Combined defuzzification under shared constraint

Defuzzification of fuzzy sets is an important aspect of fuzzy processing, as it determines how the fuzziness is dealt with when performing the final step to obtain crisp solutions. In this contribution, we consider the possibility of defuzzifying multiple general type-1 fuzzy sets, given that their defuzzified values are bound by a single, known constraint. This stems from an application in spatial data processing, where we obtained a number of fuzzy sets whose defuzzified values should sum up to a crisp and known value. It is possible to defuzzify each fuzzy set individually and rescale the outcomes to meet the constraint. However, considering that the fuzzy set contains information on what constitutes good values, accounting for the constraint in the defuzzification process has the potential to yield better results. We considered this as an optimization problem and investigated appropriate goal functions. The approach and goal functions are discussed with respect to typical properties of defuzzifiers.