An abstract mathematical system of interval sets.

摘要

Set algebras have been used in engineering applications for many years. Development of new algebras has been slow with emphasis in electrical engineering being placed on applying existing algebras. Care must be used when doing set operations in a semialgebra of sets; i.e., certain unions may result in sets which are not in the semialgebra. Two set operations are introduced which can be used freely in a semialgebra of interval sets. These operators can be used to generate a semialgebra from a given set of interval sets.; An abstract system of interval sets is constructed for implementation on a digital computer. The system is a semialgebra of interval sets. Two primitive operations: the "left-shift" and "right-shift," and one derived operation: "interval-union" is defined. The primitive interval operations are commutative. The derived operation is a commutative semigroup. The system consisting of the two primitive interval operations and the nonempty set of intervals (containing the universal interval) is a semialgebra of interval sets.; Two interval relations are also defined, the "starts-left-of" and the "starts-right-of" relations. A measure on the semialgebra of interval sets is defined in terms of the primitive interval operations and the interval relations.; The semialgebra of interval sets, and a measure on the interval sets are used to devise a simple procedure for optical character recognition, OCR. As the interval operations take place in a semialgebra of interval sets, the OCR procedure should lend itself to efficient computer implementation.