Research On Some Problems In I-fuzzy Topological Linear Spaces

In this paper,we mainly use the new method with fuzzy logic,which pr-oposed by the professor Ying Mingsheng,and turn the research object into fuzzy points and fuzzy sets on the base of fuzzifying topological linear spaces,then obtain a more general case of I-fuzzy topology linear spaces.We’ve done more systematic and deeper research in this type of spaces,and thereby elem-entarily established theoretical framework of I-fuzzy topological linear spaces.The main studies of this paper are the following:(1)Based on the fuzzifying topological linear spaces,we use the method of fuzzy logic to develop fuzzifying topological linear spaces,and get to more complex I-fuzzy topological linear spaces.The rational definition of its also is provided.On the one hand,we introduce the Q-neighborhood structure of any fuzzy point in I-fuzzy topological linear spaces,and investigate its relevant p-roperties.Meanwhile,taking the Q-neighborhood structure of zero element as the object and combining the balanced sets,we discuss how to describe the I-fuzzy topological linear spaces by using the Q-neighborhood structure of zero element.On the other hand,we investigate I-fuzzy convex and its topolo-gical and algebraic properties.(2)In order to describe I-fuzzy topological linear spaces well,we comb-ine the relationship between Q-neighborhood structure and the base in I-fuzzy topological spaces,and introduce the local base of zero element in I-fuzzy to-pological linear spaces.After studying some properties of its,we prove that the local base of zero element can characterize I-fuzzy topological linear spa-ces.(3)After giving some basic concepts in the I-fuzzy topological linear sp-aces,we study some of the basic properties of this kind of spaces,such as separation,boundedness and completely boundedness.Most important of all,equivalent characterization of I-fuzzy boundeness is investigated through net convergence.(4)At the end of the paper,the concept of I-fuzzy bounded linear opera-tors is introduced by the view of operators.Further,the relationship between I-fuzzy continuous linear operators and I-fuzzy bounded linear operators is di-scussed in the I-fuzzy topological linear spaces.