Several mathematical and computer-based approaches are mobilised to structure knowledge around a theoretical spatial and behavioural modelling action or an action oriented at decision-making in planning:

• Formalisation of spatial processes through graph theory, fractal geometry, spatial interaction models, etc.

The fractal approach as used in the team is not limited to analyses of urban textures but relies on modelling of urban fabrics based on fractal reference models. This concerns somewhat theoretical models but also the explicit use of the logic of iterative functions in the context of urban development scenario simulation.

• Formalisation of decision-making processes and behaviours by a probabilistic approach, fuzzy set theory, the idea of utility, etc.

Various approaches are used in modelling the behaviour of agents (households, individuals). Classical approaches based on utility functions are employed for example in the S-Ghost project conducted in close collaboration with the CORE (Catholic University of Louvain) laboratory and the University of Luxembourg. Fuzzy subset theory is also used in the modelling of decision making processes associated with residential choice, but also for evaluating accessibility to services and shops.

• Epistemological reflections for ontological conceptualisation of geographical space with a view to proposing a formal framework for mathematical and computer-based modelling.

• Spatial and behavioural simulations relying on various types of modelling: cellular automata, multi-agent systems, integrated urbanisation-transport models (LUTI), etc.

• Development of decision making tools in touch with social realities and planning actors: Fractalopolis and MUP-city, Geographer, Mobisim, Miro and Lucsim.

Software packages have been designed for developing urban scenarios corresponding to conceptual thinking about the value of a 'fractal city' enabling these principles to be applied to actual situations. Rules for accessibility and morphological standards are included in these decision-making aids. While MUP-city is better adapted on the scale of city districts or suburban villages, Fractalopolis can be used to work on the scale of agglomerations and metropolitan areas.

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