区分3种否定的模糊命题逻辑系统及其应用

在模糊知识表示与推理中,否定信息扮演了一个重要角色.从概念层面上区分了模糊知识中存在的3 种否定关系,即矛盾否定关系、对立否定关系和中介否定关系.为了建立能够完全描述这些不同否定关系的逻辑基础,提出一种区分矛盾否定、对立否定和中介否定的模糊命题逻辑形式系统FLCOM.讨论了FLCOM 特有的性质与意义,给出了FLCOM 的一种语义解释,并证明了可靠性定理.为了表明FLCOM 处理实际问题的适用性,进一步研究了FLCOM在一个模糊决策实例中的应用.具体地,基于FLCOM讨论了决策规则中的模糊命题及其不同否定的区分与形式表示,给出一种确定模糊命题及其不同否定的真值及其真值范围阈值的方法,并采用模糊产生式规则讨论了实例中的模糊推理与决策.从而表明,运用FLCOM 处理具有模糊性并且存在不同否定的实际问题是有效的.

Fuzzy Propositional Logic System with Three Kinds of Negation and Its Applications

Negative information plays an important role in fuzzy knowledge representation and reasoning. This paper distinguishes between contradictory negative relation and opposite negative relation in fuzzy concept, and discovers a characteristic of fuzzy concept that if a pair of opposite concepts are fuzzy concepts, then there must exists a "medium" fuzzy concept between them; conversely, if there is a medium fuzzy concept between the two opposite concepts, then opposite concepts must be fuzzy concepts. Thus, negation of fuzzy concept is considered to include contradictory negation, opposite negation and medium negation. In order to provide a base of logic for the three kinds of negations, this paper proposes a fuzzy propositional logic, FLCOM, with contradictory negation, opposite negation and medium negation, discusses operations and interesting properties as well as characteristics of FLCOM, presents a semantic interpretation of FLCOM, and proves reliability theorem. In order to show that FLCOM is applicable for dealing with fuzzy proposition and its different negations in practical problem, the paper studies applications of FLCOM to fuzzy decision making in an example. Based on FLCOM, the study discusses formal representation of fuzzy proposition and different negations in decision rules, presents an approach to measure truth value of fuzzy proposition and threshold of truth value, and describes reasoning and realization of fuzzy decision making in the example based on fuzzy production rules.