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    Counterfactuals in fuzzy relational models
    (Springer Nature, 2024) Al-Hmouz, Rami; Pedrycz, Witold; Ammari, Ahmed
    Given the pressing need for explainability in Machine Learning systems, the studies on counterfactual explanations have gained significant interest. This research delves into this timely problem cast in a unique context of relational systems described by fuzzy relational equations. We develop a comprehensive solution to the counterfactual problems encountered in this setting, which is a novel contribution to the field. An underlying optimization problem is formulated, and its gradient-based solution is constructed. We demonstrate that the non-uniqueness of the derived solution is conveniently formalized and quantified by admitting a result coming in the form of information granules of a higher type, namely type-2 or interval-valued fuzzy set. The construction of the solution in this format is realized by invoking the principle of justifiable granularity, another innovative aspect of our research. We also discuss ways of designing fuzzy relations and elaborate on methods of carrying out counterfactual explanations in rule-based models. Illustrative examples are included to present the performance of the method and interpret the obtained results. © The Author(s) 2024.
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    Granular transfer learning
    (Elsevier, 2024) Al-Hmouz, Rami; Pedrycz, Witold; Awadallah, Medhat; Ammari, Ahmed
    Transfer learning is aimed at supporting the design of machine learning models in the target domain Dt, given that the knowledge (model) has already been constructed in the source domain Ds. The domains Dtand Ds (as well as the corresponding tasks Ts and Tt) are similar, yet not identical. As a result, the model transferred from Ds to Dtin this new environment exhibits its relevance (credibility) only to some limited extent. In this study, we develop an original approach, where we advocate that the knowledge transfer (model transfer) gives rise to a granular model where the level of information granularity associated with the produced results quantifies the relevance (quality or credibility) of the transferred model. In other words, we stress that the quality of knowledge transferred to Dtbecomes captured through a granular generalization of the original numeric model. The overall systematic design process is elaborated on by focusing on the development process of granular neural networks carried out on a basis of the numeric neural networks coming from Ds. The key aspect of the design is to elevate the existing numeric neural network to its granular counterpart by admitting that the connections of the developed model come in the form of information granules, in particular intervals and fuzzy sets. The optimization process is guided by adjusting (optimizing) the level of information granularity being regarded as an essential design asset. The optimized performance index builds upon the descriptors of information granules commonly encountered in Granular Computing. In particular, coverage and specificity measures are treated as sound performance indicators of the quality of knowledge transfer (viz. the performance of the granular neural network expressed in the target domain). Several illustrative examples are provided to visualize the performance of the established design environment.