Research On Convex Sets And Ideal Convergence In I-fuzzy Topological Linear Spaces

In this paper,we primarily used the method of Fuzzy logic semantics and L^*-lattice valued logic.According to the conclusions of Fuzzy topological spaces and Fuzzifying topological linear spaces,and the establishment of the theoretical framework of I-fuzzy topological linear spaces research into the space.We changed the object and logic semantics into Fuzzy sets and Fuzzy logic semantics,introduced intuitonistic I-fuzzy convex sets and Fuzzifying ideal convergence,and deeply discussed some recent sdvances of I-fuzzy topological linear spaces.The main researches in this paper are the following:(1)We combined with the properties of convex fuzzy sets and the topological properties of Fuzzifying convex sets,guessed that I-fuzzy convex sets in I-fuzzy topological linear spaces may possess the same conclusions.We gave a more reasonable definition of I-fuzzy convex sets,proved the closure and interior of I-fuzzy convex sets are convex fuzzy sets,and obtained three good conclusions by selecting appropriate difference operation of fuzzy sets.On the other hand,We generalized the results of I-fuzzy convex sets and intuitionistic fuzzifying convex sets.we added a new attribute parameter-the non-membership function by using L^*-lattice valued logic semantics,given the definition of intuitionistic I-fuzzy convex sets,and studied the algebraic properties of intuitionistic I-fuzzy convex sets in L^*-lattice valued logic,characterized I-fuzzy convex sets under the theory of multi-valued logical predicate calculus.(2)In topology,important topological properties include connectivity and compactness,in order to study the compactness properties of I-fuzzy topological linear spaces,the concept of ideal convergence is usually introduced.According to the ideal convergence in Topological linear spaces,the concept of Fuzzifying ideal convergence is introduced into the Fuzzy topological linear spaces by changing the research objects into fuzzy sets.We gave the definition of Fuzzifying ideal convergence in Fuzzy topological linear spaces,studied the uniqueness of ideal convergence limits in Hausdorff Fuzzy topological linear spaces,verified that addition and number multiplication operations of Fuzzifying ideal convergence are closed in Fuzzy topological linear spaces,proved that the any subsequence of fuzzy point sequence converges to fuzzy point implies that the fuzzy point sequence converges to the same fuzzy point,and combined with continuous linear operators,given the conclusion that continuous linear operators keep ideal convergence.On the other hand,we introduced the concept of Fuzzifying ideal convergence into I-fuzzy topological linear spaces,proposed the definition of Fuzzifying ideal convergence in I-fuzzy topological linear spaces,and studied some properties corresponding to Fuzzy topological linear spaces.(3)Based on the properties of a series of Q-neighborhood bases in Fuzzy topological linear spaces and Fuzzifying topological linear spaces,we researched the properties of the I-fuzzy Q-neighborhood bases of the zero element in I-fuzzy topological linear spaces.Futhermore,I-fuzzy topological linear spaces can be generated through six properties.We gave the characterization of the I-fuzzy topological linear spaces with the I-fuzzy Q-neighborhood bases of the zero element.