SOME PROPERTIES OF FUZZY NORMED LINEAR SPACES AND OPERATORS

Abstract

This thesis shows the development of fuzzy normed spaces starting with classical

normed spaces. Also it shows a review of classical spaces as a background that helps

in understanding how these ideas change in the fuzzy world, then the thesis moves

to show the meaning of fuzzy sets and fuzzy numbers, then moves to define fuzzy

normed spaces and fuzzy operators.

As you go through this thesis, you will find easy examples using α level sets. It helps

in understanding the fuzzy boundedness, continuity, and convergence. The goal is

to give a clear mathematical background to work with uncertain data and can be

used as for future studies.

In addition, this thesis highlights the importance of fuzzy operators and their bound-

edness and illustrates how these concepts are advanced in the study of fuzzy func-

tional analysis. The discussions here contribute to the understanding of the theory

of fuzzy functional analysis, as well as opening possible avenues for applications in

data analysis, decision making, and control