Implementing a combined defuzzification: evaluation of COBYLA and SLSQP

Abstract The combined defuzzification of multiple fuzzy sets under a shared constraint is an extension of traditional defuzzification. The problem concerns defuzzifying multiple fuzzy sets at once, adhering to a constraint that involves their defuzzified values. This specific problem emerged in an application of fuzzy rulebase systems with the goal of regridding spatial data; the constraint stems from the need to keep the total modelled value over a region consistent. Through the introduction of goal functions, the combined defuzzification problem was translated to an optimization problem; the goal functions allow to use objective criteria to evaluate and rank different solutions. Different goal functions for the combined defuzzifier have been presented in the relevant literature, in this contribution, the aim is to evaluate solvers in order to develop a usable implementation of the novel defuzzifier and to verify their stability and performance for the presented problem.