Método para aumento de interpretabilidade em modelos de Takagi-Sugeno no sistema INFGMN

TCC(graduação) - Universidade Federal de Santa Catarina. Centro Tecnológico. Ciências da Computação.Interpretabilidade e acurácia são objetivos conflitantes em modelos de aprendizado de máquina, onde a melhora de um geralmente causa a piora do outro. A interpretabilidade dos modelos gerados é importante para que possa ser validado por especialistas do domínio e passar confiabilidade para tratar o problema. Para buscar o melhor equilíbrio entre os dois, uma abordagem comum em Sistemas de Inferência Fuzzy é empregar um Modelo Fuzzy Linguístico e melhorar sua acurácia, ou um Modelo Fuzzy Preciso e melhorar sua interpretabilidade. O INFGMN é um sistema neurofuzzy que utiliza da equivalência entre um Modelo de Mistura de Gaussianas e um Sistema de Inferência Fuzzy para extração de conhecimento, sendo capaz de gerar modelos de Mamdani- Larsen, um Modelo Fuzzy Linguístico. Neste trabalho busca-se expandir as funciona- lidades do INFGMN, proporcinando sua aplicação com modelos de Takagi-Sugeno, um Modelo Fuzzy Preciso, e melhorando sua interpretabilidade via distinguibilidade nas partições fuzzy, obtendo um bom equilíbrio entre acurácia e interpretabilidade. Para garantia de distinguibilidade, foi elaborado um método de similaridade de partição fuzzy para guiar a fusão e separação dos conjuntos fuzzy, ponderado pelos pesos das regras para gerar menores alterações nos conjuntos cujas regras descrevam melhor o sistema e não sejam oriundas de dados discrepantes. Os resultados apresentados para problemas offline demonstram a eficácia do método de similaridade utilizado, ao conseguir gerar uma partição fuzzy distinguível e, ademais, ser capaz de reduzir o overfitting. Para o experimento online com perturbações nos dados, os resultados não são muito promissores, mas sugerem ser uma boa alternativa para ambientes estáveis.Interpretability and accuracy are conflicting objectives in machine learning models, where improvement in one usually worsens the other. The interpretability of the gen- erated models is important so that it can be validated by experts in the field and pass reliability to address the problem. To seek the best trade-off between the two, a com- mon approach in Fuzzy Inference Systems is to employ a Linguistic Fuzzy Model and improve its accuracy, or an Accurate Fuzzy Model and improve its interpretability. The INFGMN is a neurofuzzy system that uses the equivalence between a Gaussian Mixture Model and a Fuzzy Inference System for knowledge extraction, being able to generate Mamdani-Larsen models, a Linguistic Fuzzy Model. This work seeks to expand the functionalities of the INFGMN, providing its application with Takagi-Sugeno models, a Precise Fuzzy Model, and improving its interpretability via distinguishability in fuzzy partitions, achieving a good trade-off between accuracy and interpretability. In order to guarantee distinguishability, a fuzzy partition similarity method was developed to guide the merging and separation of fuzzy sets, weighted by the weights of the rules to cause less changes in the sets whose rules better describe the system and are not derived from outliers. The results presented for offline problems demonstrate the effectiveness of the similarity method used, in being able to generate a distinguishable fuzzy partition and, in addition, being able to reduce overfitting. For the online experiment with data disturbances, the results are not very promising, but suggest that it is a good alternative for stable environments

Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling

This paper aims at providing an in-depth overview of designing interpretable fuzzy inference models from data within a unified framework. The objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real-world systems whose first-principle models are unknown. Because system behaviour can be described naturally as a series of linguistic rules, data-driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose. However, fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability. Model accuracy and interpretability are two conflicting objectives, so interpretation preservation during adaptation in data-driven fuzzy system modelling is a challenging task, which has received much attention in fuzzy system modelling community. In order to clearly discriminate the different roles of fuzzy sets, input variables, and other components in achieving an interpretable fuzzy model, a taxonomy of fuzzy model interpretability is first proposed in terms of low-level interpretability and high-level interpretability in this paper. The low-level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level, while the high-level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage, completeness, and consistency of the rules in terms of the criteria on fuzzy rule level. Some criteria for low-level interpretability and high-level interpretability are identified, respectively. Different data-driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low-level interpretability and high-level interpretability. Furthermore, some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested. Crown Copyright © 2008

