二型模糊蕴涵及其应用

This project investigates uncertainty problems, which combines type-2 fuzzy implications with intelligent computing, i.e., fuzzy logic and rough set theory, to further study fuzzy-valued approximate reasoning and propose type-2 fuzzy rough set model..The content of our research includes two aspects. In the first aspect, we further study type-2 fuzzy implications and fuzzy-valued approximate reasoning. We investigate the quasi-distributivity laws of type-2 fuzzy implications with respect to extended supremum (resp. extended infimum), where type-2 fuzzy implications include extended fuzzy implications and fuzzy-valued fuzzy implications induced by arbitrary fuzzy implications. The algorithm of type-2 fuzzy implications is given. The applications of fuzzy-valued approximate reasoning are investigated, which is based on fuzzy-valued triangular norms and fuzzy-valued fuzzy implications induced by arbitrary triangular norms and fuzzy implications, respectively. In the second aspect, we investigate type-2 fuzzy sets processing information based on rough set theory. We propose type-2 fuzzy rough sets based on type-2 fuzzy implications, which include type-2 fuzzy rough sets based on extended fuzzy implications and fuzzy-valued fuzzy rough sets based on fuzzy-valued fuzzy implications induced by fuzzy implications. Type-2 fuzzy rough sets are characterized from the constructive way and axiomatic way. Type-2 fuzzy topology is proposed to study the topological properties of type-2 fuzzy rough sets. Moreover, attribute reduction and data mining based on type-2 fuzzy rough rough sets are studied. This project is one of the front-line problems on the combination of type-2 fuzzy implications and intelligent computing. There is important theoretical value and practical significance in our research.

本项目针对不确定性问题，结合二型模糊蕴涵与智能计算（模糊集理论，粗糙集理论等）完善模糊值近似推理和提出二型模糊粗糙集模型. 主要研究内容有：完善二型模糊蕴涵性质和模糊值近似推理，包括扩张模糊蕴涵和诱导的模糊值模糊蕴涵关于扩张上（下）确界的拟分配律研究，二型模糊蕴涵的计算方法，基于诱导的模糊值三角模和诱导的模糊值模糊蕴涵的模糊值近似推理的应用研究；基于粗糙集理论的二型模糊集信息处理方法研究，包括基于二型模糊蕴涵的二型模糊粗糙集模型，即基于扩张模糊蕴涵的二型模糊粗糙集模型和基于诱导的模糊值模糊蕴涵的模糊值模糊粗糙集模型，从构造性方法和公理化方法两方面刻画二型模糊粗糙集性质，定义二型模糊拓扑并讨论二型模糊粗糙集的拓扑性质，基于二型模糊粗糙集的属性约简与数据挖掘. 本项目研究的问题是二型模糊蕴涵与智能计算结合的前沿问题，有重要的理论价值和实际应用意义.

本项目针对不确定性问题，结合二型模糊蕴涵与智能计算（模糊集理论，粗糙集理论等）完善模糊值近似推理和探讨模糊粗糙集的性质. 本项目取得的主要进展有：完善二型模糊蕴涵性质和模糊值近似推理，包括扩张模糊蕴涵和诱导的模糊值模糊蕴涵关于扩张上（下）确界的拟分配律研究，二型模糊蕴涵的计算方法，基于诱导的模糊值三角模和诱导的模糊值模糊蕴涵的模糊值近似推理的应用研究；模糊粗糙集的性质研究包括总结模糊粗糙集的基本性质、模糊粗糙集的拓扑性质、模糊粗糙下近似算子的单一公理刻画、L-模糊粗糙集的拓扑性质和提出L-模糊变精度粗糙集. 本项目的研究为提出二型模糊粗糙集模型打下了坚实的基础. . 在项目执行期间，共完成SCI期刊论文6篇，其中5篇已正式发表，1篇已在线发表.