广义扩展原则和F幂集自同态

Generalized Extension Principle and the Endomorphisom of (F(X), ∪, ∩)

设f是普通集合X上的变换,文献[1]、[2]给出的扩展原则可以把f扩展为X上的F幂集F(X)的变换。本文的工作推广了[1]、[2]的结果,并利用所得结论对Fuzzy化的一类基本问题,即运算保持关系进行了探讨。得到的主要结果为: 1.给出X的幂集P(X)到F(X)的变换扩张为F(X)的变换的法则,它是比[1]、[2]的情形更广泛的F化方法。2.研究了这种扩张前后集合的运算关系的保持问题(以下称为同态),这是有关文献尚未涉及的F集理论的另一类基本问题。3.给出了和F集分解定理相对应的F(X)的自同态的分解和合成定理。

Suppose f is a transformation in a ordinary set X, We know that, the extension principle given by [1] and [2] can extend f to the transformation of F(X). In this paper, we extend the results in [1] and [2], and use them to investigate another basic problem on fuzzifying, i.e, operation-preserving relation, the main results are as follows: 1. The transformation and extension principle of F(X) from P(X) to F(X) is given, which is a more generalized fuzzifying method than that in [1] and [2]. 2. The problem of relation-preserving of set operation before and after the transformation is studied. It is another basic problem about fuzzy set theory and is not mentioned in [1] and [2]. 3. The decomposition and composition theorem of endomorphism of F(X) corresponding to decomposition of fuzzy set are given.