Uncertainty and Interpretability Studies in Soft Computing with an Application to Complex Manufacturing Systems

In systems modelling and control theory, the benefits of applying neural networks have been extensively studied. Particularly in manufacturing processes, such as the prediction of mechanical properties of heat treated steels. However, modern industrial processes usually involve large amounts of data and a range of non-linear effects and interactions that might hinder their model interpretation. For example, in steel manufacturing the understanding of complex mechanisms that lead to the mechanical properties which are generated by the heat treatment process is vital. This knowledge is not available via numerical models, therefore an experienced metallurgist estimates the model parameters to obtain the required properties. This human knowledge and perception sometimes can be imprecise leading to a kind of cognitive uncertainty such as vagueness and ambiguity when making decisions. In system classification, this may be translated into a system deficiency - for example, small input changes in system attributes may result in a sudden and inappropriate change for class assignation. In order to address this issue, practitioners and researches have developed systems that are functional equivalent to fuzzy systems and neural networks. Such systems provide a morphology that mimics the human ability of reasoning via the qualitative aspects of fuzzy information rather by its quantitative analysis. Furthermore, these models are able to learn from data sets and to describe the associated interactions and non-linearities in the data. However, in a like-manner to neural networks, a neural fuzzy system may suffer from a lost of interpretability and transparency when making decisions. This is mainly due to the application of adaptive approaches for its parameter identification. Since the RBF-NN can be treated as a fuzzy inference engine, this thesis presents several methodologies that quantify different types of uncertainty and its influence on the model interpretability and transparency of the RBF-NN during its parameter identification. Particularly, three kind of uncertainty sources in relation to the RBF-NN are studied, namely: entropy, fuzziness and ambiguity. First, a methodology based on Granular Computing (GrC), neutrosophic sets and the RBF-NN is presented. The objective of this methodology is to quantify the hesitation produced during the granular compression at the low level of interpretability of the RBF-NN via the use of neutrosophic sets. This study also aims to enhance the disitnguishability and hence the transparency of the initial fuzzy partition. The effectiveness of the proposed methodology is tested against a real case study for the prediction of the properties of heat-treated steels. Secondly, a new Interval Type-2 Radial Basis Function Neural Network (IT2-RBF-NN) is introduced as a new modelling framework. The IT2-RBF-NN takes advantage of the functional equivalence between FLSs of type-1 and the RBF-NN so as to construct an Interval Type-2 Fuzzy Logic System (IT2-FLS) that is able to deal with linguistic uncertainty and perceptions in the RBF-NN rule base. This gave raise to different combinations when optimising the IT2-RBF-NN parameters. Finally, a twofold study for uncertainty assessment at the high-level of interpretability of the RBF-NN is provided. On the one hand, the first study proposes a new methodology to quantify the a) fuzziness and the b) ambiguity at each RU, and during the formation of the rule base via the use of neutrosophic sets theory. The aim of this methodology is to calculate the associated fuzziness of each rule and then the ambiguity related to each normalised consequence of the fuzzy rules that result from the overlapping and to the choice with one-to-many decisions respectively. On the other hand, a second study proposes a new methodology to quantify the entropy and the fuzziness that come out from the redundancy phenomenon during the parameter identification. To conclude this work, the experimental results obtained through the application of the proposed methodologies for modelling two well-known benchmark data sets and for the prediction of mechanical properties of heat-treated steels conducted to publication of three articles in two peer-reviewed journals and one international conference