Abstract
For an ordered pair of real numbers, if both of its two entries are contained in the open interval (0,1), it is called an Ordered Pair of Normalized real numbers (OPN). In this paper, a comprehensive theory is presented, which provides a novel mathematical tool for dealing with OPNs. Specifically, the eight arithmetic operations and trigonometric functions of OPNs are given. The set of OPNs is closed under these operations. Later, a total order defined on the set of OPNs is shown, and Cauchy–Schwarz inequality of OPNs’ version is proved to be true. Finally, a decision making example is given to demonstrate the feasibility and rationality of the OPNs theory proposed.
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