Towards a Meaningful Fuzzy Analysis of Urbanistics Data

We present and elaborate on a method for analyzing and interpreting data from an Urbanistics project. A fuzzy Hassefication technique was applied to data gathered from this project. Then an algorithm that compares Hasse diagrams was u~d. The resulting mappings are evaluated for their "goodness of fit." These results were then interpreted and summarized in order to determine if the methodology is plausible. 1. I N T R O D U C T I O N Society, just as humankind, continues to evolve into a more complex, dynamic system. The urban environment, in particular, is always plagued with problems and dissatisfied inhabitants. In this paper, we develop a method for analyzing and interpreting interview data from inhabitants of a city. These data are in the form of mathematical relations. The motivation for this investigation was to eventually design a consultative system for urban problems. Mathematical relations are normally processed by extracting their deep structure. This may be achieved by obtaining certain closures and interiors depending on the relational propert ies under investigation. Perhaps one of the most interesting group of properties are those exhibited by orders and preorders. H a s s e diagrams are used to graphically illustrate the different categories hidden by such relations. In a sense, these diagrams represent high-level knowledge that may not normally be evident. One of the most interesting aspects that has to be considered when comparing Hasse diagrams is the fact that the reference sets are actually (disjoint) partitions of the original reference sets. Hence, each node on a Hasse diagram may constitute, for example, an equivalence class. In an INFORMATION SCIENCES 94, 191-212 (1996) © Elsevier Science Inc. 1996 0020-0255/96/$15.00 655 Avenue of the Americas, New York, NY 10010 PII $0020-0255(96X)0077-1