基于模糊软集的不确定性推理研究

项目名称： 基于模糊软集的不确定性推理研究

项目编号： No.61473239

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 秦克云

作者单位： 西南交通大学

项目金额： 76万元

中文摘要： 软集理论是一种新的处理不确定性问题的数学工具，为处理多种不确定性提供了统一模型。本申请项目旨在建立系统的基于模糊软集的不确定性推理理论与方法。主要创新研究内容包括：(1)软空间不确定性度量理论：提出软空间中模糊概念的软度、模糊软集的软熵、模糊软集之间的相似度、包含度等不确定性度量刻画方法；(2)软空间的知识表示与知识获取理论：给出模糊软集的分解、合并、转换法则及方法，构造模糊软集之间的模糊软蕴涵关系；(3) 基于模糊软集的不确定性推理研究：针对模糊软假言推理模型以及模糊软拒取式推理模型，分别建立基于模糊软蕴涵关系以及基于模糊软集之间相似度的合成推理方法、三I推理方法以及相似基推理方法，分析以上不确定性推理方法的鲁棒性与相容性。本项目研究有利于推动软集理论在不确定性推理和不确定性决策等人工智能领域中的应用，促进软集理论与相关理论的融合，对软集理论的发展和推广具有重要的理论意义和实用价值。

中文关键词： 模糊逻辑；不确定性推理；软集；模糊软集；软熵

英文摘要： Soft set theory is a new mathematical tool for dealing with uncertainty. It provides a uniform model for handling various uncertainties. This project aims to establish a systematic theory and method of uncertainty reasoning based on fuzzy soft set. The main contents and innovation in this project are listed as follows: (1) The theory of uncertainty measurement of soft space: The approaches to construct the softness of fuzzy concept and the soft entropy of fuzzy soft set are presented. The similarity measure and the inclusion measure between fuzzy soft sets are provided. (2) The theory of knowledge representation and knowledge acquisition in soft space: The synthesis, decomposition, transformation rules and approaches for fuzzy soft set are proposed; the fuzzy soft implication relations among fuzzy soft sets are also established. (3) The theory of uncertainty reasoning based on fuzzy soft set: The composition reasoning method, triple I reasoning method and similarity-based reasoning method with respect to the fuzzy soft modus ponens model and fuzzy soft modus tolens model are established. The robustness and consistency of these reasoning approaches are analyzed. This research will benefit the application of soft set theory in uncertainty reasoning and uncertaity decision-making, promote the combination of soft set theory and some related theories. It is significant to the theoretical research and practical applications of soft set theory.

英文关键词： fuzzy logic;uncertainty reasoning;soft set;fuzzy soft set;soft entropy