Comparison of Defuzzification Operators on Geographic Data of Ratio Scale

Abstract

Fuzzy logic is a contemporary theory that has found numerous applications in Geographic Information Systems (GIS). Fuzzy logic allows for the representation of uncertainty and imprecision in spatial data, making it a valuable tool for dealing with the inherent ambiguity present in many geographic datasets. To solve a problem using a knowledge-based fuzzy system, the description and processing of the influencing factors or variables in fuzzy terms is required. The key components of a knowledge-based fuzzy system within the context of GIS are: Fuzzification, definition of the knowledge base, processing of the rules and finally defuzzification. Defuzzification is an important aspect of fuzzy logic and fuzzy set theory, as it helps convert fuzzy linguistic terms or fuzzy sets into crisp values that can be used in decision-making or analysis. Moreover, this might seem contradictory to the primary objective of fuzzy set theory, which is to model and work with uncertainty and imprecision. The aim of this paper is, first, to review defuzzification operators that are suitable for handling geographic data of ratio scale and second to compare these defuzzification operators by applying them to actual geographic data sets. For this reason, a case study based on pollution data of the municipality of Athens, Greece, was carried out to estimate pollution produced by SO 2 . The results of the application of defuzzification operators for the above geographic data set are compared and final conclusions are presented.