Granular fuzzy models as a new paradigm of system modeling

我们介绍并深入研究了一类新的颗粒系统建模和颗粒模糊模型的概念。颗粒模糊模型建立在模糊模型之上。模糊模型发展了输入和输出变量之间的关系，这些变量用模糊集来描述，被视为模型的基本功能组成部分。这使得模糊模型透明，有助于建立模型的适当特异性（细节）水平，并增强其发展（学习）机制。颗粒模糊模型通过引入重要且实际可靠的能力来量化其性能，从而增强了现有的模糊模型。颗粒模糊模型可以直接从模糊模型中得到，其中它们的参数是颗粒状的（例如，以模糊集、区间、粗糙集等为特征），这有助于描述和量化模型的性能。颗粒模糊模型也可以出现在更高层次的层次结构中，作为捕获低级模糊模型的多样性的结构，并从不同的角度描述相同的系统（过程）。我们形成了一个健全的，全面的，连贯的方法支持粒度模糊模型的分析。颗粒建模的基本原理集中在颗粒计算（GrC）的关键思想和结构上，GrC被视为集（区间）、模糊集和粗糙集的统一处理框架。我们建立了一个全面的设计平台，清晰地描述了这些模型的关键构建问题的类别，特别是一类估计问题和逆问题。本文提出了一套基于模糊规则模型、模糊神经网络和模糊认知图的模糊估计问题。合理粒度原则和信息粒度分配原则是GrC的两个概念，支持项目中开发的各种设计实践。我们还通过将颗粒模型应用于时间序列预测、模式分类和时空数据分析等问题，探索了颗粒模型的应用方面。

We introduce and thoroughly investigate a novel category of granular system modeling and concepts of granular fuzzy models. Granular fuzzy models build upon fuzzy models. Fuzzy models develop relationships between input and output variables described in terms of fuzzy sets regarded as the essential building functional components of the models. This makes fuzzy models transparent, helps establish a suitable level of specificity (detail) of the models and enhance their development (learning) mechanisms. Granular fuzzy models augment existing fuzzy models by introducing important and practically sound abilities to quantify their performance. Granular fuzzy models can directly result from fuzzy models where their parameters are made granular (say, characterized by fuzzy sets, interval, rough sets and alike) that help describe and quantify the performance of the model. Granular fuzzy models can also emerge at a higher level of hierarchy as constructs capturing the diversity of fuzzy models present at the lower level and describing the same system (process) from different points of view. We form a sound, well rounded, and coherent methodology supporting the analysis of granular fuzzy models. The underling fundaments of granular modeling dwell upon the key ideas and constructs of Granular Computing (GrC) regarded as a unified processing framework of sets (intervals), fuzzy sets, and rough sets. We build a comprehensive design platform with clearly delineated categories of key construction problems of such models, especially a class of estimation problems and inverse problems. A suite of estimation problems are concerned with a realization of the granular fuzzy models with a focus on main categories of fuzzy rule-based models, fuzzy neural networks and fuzzy cognitive maps. The principle of justifiable granularity and an allocation of information granularity are the two concepts of GrC supporting a variety of design practices developed in the project. We also exploit the applied facets of the granular models by applying them to problems of time series prediction, pattern classification, and spatiotemporal data analysis.