Fuzzy rule-based systems (FRBSs) are a common alternative for applying fuzzy logic in different areas and real-world problems. The schemes and algorithms used to generate these types of systems imply that their performance can be analyzed from different points of view, not only model accuracy. Any model, including fuzzy models, needs to be sufficiently accurate, but other perspectives, such as interpretability, are also possible for the FRBSs. Thus, the Accuracy-Interpretability trade-off arises as a challenge for fuzzy systems, as approaches are currently able to generate FRBSs with different trade-offs. Here, rule Relevance is added to Accuracy and Interpretability for a better trade-off in FRBSs. These three factors are involved in this approach to make a rule selection using a multi-objective evolutionary algorithm. The proposal has been tested and compared with nine datasets, two linguistic and two scatter fuzzy algorithms, four measures of interpretability and two rule relevance formulations. The results have been analyzed for different views of Interpretability, Accuracy and Relevance, and the statistical tests have shown that significant improvements have been achieved. On the other hand, the Relevance-based role of fuzzy rules has been checked, and it has been shown that low Relevance rules have a relevant role for trade-off, $ This work has been partially supported by the Spanish Ministry of Economy and Competitiveness through the Project no. DPI2015-67341-C2-2-R
Fuzzy modeling is one of the most known and used techniques in different areas to model the behavior of systems and processes. In most cases, as in data-driven fuzzy modeling, these fuzzy models reach a high performance from the point of view of accuracy, but from other points of view, such as complexity or interpretability, they can present a poor performance. Several approaches are found in the bibliography to reduce the complexity and improve the interpretability of the fuzzy models. In this paper, a post-processing approach is carried out via rule selection, whose aim is to choose the most relevant rules for working together on the well-known accuracy-interpretability trade-off. The rule relevancy is based on Orthogonal Transformations, such as the SVD-QR rank revealing approach, the P-QR and OLS transformations. Rule selection is carried out using a genetic algorithm that takes into account the information obtained by the Orthogonal Transformations. The main objective is to check the true significance, drawbacks and advantages of the rule selection based on the orthogonal transformations via the rule firing strength matrix. In order to carry out this aim, a neuro-fuzzy system, FasArt (Fuzzy Adaptive System ART based), and several case studies, data sets from the KEEL Project Repository, are used to tune and check this selection of rules based on orthogonal transformations, genetic selection and accuracy-interpretability trade-off. This neuro-fuzzy system generates Mamdani fuzzy rule based systems (FRBSs), in an approximative way. NSGA-II is the MOEA tool used to tune the proposed rule selection.
Fuzzy modeling is one of the most known and used techniques in different areas to emulate the behavior of systems and processes. In most cases, as in data-driven fuzzy modeling, these fuzzy models reach a high performance from the point of view of accuracy, but from other points of view, such as complexity or interpretability, the models can present a poor performance.Several approaches are found in the specialized literature to reduce the complexity and improve the interpretability of the fuzzy models. Here, a post-processing approach is taken into account via the definition of the rules selection criterion that aims to choose the most relevant rules according to the wellknown accuracy-interpretability trade-off. This criterion is based on Orthogonal Transformations, here the QRP transformation is taking into consideration, and its parameters are tuned genetically. The main objective is to check the true significance, drawbacks and advantages the firing matrix of the rules, that is the foundation of the most usual approaches based on orthogonal transformations for the complexity reduction of the fuzzy models.A neuro-fuzzy system, FasArt (Fuzzy Adaptive System ART based), and several case studies, data sets from the KEEL Project Repository, are used to tune and check this approach. This neuro-fuzzy system generates Mamdani fuzzy rule based systems (FRBSs), each with its own particularities and complexities from the point of view of fuzzy sets and rule generation. NSGA-II is the MOEA tool used to tune the criterion parameters based on accuracy-interpretability ideas.
Fuzzy modeling is one of the best known techniques to model systems and processes. In most cases, as in data-driven fuzzy modeling, these fuzzy models reach a high accuracy, but show poor performance in complexity or interpretability, which are key aspects of Fuzzy Logic.There are several approaches in the literature to deal with the complexity and interpretability challenges for fuzzy rule based systems (FRBSs). In this paper, a post-processing approach is proposed via a genetic rule selection based on the relevance of each rule (using Orthogonal Transformations (OTs), in this case P-QR) and the well-known accuracy-interpretability trade-off. The main objective is to check the true significance, drawbacks and advantages of the rule selection based on OTs to manage the accuracy-interpretability trade-off.In order to achieve this aim, a neuro-fuzzy system (FasArtFuzzy Adaptive System ART based) and several case studies from the KEEL Project Repository are used to tune and check this selection of rules based on rule relevance by OTs, genetic selection and accuracy-interpretability trade-off. This neuro-fuzzy system generates Mamdani FRBSs, in an approximate way. SPEA2 is the multi-objective evolutionary algorithm (MOEA) tool used to tune the proposed rule selection, and different interpretability measures have been considered.
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