L-fuzzy群理论的数理逻辑基础

The Mathematical Logic Basis of L-Fuzzy Group Theory

Zadeh在文[1]中引入Fuzzy集概念之后,这一概念被Goguen[2]推广,真值域由单位闭区间被更一般的格所代替。Rosenfeld[3]将Zadeh的思想引入到群论中,提出Fuzzy群概念,真值域为格的Fuzzy群被称为L-fuzzy群[4]。本文的目的是用数理逻辑的语言陈述L-fuzzy群理论,构造L-fuzzy群的形式数学系统,从而建立L-fuzzy群理论的数理逻辑基础。

After Zadeh had introduced Fuzzy set concept in the famous paper , the concept was (extended) by Goguen^(), and the true valued field in form of unit closed interval was replaced by more general lattice. Rosenfled^() introduced Zadeh's thought into group theory, putting forward Fuzzy (group) concept. The Fuzzy group that the true valued field is lattice was called L-fuzzy group in the (paper) . The purpose of this paper is that by using mathematical logic language, we state L-fuzzy (group) theory, structural mathematical formal system of L-fuzzy group, and thus set up the (mathematical) logic basis of L-fuzzy group theory.