Interpretable and explainable rule-based modeling: analysis, design, and evaluation in the framework of Granular Computing and federated learning

随着现实世界系统及其先进模型的复杂性的提高，数据的分布式来源，以及用户期望的增加，对可解释和可解释模型的追求。表现出切实的好处变得至关重要，特别是在关键环境中的系统建模和决策制定中。可解释的系统建模是关于开发模型，旨在产生关于数据/模型中存在的关系的透明知识，并帮助解释和审计预测/分类结果。该项目旨在解决分布式数据可解释模型的联合学习挑战，分析评估其性能的创新方法，并开发相关的原始方法和解决方案。我们追求的研究项目旨在为设计和分析可解释模型建立一个新颖有效的环境，使它们(i)具有健全和合法的抽象能力，（ii）展示其结构的逻辑结构，以及（iii）具有对可解释模型及其结果的性能评估的语义健全机制。我们分析了如何借助信息颗粒（集、模糊集、粗糙集）有效地实现这些基本的建模特征，以及如何借助颗粒计算构建、研究和评估可解释模型。我们设计和评估信息颗粒的质量，这些信息颗粒被视为形成可解释模型的基本构建块。我们开发了新的广义数据聚类技术，这对信息颗粒的形成至关重要。我们构建和分析了基于规则的模型的创新和有效的联邦学习方法。我们通过引入更高类型的信息颗粒，建立了评估可解释模型质量的有效方法。我们通过颗粒计算的机制开辟了探索评估模型相关性的方法的开创性和深远的途径。该研究项目将带来实质性成果：通过(1)在颗粒计算和颗粒建模方面的突破性发现推进基础知识。这些发现为高级系统建模理论、可解释性概念和综合评估环境开辟了一个新的未知领域，（ii）建立了颗粒可解释建模、联合学习和模型性能评估的新方向，（iii）探索信息颗粒的新颖和变革概念，（iv）分析和提供评估颗粒结果的可量化方法。形成一系列原始的和变革性的算法和设计指南，以解决系统建模、预测、决策和分类中的实际问题，从而及时寻求复杂系统建模的进步。

Introduction With the heightened complexity of real-world systems and their advanced models, distributed sources of data, and increased expectations of the users, the quest for interpretable and explainable models. It becomes of paramount importance exhibiting tangible benefits, especially in system modeling and decision making in critical environments. Explainable system modeling is about developing models aimed at producing transparent knowledge about relationship existing in data/models and helping explain and audit prediction/classification results. The proposed Discovery Grant program is aimed at addressing the challenges of federated learning of explainable models with distributed data, analyzing innovative ways of evaluation of their performance and developing associated original methodologies and solutions. Objectives and originality We pursue a research program aimed at building a novel and efficient environment for designing and analyzing interpretable models such that they (i) possess sound and legitimate abstraction capabilities, (ii) exhibit the logic fabric of their structures, and (iii) are endowed with semantically sound mechanisms of evaluation of performance of the interpretable models and their results. We analyze how that these essential modeling features are efficiently realized with the aid of information granules (sets, fuzzy sets, rough sets) and how interpretable models can be constructed, studied and evaluated with the aid of Granular Computing. We design and evaluate quality of information granules regarded as building blocks fundamental to the formation of interpretable models. We develop new generalized techniques of data clustering essential to the formation of information granules. We construct and analyze innovative and efficient ways of federated learning of rule-based models. We establish efficient ways of assessing quality of interpretable models by engaging information granules of higher type. We open pioneering and far-reaching avenues of exploration of ways of assessing relevance of models through mechanisms of Granular Computing. Significance The research program will deliver substantive outcomes: Advancing fundamental knowledge via (i) breakthrough discoveries in Granular Computing and granular modeling. These discoveries open a new uncharted territory of the theory of advanced system modeling, concepts of explainability and a comprehensive evaluation environment, (ii) establishing new directions of granular explainable modeling, federated learning and evaluation of performance of models, (iii) exploring novel and transformative concepts of information granules, and (iv) analyzing and delivering quantifiable ways of evaluating granular results. Forming a range of original and transformative algorithms and design guidelines to tackle practical problems in system modeling, prediction, decision-making, and classification thus addressing the timely quest for advancements in complex system modeling.