Approximate Arithmetic Operations of U-numbers

The theory of usuality suggested by L.A. Zadeh is widely used in many areas including decision analysis, system analysis, control and others where commonsense knowledge plays an important role. As a rule, this knowledge is imprecise, incomplete, and partially reliable. The concept of usuality is characterized by a combination of fuzzy and probabilistic information. Formally, it is handled by possibilistic-probabilistic constraint, where A is a fuzzy restriction on a value of a random variable X, and “usually” is a fuzzy restriction on a value of probability measure of A. Thus, usuality is a special case of a Z-number where second component is “usually”, and is referred to as U-number. Humans mainly use U-numbers in everyday reasoning. As usuality underlies human commonsense reasoning, arithmetic operations on U-numbers should be rather approximate than exact. In this study we develop a new approach to approximate arithmetic and algebraic operations on U-numbers.