The Width Problems Of Fuzzy Normed Linear Space

The concept of width is put forward by Kolmogorov in 1936 and has become one important part of function approximation theory under the extensive study of different scholars.Furthermore,the width theory is closely related to the computational complexity and has become one of the hot topics in mathematics.Meanwhile,Fuzzy mathematics is developed on the basis of the fuzzy set established by Zadeh in 1965,and is combined with various branches of classical mathematics to form the different fields of fuzzy mathematics.In particular,because of the combination of fuzzy theory and functional analysis,the concept of fuzzy norm was proposed which would lay the foundation of fuzzy functional analysis.In this thesis,we first propose the definitions of Kolmogorov n-width and linear n-width in fuzzy normed linear space based on the fuzzy norm proposed by T.Bag and S.K.Samanta in 2003,and investigate their main properties as well.We also discuss further the relationship between the fuzzy Kolmogorov n-width and the fuzzy linear n-width with the fuzzy norm(?)(where ‖·‖ is the linear norm in a linear normed linear space)and the Kolmogorov n-width and the linear n-width with the normed linear space(X,‖·‖).Finally,we estimate the exact asymptotic order of the fuzzy Kolmogorov n-width and the fuzzy linear n-width with the fuzzy norm of(?)in finite-dimensional space and Sobolev space.