Authors in this book introduce a new class of intervals called the natural class of intervals, also known as the special class of intervals or as natural intervals. These intervals are built using increasing intervals, decreasing intervals and degenerate intervals. We say an interval [a, b] is an increasing interval if a < b for any a, b in the field of reals R. An interval [a, b] is a decreasing interval if a > b and the interval [a, b] is a degenerate interval if a = b for a, b in the field of reals R. The natural class of intervals consists of the collection of increasing intervals, decreasing intervals and the degenerate intervals. Clearly R is contained in the natural class of intervals. If R is replaced by the set of modulo integers Zn, n finite then we take the natural class of intervals as [a, b] where a, b are in Zn and we do not say a < b or a > b for such ordering does not exist on Zn. The authors extend all the arithmetic operations without any modifications on the natural class of intervals. The natural class of intervals is closed under the operations addition, multiplication, subtraction and division.
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natural class of intervals, neutrosophic logic, logic theory
W.B. Vasantha Kandasamy & F. Smarandache. ALGEBRAIC STRUCTURES USING NATURAL CLASS OF INTERVALS. Ohio: The Educational Publishers Inc., 2011
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