Constrained Defuzzification

Abstract

The output of a fuzzy rulebase system is a fuzzy set. In a typical application of a fuzzy rulebase system, this fuzzy set is sufficient for the end result, and defuzzification of it results in the final outcome. However, in the spatial application, there are a number of rulebase applications that together form the end result. This chapter elaborates on the interpretation of the results and the postprocessing necessary to properly interpret the results and explains the shortcomings of the current methodology, justifying the development of new methods explained in this chapter. This concerns the defuzzification of fuzzy sets, where a method was developed to defuzzify multiple fuzzy sets in parallel, under the condition that the result should sum up to a given value. This constrained defuzzification allows for better results in the context of the spatial processing, but can also have wider applications.