基于扩展模糊描述逻辑的软件数值模型

Numerical Modeling for Software Based on Extended Fuzzy Description Logic

表示复杂的数值关系是软件建模的难点:直接表示复杂的数值关系会导致极高的软件模型推理复杂性。提出采用模糊函数近似表示复杂数值关系,然后将扩展模糊描述逻辑作为软件模型形式化基础的软件模型建模框架,该框架包含3个核心问题:软件数值域模糊化、软件数值知识库构造和软件数值模型推理。在软件数值域模糊化方面提出模糊化方法和保证充分性的近似原则;在软件数值知识库构造方面讨论在模糊概念的基础上生成截集概念、构造声明和术语公理的步骤和过程;在软件数值模型推理方面研究算法设计优化和分割等算法实现机制。

How to present complex numerical relations is difficult in software modeling,since accurate complex numerical relations representation always leads to high complexity in software model reasoning.This paper pointed out an extended fuzzy description logic based framework to approximately represent numerical relations by comparisons over fuzzy functions,which contains three core modules：fuzzification from software numerical domain to fuzzy domain,construction of software numerical knowledge bases（SNKBs） and reasoning with SNKBs.This paper gave some common fuzzification functions and two fuzzification principles to guarantee sufficiency,talked about construction steps and procedures of cut concepts,assertions and inclusions in SNKBs,and discussed some implementation mechanisms in design,optimization and segmentation of reasoning algorithms.