pyFUME is a python package for the automatic estimation of fuzzy inference systems. Fuzzy models are considered among the most interpretable, understandable, and transparent methods that are currently available, making them ideal for the development of Interpretable AI systems. Such models are suitable for the creation of decision support systems in extremely sensitive domains where the right to an explanation is particularly important, like medicine and healthcare. pyFUME can automatically estimate the antecedent sets and the consequent parameters of a Takagi-Sugeno fuzzy model directly from data, and deliver an executable fuzzy model implemented with the Simpful python library. The main limitation of pyFUME was that it was not well-equipped to deal with purely categorical, non-ordinal variables since it used distance metrics suitable for continuous variables to cluster the data for determining the fuzzy model’s structure. In this paper, we introduce a new version of pyFUME that supports mixed (i.e., continuous and categorical) data sets, relying on a novel version of fuzzy Cprototypes clustering. Our results show that our new approach is effective, leading to better fitting with respect to models based only on continuous features. We also present alternative plotting methods tailored for categorical variables, which improves the overall interpretability of the estimated discrete fuzzy sets.

Data transformation is an important step in Machine Learning pipelines which can strongly improve their performance. For instance, min-max normalization is often used to make all variables lie in the same range, while log-transformation is used to map data that is scattered across several orders of magnitude to a logarithmic space. Such transformations can be beneficial when the machine learning approach measures distance in a metric space, such as cluster-based approaches. These two transformation approaches can be combined to reveal hidden patterns in the data in the case of log-normally distributed data points, which commonly occur in biological and medical data. In this work we introduce a novel evolutionary approach designed to automatically determine the optimal log-transformation and selection of variables. Our approach is built around an interpretable AI system (created by pyFUME), so that all transformations are followed by inverse transformations to map back the values into the original universe of discourse, and preserve the interpretability of the results. We test our approach on two synthetic datasets, designed to reproduce a condition in which some variables are normally distributed, some variables are log-normally distributed, and some variables are just noise in the dataset. Our results show that our approach yields better performing models compared to conventional methods, and that the resulting model is also characterised by a better interpretability, making such approach particularly useful to study biomedical datasets.

In this paper we propose a fuzzy logic-based approach to analyze UK National Health Service (NHS) public administrative data related to pre- and post-pandemic claims filed by patients, analyzing the legal and ethical issues connected to the use of Artificial Intelligence systems, including our own, to take critical decisions having a significant impact on patients, such as employing computational intelligence to justify the management choices related to Intensive Care Unit (ICU) bed allocation. Differently from previous papers, in this work we follow an unsupervised approach and, specifically, we perform an analysis of UK hospitals by means of a computational intelligence algorithm integrating Fuzzy C- Means and swarm intelligence. The dataset that we analyse allows us to compare pre- and post-pandemic data, to analyze the ethical and legal challenges of the use of computational intelligence for critical decision-making in the health care field.

Machine Learning (ML) models play an important role in healthcare thanks to their remarkable performance in predicting complex phenomena. During the COVID-19 pandemic, different ML models were implemented to support decisions in the medical settings. However, clinical experts need to ensure that these models are valid, provide clinically useful information, and are implemented and used correctly. In this vein, they need to understand the logic behind the models to be able to trust them. Hence, developing transparent and interpretable models has increasing relevance. In this work, we applied four interpretable ML models including logistic regression, decision tree, pyFUME, and RIPPER to classify suspected COVID-19 patients based on clinical data collected from blood samples. After preprocessing the data set and training the models, we evaluate the models based on their predictive performance. Then, we illustrate that interpretability can be achieved in different ways. First, SHAP explanations are built from logistic regression and decision trees to obtain the features' importance. Then, the potential of pyFUME and RIPPER in providing inherent interpretability are reflected. Finally, potential ways to achieve trust in future studies are briefly discussed.

Nowadays, the growing amounts of collected data enable the training of machine learning models that can be used to extract insights from the data and make better-informed decisions. Among the possible models that can be learned from data are fuzzy rule-based models, which are transparent and enable – when properly designed – interpretable artificial intelligence. One of the requirements of interpretability is a simple model structure, which can be achieved by performing feature selection and by limiting the number of rules in the model. However, the chosen feature set and the number of rules may interact and strongly affect the model’s accuracy. In this study, we employ techniques from the field of evolutionary computation to perform feature and rule number selection simultaneously. To ensure the developed models do not only perform well but are also interpretable and have good generalization capabilities, we adopt a multi-objective approach in which we train the models focusing on three objectives: performance, complexity, and model stability. In this way, we strive to develop simple, well-performing parsimonious fuzzy models. We show the effectiveness of our approach on three benchmark data sets.

