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 distribution. This paper proposes a Fuzzy Agent-based Model simulation (SPERB, 2002) 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
Agent-based Model - ABM is a recent simulation approach that involves reproducing a real world system into a virtual one, where experiments shall be performed (BOX, 2000; TESFATSION, 2002). In the virtual universe, each agent is represented by an independent entity that is capable of acting locally in response to its perception, coded behavior and environmental changes. Fuzzy logic (ZADEH, 1965), in addition, has been used with relative success to handle real world uncertainty and linguistic terms in computational systems. A software prototype of a hybrid model (Fuzzy Agent-based Model - FAM) that combines both approaches previously described was developed in order to address the following questions:

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 attribute. 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 as their synthesis represented in a map. This map is what the agent sees in the virtual world (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 gradient each time step until it falls in a "stable state". Whenever there are two or more values that hold the same highest value, a random choice is made 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.

Study Case
A study case was constructed to answer those three questions. The rapid growth in Ingleses beach, Santa Catarina - Brazil was selected as study case. A GIS study was conduced in order to identify spatial attributes and user groups for a period of 20 years, defining, at macro level, the central area, periphery and roads as spatial attributes (Figure 5). Spatial attributes and perception maps are presented in Figure 6. Preference rules were set in the inference system resulting in mental maps for each agent (Figure 7).

Figure 5. Spatial attributes and user groups.
 

Figure 6. Spatial attributes and their perception maps
 

Figure 7. Mental maps

Conclusion
Simulations results with 92% of similarity with real data distribution (Figure 8) have demonstrated the model viability as well as its ability to handle people's spatial perception and behavior. The study case has shown that spatial analysis can be used to define user groups' behavior, verifying the model potential application in studies and predictions of land occupation in a coastal area. The results allow assuring that FAM was able to capture general rules of perception and behavior that defines user groups' spatial distribution.

Figure 8. (a) Real data and (b) simulated one