maintaining its functions. It is important to consider how individuals tend to organize themselves, as pointed out earlier. Not less important is to understand user groups' values and necessities towards the environment. In other words, user groups' perception of coastal attributes controls their relation and behavior. Therefore, understanding user groups' perception and behavior has an instrumental feature to those attempting to develop management plans and measures.
Combining perception and spatial behavior of user groups with land use and environmental changes studies in coastal zones is not an easy task. There are not many tools to support complex systems exploration such as human and natural systems. Numerical models have been used with limited success through the years (e.g. CONSTANZA, WAINGER & BOCKSTAEL, 1996; VOINOV et. al., 1999). Furthermore, any research that attempts to study user groups' perception and behavior should be based on socioeconomic and cultural information, as well as in the inner relation between people and their environment. It is inevitable a multidisciplinary approach and the deployment of questionnaires, interviews, observation, plus any other form of information source for supporting hypothesis generation of spatial perceptions and behavior. As a result, a considerable amount of information is, by nature, subjective, uncertain, derived from heuristics, and many times expressed in linguistic terms. These characteristics make hard an attempt to develop a mathematical model. The emergence of Fuzzy Logic in 1965 (KLIR & YUAN, 1995; KLIR, CLAIR & YUAN, 1997) has opened new perspectives to explore the kind of information previously presented in models, due to its ability to handle uncertainty of linguistic terms and human reasoning process. This ability allows codification of simulation rules in natural language instead of meaningless equations that only few people can understand.
The idea of combining Fuzzy Logic with Agent-based Modeling (ABM) has potentials that are unexplored at this moment. ABM is a new modeling paradigm that has been quite successful to simulate complex systems. Its methodology is centered in the construction of an artificial universe inhabited by agents that have a straight relation to the environment attributes, and among themselves. This approach has great appeal for simulations that are based on perception and behavior, items that might be coded through Fuzzy Logic. Besides this potential, two important aspects regarding ABM are important: firstly, its capacity to easily include new simulation elements (agents and attributes), what is not so simple in numerical models; secondly, the notion of emergence, a simulation property that relies on the fact that agents' simple interaction rules may lead to a more complex system's functioning pattern of behavior.
This association of paradigms has been explored in robotics, specifically to code navigation rules (SAFFIOTTI, 1997). However, for environmental applications one might say that it is a brand new field of research in artificial intelligence and environmental sciences. Its potentials can be enhanced by evolutionary approaches such as neural networks and genetic algorithms, resulting in evolution and adaptation characteristics to the models themselves (MICHAUD, LACHIVER & DINH, 1996).
For Coastal Zone Management, Fuzzy Intelligent Agents can be used to explore user groups' environmental perception and spatial behavior. An analogy between a coastal system and an artificial universe allows the use of agents as user groups, providing ground for hypothesis formulation and test. Fuzzy Logic provides agents' codification of user groups' perception and behavior through natural language. In this context, Fuzzy Agent-based Modeling should be seen as an exploration tool to understand the dynamics of user groups towards the environment, and the implications to land use patterns. Considering this potential application, this work look for answers to the following questions: (a) is it viable to develop spatial dynamic simulation model for coastal zones that are based on ABM and Fuzzy Logic?; (b) coastal users' pattern of behavior obtained through spatial analysis might be used to construct such models?; and (c) this kind of model provides results that correspond to the real behavior of coastal users?

Conceptual Model
In order to test the FAM ability to study coastal zone spatial processes it is assumed that particular patterns of behavior might be observed for each coastal user group as response to their perception and needs towards environmental resources (environmental attributes). Both perception and behavior are studied through natural language and coded as fuzzy rules in an inference system, which is the decision engine behind each agent behavior. The inference system employs perception maps that derive from spatial analysis as the agent input information, while the output is a synthesis of the spatial perception. This synthesis is represented as a mental map and stands for the artificial world were the agent lives. The agent's agenda (behavior) is to seek in this artificial world the place that best fulfills its needs. This conceptual model is presented in Figure 1.

