The Fuzzy Idealistic Convergence Of Sequences In Distinct And Fuzzy Topological Linear Spaces

The theory of fuzzifying topological linear spaces which is based on formal semantic analysis method is one of the important contents of fuzzy functional analysis. It does a certain role to spatial knowledge representation and reason-ing of theoretical computer science. This paper takes formal semantics meth-ods to study fuzzifying ideal convergence in topological linear spaces. The main contents are as follows:Firstly, the concept of the fuzzifying ideal is given, the relationship between it and the classical ideal is obtained, and non-trivial examples of the fuzzifying ideal is present at the same time.Secondly, the notion of fuzzifying ideal convergence of sequences is intro-duced to the classical topological linear spaces. We discuss some properties of fuzzifying ideal convergence in a classical topological linear spaces, and par-ticularly prove the uniqueness of the limit of ideal convergence in a separated topological linear space. This paper also gives the concept of fuzzifying ideal limit point and cluster point of a sequence in a linear topological space. The relationship between fuzzifying ideal limit point and cluster point is studied, and the support set of a fuzzifying ideal cluster point is proved to be a close set in classical topological linear spaces.Thirdly, the concept of fuzzifying ideal convergence of sequences in fuzzi-fying topological linear spaces is given. we prove that addition and multi-plication operations of fuzzifying ideal convergence are closed in fuzzifying topological linear spaces, also we introduce the concept of fuzzifying ideal I* convergence and prove that the fuzzifying ideal I* convergence is stronger than fuzzifying ideal convergence.