Aggregation here refers to as the combination of meanings of two or more statements (expressions). One can think of this as a logical combination of the meanings in these expressions. Aggregation naturally involves the use of a logical framework, a principle under which the meaning of an expression is understood. For example, “Come to see me at 2 p.m.” can be understood very differently under different logic frameworks. One logic framework would dictate that the person be there at 2 p.m. sharp while another logic framework would imply around 2 p.m. We humans adopt the latter but computers by default use the former.
Fuzzy aggregation is then naturally an aggregation under the fuzzy logic. Under fuzzy logic, an item can be assigned to a class (or set) in partial degree of belonging, ranging from 0 to 1 with 0 meaning no belonging at all and 1 meaning full membership, with anything between 0 and 1 being a partial belonging. The “around 2 p.m.” above is the result under fuzzy logic. By the same token, there is an aggregation that is done under the Boolean logic which only admits belonging (1) or not belonging at all (0) with nothing between. The “2 p.m. sharp” above is the result under Boolean logic.
GIS analysis has mostly been done under Boolean logic. Recently, analysts started to see the suitability and appropriateness in applying fuzzy aggregation in GIS, mainly because of two reasons: first we humans are more accustomed to the fuzzy approach (we hardly enforce the 2 p.m. sharp notion), second, geographic phenomena more than often vary in gradation (for example, the variation of soil over space) which is more suited for representation under fuzzy logic.
For this entry, the concept of a set which is the foundation of any logic framework will be introduced first. This is then followed by the introduction of fuzzy aggregation, in comparison to the aggregation under Boolean logic. This Fuzzy vs. Boolean comparison is further illustrated through an example of their applications in Geography.