| 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. |
