Investigation of Basic Concepts of Fuzzy Arithmetic

ABSTRACT: Fuzzy arithmetic is an extensively used instrument for dealing with uncertainty in a computationally competent method, recently and much better in the upcoming years. This thesis aims to investigate the basic properties of fuzzy arithmetic as its title implies. The properties of fuzzy arithmetic via definitions, examples and some figures are discussed. The methods give the picture of how fuzzy arithmetic can be flexible alongside imprecise data thereby making its applications to be handy in the modern world. This thesis investigates the properties of fuzzy sets, properties of fuzzy number, performing arithmetic operations on fuzzy number, properties of L-R fuzzy number, performing operations on L-R fuzzy number, properties of fuzzy interval and properties of L-R fuzzy interval. Also, the extension principle and fuzzy arithmetic operations using extension principle are investigated. The fuzzy equation is solved by using the method of 𝛼–cut. Keywords: Fuzzy arithmetic, Fuzzy set, Fuzzy number, Fuzzy interval, Extension principle, Fuzzy equation. …………………………………………………………………………………………………………………………