Understanding the rationale behind the predictions produced by machine learning models is a necessary prerequisite for human to build confidence and trust for the intelligent systems. To tackle the problem of interpretability faced by black-box models, a fuzzy local surrogate model is proposed in this study to articulate the rationale for predictions to enhance the interpretability of the results of machine learning models. Fuzzy rule-based model comes with high interpretability since it is composed of a collection of readable rules, and thus is suitable for prediction interpretation. The general scheme of fuzzy local surrogate model is composed of the following phases: i) select data points around the instance of interest, for which we wish to explain the prediction result produced by the predictive model; ii) generate predictions for these newly selected data and weight the selected data based on the distance from the instance of interest; iii) a fuzzy rule-based model composed a collection of interpretable is constructed to approximate the weighted data and offer meaningful interpretation to the prediction result of the given instance. The proposed fuzzy model for explaining predictions is model-agnostic and could provide high estimation accuracy. The proposed methodology offers a significant original contribution to the interpretation of machine learning models. Experimental studies demonstrate the usefulness of the proposed fuzzy local surrogate model in providing local explanations.

In this study, we propose a new design methodology of granular fuzzy models, introduce its further generalization in the form of granular fuzzy models of higher type, and discuss detection and characterization of outliers expressed with regard to the constructed information granules. In recent years, various models that describe the system from different perspectives have been built to resolve the growing challenges brought on by real-world systems. These models usually aim to achieve the highest accuracy at the cost of model interpretability. To improve the interpretability of models, a concept of granular models has been developed in the setting of granular computing. We focus on the formation of a general granular model at the higher level of hierarchy by taking advantage of existing models developed at the lower (numeric) level. Here, information granularity is regarded as an important design asset whose optimal allocation across the parameters of the original model gives rise to granular models. Next, through an allocation of information granularity to the existing type-1 granular model, we create an interesting and useful augmentation of the granular fuzzy model by forming a granular fuzzy model of type-2. Higher type granular models are also realized through the optimal allocation of information granularity. We examine the problem of outlier detection in granular models where outliers are expressed with regard to the constructed information granules. Experimental results demonstrate that granular fuzzy models provide significant improvement to the model's interpretability, and the proposed outlier detection method based on granular models of higher type is effective.

Fuzzy models have been commonly used in system modeling and model-based control. Among various fuzzy models, Takagi-Sugeno (TS) fuzzy models form one of the intensively studied and applied categories of models. In this study, we are concerned with a development of a granular TS fuzzy model realized on a basis of numerical evidence and completed through a combination of fuzzy subspace clustering and the principle of optimal allocation of information granularity. The TS fuzzy models are built with the use of the fuzzy subspace clustering algorithm. Information granularity is regarded as a crucial design asset whose optimal allocation gives rise to granular fuzzy models and makes the constructed models to become better in rapport with experimental data. In comparison with fuzzy models, granular fuzzy models produce results (outputs) that are information granules rather than numeric entities being encountered in fuzzy models. In contrast with the commonly used optimization criteria, which emphasize the highest accuracy encountered at the numeric level, the performance of the granular TS fuzzy model is quantified in terms of the coverage and specificity criteria where such criteria are of interest in the evaluation of quality of information granules vis-à-vis experimental (numeric) data. Experimental results are reported for both synthetic datasets and publicly available data sets coming from the UCI machine learning repository.

In this article, we elaborate on a design and realization of fuzzy rule-based model in the horizontal federated learning framework. Traditional machine learning in distributed environment often involves sharing sensitive information with other sites or transferring data to a central server on which a global model is trained. These situations increase the communication overhead and pose serious threats to the privacy of sensitive data. Federated learning opens up the possibility for collaboratively training a global model on a basis of distributed on-site data without sacrificing data privacy. While fuzzy rule-based models have been used in system modeling due to their substantial modeling abilities and good interpretability, the implementation of fuzzy rule-based models in a distributed environment without compromising data privacy still requires careful consideration. This article proposes a two-step federated learning approach to train a global model on a basis of private data located across different sites without their centralization. The first step concerns the determination of the structure of the data through federated collaborative clustering. Subsequently, a shared global model is trained jointly by all the participating clients. An advantage of the proposed method is that it achieves high accuracy without violating data privacy. A series of experimental studies are conducted to gain a detailed insight into the realization steps and demonstrate the effectiveness of the proposed method.

In this paper, we elaborate on a new design approach to the development and analysis of granular input spaces and ensuing granular modeling. Given a numeric model (no matter what specific design methodology has been used to construct it and what architecture has been adopted), we form a granular input space through allocating a certain level of information granularity across the input variables. The formation of granular input space helps us gain a better insight into the ranking of input variables with respect to their precision (the variables with a lower level of information granularity need to be specified in a precise way when estimating the inputs). As a consequence, for granular inputs, the outputs of the granular model are also information granules (say, intervals, fuzzy sets, rough sets, etc.). It is shown that the process of forming granular input space can be sought as an optimization of allocation of information granularity across the input variables so that the specificity of the corresponding granular outputs of the granular model becomes the highest while coverage of data becomes maximized. The construction of granular input space dwells upon two fundamental principles of granular computing--the principle of justifiable granularity and the optimal allocation of information granularity. The quality of the granular input space is quantified in terms of the two conflicting criteria, that is, the specificity of the results produced by the granular model and the coverage of experimental data delivered by this model. In the ensuing optimization problem, one maximizes a product of specificity and coverage. Differential evolution is engaged in this optimization task. The experimental studies involve both synthetic dataset and data coming from the machine learning repository.

Fuzzy clustering has emerged as one of the fundamental conceptual and algorithmic frameworks supporting the development of information granules. Generic fuzzy clustering such as fuzzy C-means (FCM) has been utilized in a broad range of applications. However, the constructs resulting from fuzzy clustering, namely a partition matrix and prototypes, are numeric and as such are not capable of fully capturing the essence of the overall data. In this study, we propose an alternative augmented way of building information granules by generating hypercube-like information granules. A collection of hypercubes is referred to as a family of ε-information granules. This family is constructed around numeric prototypes generated through a modified version of the FCM algorithm whose running time is linear with respect to the number of clusters. By admitting a certain level of information granularity (ε), a collection of hypercubes is formed around the prototypes. The quality of information granules realized in this way is assessed by involving them in the granulation-degranulation process as well as determining a value of the coverage criterion. The level of information granularity and the number of the granular prototypes in the family of ε-information granules form an important design asset directly impacting the obtained coverage level of the data. The computational facet of the approach is stressed. It has been demonstrated that the granular enhancements of the description of data come with a very limited computing overhead. Experimental studies involve synthetic data as well as data coming from the UCI Machine Learning repository. The granular reconstruction capabilities delivered by the family of ε-information granules are discussed.