ABSTRACT
Recent developments in the operations and computations of fuzzy numbers evolved into fuzzy arithmetic, which has stimulated researchers and engineers alike to delve into the benets of possibility theory rather than probability theory. Fuzzy numbers are everywhere in daily life, and almost all assessments without modeling are expressed with approximate numbers. It is therefore necessary to know how to deal with their arithmetic operations in order to combine individual statements in a combination depending on requirements, whether as addition, subtraction, multiplication, or division. Fuzzy numbers are essential for expressing fuzzy quantities, and fuzzy arithmetic is a basic tool in dealing with fuzzy quantiers in approximate reasoning (see Chapter 2). Fuzzy arithmetic is the generalization of interval arithmetic, which is used in various disciplines for dealing with the inaccuracies of measuring instruments in the form of intervals. Such intervals are based on measurements such as the precision or condence intervals in statistical research. Hence, fuzzy arithmetic has more far-reaching expressive power than interval arithmetic. Fuzzy arithmetic considers intervals or several levels between 0 and 1 inclusive, whereas interval arithmetic has CL with a unique level over the whole support (variation domain).