Figure 1. FAM conceptual Model

Behavior Codification: spatial attributes are considered the driving force for user groups' spatial distribution. Thus, an agent will behave according to its perception towards one or more spatial attributes. For example, a tourist might seek for a quiet place with waves to stay in a beach. Quiet place and waves are spatial attributes that fulfill his needs. This rule can be expressed through fuzzy logic, as presented in Figure 2. It should be noticed that quiet and waves are actually values related to the attribute human density and beach dynamics, respectively. Perception towards these two attributes may assume several values, such as quiet.

Figure 2. Example of an inference rule expressed in natural language

Mental Map: a mental map is built upon perception maps and coded behavior in the agent's fuzzy inference engine and their synthesis represented in a map. This map is what the agent sees in the virtual world, representing its preferences (Figure 3).

Figure 3. Mental map construction.

Agent's Agenda: it consists in the search for the area that has the highest values in the mental map. This is done via a simple scan for the highest neighborhood cell value (Figure 4). The agent moves to the highest value cell each time step until it is in a "stable state". Whenever there are two or more values that hold the same highest value, a random decision is taken among those cells.

Figure 4. Agent's cell election and movement to accumplish with his agenda.

The presence of an agent in a cell might impact any spatial attribute (perception map) that is considered in the artificial universe. If two or more agent group share perception maps, then an agent can sense others presence indirectly. This is called agent impact and it consists of a penalization in the value of the cell in the perception maps. In fact, the impact can be either positive or negative, depending on coded perception and behavior.

Study Case
Considering that fuzzy ABM is concerned with spatial processes, it was required a study case that best suited to the purpose of testing this kind of approach. Therefore, problem and study area should fulfill this purpose. Selecting a study area and problem, in fact, is the first step towards a study case construction, as presented in Figure 5.

Figure 5. Steps towards a study case construction

Step I: The rapid growth of Ingleses beach, Santa Catarina - Brazil (Figure 6) was selected for its consistent historical series of aerial pictures that would allow spatial processes exploration; rapid and chaotic pattern of growth in the last 25 years; proximity of the study area, which facilitates field work; and environmental legislation disrespect during this period.

Figure 6. Aerial view of Ingleses beach (IPUF, 2000).

Step II: A GIS study was conduced in order to identify spatial attributes and user groups in the study area. Time window was set for 20 years, from 1978 to 1998. During this period the major growth happened in areas close to the beach (central area) and periphery zones, between dune systems, wherever roads were available (Figure 7). It is interesting to realize that new roads had their origin in walk paths throughout the area.

Figure 7. Time window analysis (1978-1998)

The growth it the periphery has several motivations, such as plot prices that are lower than in central areas. On the other hand, central areas hold facilities such as transportation, commerce, and other attributes that attract people. For the sake of modeling simplicity it was assumed that all possible spatial motivations for a user group preference is summarized by these two spatial attributes. Thus, there are two user groups: those who prefer to live in central areas, and those who are led to live in the periphery. Besides these two attributes, it is clear from the spatial analysis that road proximity is a common preference to both user groups. This preference is based on transport; electricity and water facilities availability. The system functioning for the study case can be visualized in Figure 8. A more detailed analysis could be developed in order to unfold a more detailed spatial perception and behavior. However this level of abstraction suffices the objective of this work.

Figure 8. Spatial attributes and user groups

Perception maps were constructed using the distance algorithm from the limits of the attributes, as shown in Figure 9. Distance values will be used in step IV by the inference engine.

Figure 9. Example of a spatial attribute and its respective perception map

Step III: After attributes and user groups definition, and perception maps construction, it is necessary to model user groups' behavior, as well as to define operational information for the simulation, such as number of agents to each user group. Fuzzy sets and ranges were defined from observation and tests (Figure 10).

Figure 10. Fuzzy sets graphical representation for preference

Spatial preferences (behavioral rules) were defined for the attributes. A simple matrix analysis has provided preferences to each agent group, as show in Table 1. Based on these preferences, the agent's behavioral rules were built, as shown in Table 2.

