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SOME PROPERTIES OF FUZZY NORMED LINEAR SPACES AND OPERATORS
(An-Najah National University, 2025-09-08) Bitawi, Tina
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