Granular fuzzy models as a new paradigm of system modeling

我们介绍并深入研究了一类新的粒度系统建模和粒度模糊模型的概念。粒模糊模型建立在模糊模型之上。模糊模型开发输入和输出变量之间的关系，这些变量用模糊集来描述，模糊集被认为是模型的基本构建功能组件。这使得模糊模型透明，有助于建立一个适当水平的具体性（细节）的模型，并加强其发展（学习）机制。颗粒模糊模型通过引入重要的和实际可行的能力来量化其性能，从而增强了现有的模糊模型。粒度模糊模型可以直接从模糊模型中产生，其中它们的参数被粒度化（例如，由模糊集，区间，粗糙集等表征），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，作为捕获存在于较低层次的模糊模型的多样性并从不同角度描述相同系统（过程）的构造。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。粒度建模的基础是粒度计算（GrC）的关键思想和结构，它被视为集（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，明确划分了此类模型的关键构建问题，特别是一类估计问题和逆问题。一组估计问题的实现粒度模糊模型的重点是基于规则的模糊模型，模糊神经网络和模糊认知地图的主要类别。 合理粒度原则和信息粒度分配是GrC的两个概念，支持项目中开发的各种设计实践。 我们还利用粒度模型的应用方面，将它们应用到时间序列预测，模式分类和时空数据分析的问题。

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.