The influence of fuzzy set theory on the areal extent of thematic map classes

In thematic maps information is traditionally represented in a one-polygon-one class method which assumes each polygon in the map can be assigned unambiguously to a single class. Additionally, thematic map classes are assumed to be exhaustive and mutually exclusive. The introduction of fuzzy classifications overcomes the traditional limitations on the mutually exclusive nature of map classes assigning varying levels of class membership for individual map polygons. As a consequence, fuzzy set theory expands the conventional assumptions regarding the total areal extent of thematic map classes. Considering that a map polygon may simultaneously belong to more than one thematic map class, the total areal extent of all classes in a thematic map need not be equal to the geographical extent of the study area. Although this apparent paradox has already been noted in previous papers, as far as we know, an analytical formulation of the influence of fuzzy classifications on the areal extent of thematic map classes has never been provided. This Letter offers an analytical solution to evaluate the total areal extent of thematic map classes as a function of fuzzy class membership levels.