Table 1. Preference matrix for each user group.

Table 2. Preference rules for user 2 (center)

The inference system evaluates pixel-by-pixel input information (perception maps) in order to create a mental map for each agent (Figure 11). This map is in fact how the agent see the artificial world.

Figure 11. Mental maps

Step IV: Running the simulation consists in allowing the agents to seek their goal, waiting for their stabilization. In order to check how similar simulation results were to real data, this work has applied a simple similarity index test. The test, which is performed through overlay operation, consists of an intersection analysis of real data and simulated one. As both sets of data are points, a 10 meters buffer operation is developed prior the analysis. Total area calculation for real data and intersected one can, therefore, be performed, and from comparing both areas one will find how similar they are. The closest these values are the more similar they will be.
Since the idea of this kind of simulation is not to obtain precise results, but rather to understand tendencies of land use based on perceptions and needs, similarity analysis is developed for three other buffer values for real data: 15, 30 and 45 meters. For these three other values, simulated data buffer remains10 meters (Figure 12). Similarity Index is obtained from the following formula:

Figure 12. Similarity analysis graphical representation

Based on the actual size of a regular plot in Ingleses beach, which ranges from 300 to 800m2, it was considered four similarity indexes: S10, S15, S30 e S45, respectively representing 315, 707, 2.827 e 6.361m2. Results from the simulation are presented in Figure 13.

Figure 13. (a) Real data, (b) simulated one and similarity analysis

Discussion
The idea of using mental maps built upon fuzzy logic and people's perception, preferences and behavior rules has given a positive feedback from the test. Limitations to this kind of application can be identified; such as the presence of local maximum and minimum areas (Figure 14A) that affect agents agenda search. This is especially true to the agenda mechanism adopted, which creates a limited vision to the agent, as well as a bounded rationality situation (Figure 14B). In spite of this limitation, it is clear, from the results achieved in the study case, that this approach can provide good results. This problem was overcome by avoiding a random agents' distribution at the beginning of the simulation.

Figure 14. (A) Local maximum and minimum, (B) effect on simulation results, (C) behavior distortion and (D) emergent properties in the results


Besides this limitation, distortions in the simulation results also occur when perception and behavior rules are not well defined (Figure 14C). Mistakes or misunderstandings can occur in the definition of the attributes and their values; in the fuzzy set configuration; and in the rules and their real importance. In part, these distortions can be avoided with the employment of questionnaires and interviews, instead of supporting modeling activities solely on spatial analysis.
An important aspect in the study case was the identification of emergent properties, in spite of modeling simplicity. The mixture of agents (center and periphery) in the interface between these two spatial attributes was not modeled or even foreseen (Figure 14D). It can be assumed that this sort of property will gain more expression as new elements and agents are added to the simulation itself.

Conclusion
In spite of the methodological weakness described previously, the prototype has answered positively to those three questions posed to this work. ABM and Fuzzy Logic can and have great potential to deal with spatial dynamic models, not only in coastal zones. This potential is enhanced by fuzzy logic ability to handle natural language information and rules that code people's perception and behavior. Observation has proven to be a key element in this kind of representation of real world. Spatial analysis might help to understand spatial processes and build models, however the modeler has to have deep knowledge on local information.
Considering whether the model represents real world phenomena, there is no doubt that it can imitate reality. However, it must be kept in mind that it is an approximation of reality rather than a precise model, such as physical models. Its basic function is to understand tendencies that result from global system behavior. In this sense, this model approach must be seen as an exploring machine through which the modeler tests systems' reactions to proposed changes, to better understand its functioning.
As a new approach, this kind of application has ahead a challenge to consolidate both concepts and methodology. In terms of prototype, a second version shall include agents' reproduction and die of, agents' direct communication and a view mechanism that avoids bounded rationality. Desired evolutions include cellular automata to run environmental attributes autonomous processes to be modeled.

References