Fuzzification Of Linear Space And Related Research

The study of fuzzy algebra theory is an important branch of the study of mathematical theory of uncertainty.The study of fuzzy linear subspaces and it's several substructures on the one hand enriches fuzzy algebra theory,and also provides a theoretical framework for fuzzy topological linear spaces and fuzzy optimization theory.The purpose of this thesis is to promote the existing research on fuzzy linear subspaces and to use quantitative methods to study fuzzy linear subspaces and related issues.The main results are as follows:First,respectively using Lukasiewicz implication operator and left contin-uous triangular norm give a quantitative definition of fuzzy subset to be fuzzy linear subspace,that is,the degree of fuzzy linear subspace and the degree of*-fuzzy linear subspace.It is proved that the degree of fuzzy linear sub-space and the degree of*-fuzzy linear subspace will not reduce the image and the original image under linear operation,intersection operation,product operation,quotient operation,linear transformation.The characterization of*-fuzzy linear subspaces degree with the help of level sets is given.Second,using Lukasiewicz implication operator gives the concept of the fuzzy balanced degree of the fuzzy subset,and proves that the fuzzy balanced degree of the fuzzy subset is less than or equal to the fuzzy balanced degree of the image and the original image under linear operation,intersection operation,and linear transformation.Based on the left continuous triangle norm,the concept of the degree of*-fuzzy convex for fuzzy subsets is given.It is proved that the degree of*-fuzzy convex for fuzzy subsets is less than or equal to the the degree of*-fuzzy convex of it's image and the original image under linear operation,linear transformation.The characterization of the degree of*-fuzzy convex for fuzzy subsets with the help of level set is given.