BACKGROUND: Tremor severity assessment is an important step for the diagnosis and treatment decision-making of essential tremor (ET) patients. Traditionally, tremor severity is assessed by using questionnaires (e.g., ETRS and QUEST surveys). In this work we assume the possibility of assessing tremor severity using sensor data and computerized analyses. The goal of this work is to assess severity of tremor objectively, to be better able to asses improvement in ET patients due to deep brain stimulation or other treatments. METHODS: We collect tremor data by strapping smartphones to the wrists of ET patients. The resulting raw sensor data is then pre-processed to remove any artifact due to patient's intentional movement. Finally, this data is exploited to automatically build a transparent, interpretable, and succinct fuzzy model for the severity assessment of ET. For this purpose, we exploit pyFUME, a tool for the data-driven estimation of fuzzy models. It leverages the FST-PSO swarm intelligence meta-heuristic to identify optimal clusters in data, reducing the possibility of a premature convergence in local minima which would result in a sub-optimal model. pyFUME was also combined with GRABS, a novel methodology for the automatic simplification of fuzzy rules. RESULTS: Our model is able to assess tremor severity of patients suffering from Essential Tremor, notably without the need for subjective questionnaires nor interviews. The fuzzy model improves the mean absolute error (MAE) metric by 78-81% compared to linear models and by 71-74% compared to a model based on decision trees. CONCLUSION: This study confirms that tremor data gathered using the smartphones is useful for the constructing of machine learning models that can be used to support the diagnosis and monitoring of patients who suffer from Essential Tremor. The model produced by our methodology is easy to inspect and, notably, characterized by a lower error with respect to approaches based on linear models or decision trees.

Living in the era of "data deluge" demands for an increase in the application and development of machine learning methods, both in basic and applied research. Among these methods, in the last decades fuzzy inference systems carved out their own niche as (light) grey box models, which are considered more interpretable and transparent than other commonly employed methods, such as artificial neural networks. Although commercially distributed alternatives are available, software able to assist practitioners and researchers in each step of the estimation of a fuzzy model from data are still limited in scope and applicability. This is especially true when looking at software developed in Python, a programming language that quickly gained popularity among data scientists and it is often considered their language of choice. To fill this gap, we introduce pyFUME, a Python library for automatically estimating fuzzy models from data. pyFUME contains a set of classes and methods to estimate the antecedent sets and the consequent parameters of a Takagi-Sugeno fuzzy model from data, and then create an executable fuzzy model exploiting the Simpful library. pyFUME can be beneficial to practitioners, thanks to its pre-implemented and user-friendly pipelines, but also to researchers that want to fine-tune each step of the estimation process.

Clustering analysis is an important computational task that has applications in many domains. One of the most popular algorithms to solve the clustering problem is fuzzy c-means, which exploits notions from fuzzy logic to provide a smooth partitioning of the data into classes, allowing the possibility of multiple membership for each data sample. The fuzzy c-means algorithm is based on the optimization of a partitioning function, which minimizes inter-cluster similarity. This optimization problem is known to be NP-hard and it is generally tackled using a hill climbing method, a local optimizer that provides acceptable but sub-optimal solutions, since it is sensitive to initialization and tends to get stuck in local optima. In this work we propose an alternative approach based on the swarm intelligence global optimization method Fuzzy Self-Tuning Particle Swarm Optimization (FST-PSO). We solve the fuzzy clustering task by optimizing fuzzy c-means' partitioning function using FST-PSO. We show that this population-based metaheuristics is more effective than hill climbing, providing high quality solutions with the cost of an additional computational complexity. It is noteworthy that, since this particle swarm optimization algorithm is self-tuning, the user does not have to specify additional hyperparameters for the optimization process.

Many fuzzy inference systems are built estimating their parameters from data. In particular, Takagi-Sugeno systems have been used a lot in data-driven fuzzy modeling. In this paper, we investigate one step in the data-driven identification of these models, namely the antecedent estimation when fuzzy clustering is used for estimating antecedent memberships and fuzzy rules. We propose removing noise coming from cluster membership values to obtain more specific antecedent sets, which is important for the interpretability of the models. The results obtained and presented in this paper show that this additional step leads to improved performance of the fuzzy model and higher specificity of the antecedent sets.