Fuzzy Spatial Algebra (FUSA): Formal Specification of Fuzzy Spatial Data Types and Operations for Databases and GIS

Spatial database systems and Geographic Information Systems (GIS) are mainly able to support geographical applications that deal with crisp spatial objects , that is, objects whose extent, shape, and boundary are precisely determined. But geoscientists have pointed out for a long time that there is also a need to represent fuzzy spatial objects that reveal an intrinsically vague or blurred nature and structure and feature indeterminate boundaries and/or interiors. A spatial object is fuzzy if locations exist that cannot be assigned completely to the object or to its complement. In this article, we propose an abstract, formal, and conceptual type system called Fuzzy Spatial Algebra ( FUSA ) that provides a collection of fuzzy spatial data types for fuzzy points , fuzzy lines , and fuzzy regions in the two-dimensional Euclidean space. We introduce a set of expressive spatial operations such as fuzzy union , fuzzy intersection , and fuzzy difference to perform geometric computations on fuzzy spatial objects. As a specialty, users may exert influence on how spatial fuzziness is interpreted and handled in these operations. Our formal framework is based on fuzzy set theory and fuzzy topology. FUSA is designed to serve as a specification of its implementation in a spatial database and GIS context. We show the applicability of FUSA and its possible embedding into the query languages of extensible database systems by employing a running example.