Abstract
We study the influence of fuzziness of trapezoidal fuzzy sets in the strong fuzzy partitions (SFPs) that constitute the database of a fuzzy rule-based classifier. To this end, we develop a particular representation of the trapezoidal fuzzy sets that is based on the concept of cuts, which are the cross-points of fuzzy sets in a SFP and fix the position of the fuzzy sets in the Universe of Discourse. In this way, it is possible to isolate the parameters that characterize the fuzziness of the fuzzy sets, which are subject to fine-tuning through particle swarm optimization (PSO). In this paper, we propose a formulation of the parameter space that enables the exploration of all possible levels of fuzziness in a SFP. The experimental results show that the impact of fuzziness is strongly dependent on the defuzzification procedure used in fuzzy rule-based classifiers. Fuzziness has little influence in the case of winner-takes-all defuzzification, while it is more influential in weighted sum defuzzification, which however may pose some interpretation problems.
Highlights
The design of fuzzy inference systems promotes interpretability as a key factor to express the embedded knowledge in a plain readable and understandable way
We already mentioned how this idea has been injected in the very definition of the previously discussed particle swarm optimization (PSO) algorithm, whose objective function is represented by the accuracy evaluation of the resulting fuzzy system applied on some dataset
Our goal is to test the suitability of the developed PSO strategy in fine-tuning the design of trapezoidal strong fuzzy partitions (SFPs) based on cuts, instead
Summary
The design of fuzzy inference systems promotes interpretability as a key factor to express the embedded knowledge in a plain readable and understandable way. As a matter of fact, interpretability is the most important quality that justifies the adoption of fuzzy inference systems in real-world applications [1,2,3,4] When such systems have to be acquired through data-driven approaches, two main design issues arise: (i) the resulting fuzzy inference system should adequately fit data; (ii) the knowledge base should be interpretable to end-users. This led to the development of design methodologies that take into account both accuracy and interpretability [5,6,7,8,9,10,11]; in parallel, the very concept of interpretability, its definition and assessment are matter of current research [12,13,14,15].
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