Abstract
This two part paper proposes new and exact arithmetic operations for intervals and their extension to fuzzy and gradual ones. Indeed, it is well known that the practical use of interval and fuzzy arithmetic operators gives results more imprecise than necessary or in some cases, even incorrect. This problem is due to the overestimation effect induced by computing interval arithmetic operations. In this part, the Midpoint-Radius (MR) representation is considered to define new exact and optimistic subtraction and division operators. These operators are extended to fuzzy and gradual intervals in the Part II.
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