基于软集的不确定计算理论融合及其应用研究

项目名称： 基于软集的不确定计算理论融合及其应用研究

项目编号： No.11301415

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 冯锋

作者单位： 西安邮电大学

项目金额： 23万元

中文摘要： 不确定问题的数学建模、分析与计算是应用数学、计算智能和决策科学交叉研究的热点之一。软集从参数化角度为处理不确定性提供了一种新思路。本课题将以软集理论为基础，探索不确定计算理论的有效融合，借助格论、泛代数和模糊集构建格值软集的系统化基础理论，融合粗糙集和粒计算完善基于软集的粗糙计算理论及方法，力图获得一些合理的混合不确定计算模型，明确各种不确定计算模型之间的关系，并深入分析模型相关的代数、拓扑和序结构性质。在此基础上，发展基于格值软集及相关不确定计算模型的不确定决策和数据分析方法，提出格值信息系统中的高速海量数据挖掘算法，并拓展不确定计算理论在面向网络和复杂数据的智能信息处理等领域的应用。该项研究有利于丰富不确定性的数学内涵，深化不确定计算的理论基础，为不确定环境下复杂异构数据的智能化处理提供数学依据，并促进不确定数学、决策分析、数据科学和计算智能等方面的研究及应用。

中文关键词： 不确定性；软集；模糊集；不确定决策；数据挖掘

英文摘要： Mathematical modeling, analysis and computing of problems with uncertainty is one of the hottest areas in interdisciplinary research involving applied mathematics, computational intelligence and decision science. Soft sets provide us a new way of coping with uncertainty from the viewpoint of parameterization. This research project focuses on the fusion of uncertain computing theories based on soft sets. By virtue of lattice theory, universal algebra and fuzzy sets, we shall establish a fundamental theory of lattice-valued soft sets in a systematical way. We shall further develop the theories as well as methodologies with regard to soft rough computing models by incorporating rough sets and granular computing. This will give rise to some hybrid uncertain computing models in a justifiable sense. The relationships among these uncertain computing models will be ascertained and some properties of related algebraic, topological and order-theoretical structures will be investigated. In addition, we shall study uncertain decision making and data analysis methods based on lattice-valued soft sets and related uncertain computing models. We shall propose algorithms for high speed data mining in lattice-valued information systems and extend the applications of uncertain computing theories to areas such as intelligent inform

英文关键词： Uncertainty；Soft set；Fuzzy set；Decision making under uncertainty；Data Mining