Fuzzy Set and Fuzzy Logic

Abstract

Development and applications of the fuzzy-set and fuzzy-logic approach to geographical research is reviewed in this article. It first points out the paradigm shift in geographical analysis under uncertainty. Instead of solely equating uncertainty with randomness, the fuzzy-set approach addresses uncertainty due to fuzziness/imprecision. It reintroduces value judgment to the analysis of human behaviors in space. It builds a bridge between quantitative and qualitative analysis so that natural languages can be used in geographical investigations with scientific rigor. The article examines the fuzzy-sets approach to spatial characterization, spatial classification, and regionalization that are fundamental in geographical analysis. It compares the ways in which it differs from the conventional approach in terms of philosophy, analytical methods, and results. The discussion then extends to the investigation of fuzziness in spatial economic analysis, spatial optimization, and planning. After that, the focus shifts to the employment of fuzzy logic to spatial reasoning and decision making. It contrasts the reasoning by conventional logic. The application of fuzzy logic in expert systems and spatial decision support systems is also discussed. The article then concludes with an integration of probability, fuzzy set, and rough set to form a unified framework for uncertainty analysis in geography. It also points to the integration of fuzzy set and logic with paradigms such as neural networks and genetic algorithms for the analysis of complex spatial systems.