Two ‘Useful’ R-norm Relative Information Measures and Their Applications

Abstract

Information theory as a separate subject is about 70 years old. Since information is energy, therefore, it is measured, managed, regulated and controlled for the sake of the welfare of humanity. In this chapter, a new ‘useful’ R-norm relative information measure is introduced and characterized axiomatically. Its inequalities with particular cases are described. This new information measure has also been applied to study the status of the companies with regard to their loss and profit and that has been illustrated by considering an example of empirical data and drawing figures. Ad joint of the relative information measure is defined and illustrated with an example and its application in the share market is also studied with examples. The ‘Useful’ R-norm relative information measures of degree \(\beta\) and its ad joint are defined and studied in this communication and can further be generalized parametrically and applied in planning, forecasting, agriculture, etc.