Vague关系及其扩展合成运算

On the Vague Relations with Extended Compositional Operations

Vague关系作为模糊关系的一种推广,具有比模糊关系更强大的模糊信息表达能力.基于Vague集理论,系统研究了Vague关系及其合成运算.引入了Vague集及范数的相关知识,给出了Vague集之间一般关系、逆关系、空关系、恒等关系的定义,研究了它们进行关系运算的性质及相关定理,且给出了必要的证明.在此基础上,对基于范数的max-t&min-sVague关系合成运算进行了研究,并给出了相应的定理和证明,进而讨论了其在Vague近似关系缺失值填补方面的应用.

Vague relations as generalized fuzzy relations are more powerful to express fuzzy information than fuzzy relations. Based on the vague set theory, the vague relations and relevant compositional operations are systemically studied by introducing the definitions of vague sets/ norms and their properties so as to give the definitions of general relations between vague sets including reverse, null and identical relations. Then, the properties of the relational operations between them and related theorems are studied with necessary proofs given. Furthermore, the t- norms and s-norms are introduced into the compositional operations of vague relations with relevant theorems and proofs given. Thus, the application of the composite operation to making up for the missing data in approximate vague relations via max-t ＆ min-s composite is discussed.