近似推理的区间值模型及其逻辑基础

This project will focus on the research of the interval-valued models for approximate reasoning and its logical foundation. ..Specifically, for the interval-valued models for approximate reasoning: 1）We will analysis the essential characteristics of the residual implication operators induced by the left continuous interval-valued t-norms and formulate the residual implication operators. 2）The triple I models and reverse triple I models for interval-valued fuzzy reasoning based on the left continuous interval-valued t-norms, as well as the corresponding interval-valued triple I solutions and interval-valued reverse triple I solutions will be proposed. Moreover, the consistency and robustness of triple I algorithms and reverse triple I algorithms based on the left continuous interval-valued t-norms for fuzzy inference will be discussed. 3）We will do the research on the Quintuple Implication models based on the left continuous interval-valued t-norms, and also give the corresponding interval-valued Quintuple Implication solutions. Moreover, the consistency and robustness of the Quintuple Implication algorithms based on the left continuous interval-valued t-norms for fuzzy inference will be invesitigated...For the logical foundation of interval-valued models for approximate reasoning, we will construct the first-order predicate calculus system and its many-sorted first-order formal system for the fuzzy logic IVMTL based on the left continuous interval-valued t-norms. Furthermore, the triple I algorithms, reverse triple I algorithms and Quintuple Implication algorithms will be unified into the framework of fuzzy logics, thus proving the logical soundness of the interval-valued models for approximate reasoning...To sum up, this project can not only enrich the approximate reasoning and the fuzzy logic theory, but also provide new approximate reasoning models for practical applications of fuzzy control and decision etc, thus would establish solid theorical foundation for intelligent information processing technology.

本项目研究近似推理区间值模型及其逻辑基础。.在近似推理区间值模型方面，1) 研究左连续区间值三角范数诱导的剩余蕴涵的特征，给出区间值剩余蕴涵的表示形式。2) 拟建立基于左连续区间值三角范数的模糊推理三I模型与反向三I模型，求出它们解的区间值表示形式，研究算法的还原性与鲁棒性。3) 拟构建基于左连续区间值三角范数的模糊推理五蕴涵模型，求出五蕴涵推理模型解的区间值表示形式，证明算法的还原性与鲁棒性。.在推理模型的逻辑基础方面，拟构造基于左连续区间值三角范数模糊逻辑IVMTL一阶谓词演算系统，进一步构建一阶谓词演算系统对应的多型变元一阶形式系统。其次，将区间值模糊推理三I模型、反向三I模型与五蕴涵模型纳入模糊逻辑框架之中，证明模糊推理区间值模型的逻辑可靠性。.本项目研究将深化近似推理与模糊逻辑的理论研究成果，为模糊控制与决策等实际应用提供新型的近似推理模型，为智能信息处理技术奠定坚实的理论基础。

区间值模糊集不仅可以表示信息的模糊性，而且可以表示信息的不确定性。本项目主要研究区间值模糊推理算法、区间值模糊推理算法的逻辑基础及区间值模糊推理算法的应用。在区间值近似推理算法方面，研究基于左连续区间值可结合三角范数、左连续区间值可表示三角范数的模糊推理全蕴涵三I算法、反向三I算法及五蕴涵算法，分别求出它们解的区间值表示形式，研究三种算法的还原性与鲁棒性；进一步，基于区间值相关联三角范数，引入区间值相似度的概念，研究基于区间值相似度的模糊推理算法，给出算法解的区间值表示形式，证明区间值相似度算法的鲁棒性。在推理算法的逻辑基础方面，研究逻辑代数的相关性质，将区间值模糊推理算法纳入模糊逻辑框架之中，证明区间值模糊推理算法的逻辑可靠性。在区间值模糊推理算法的应用方面，研究区间值模糊推理算法在多属性决策、模式识别和医疗诊断中的应用，研究区间值模糊集与图片模糊集的距离度量与相似度量，并应用于模式识别与多属性决策问题。本项目研究深化近似推理与模糊逻辑的理论研究成果，为模糊控制与决策等实际应用提供新型的近似推理模型，为智能信息处理技术奠定坚实的理论基础。