Reducing uncertainty and obtaining superior performance by segmentation based on algebraic inequalities

Abstract

The paper demonstrates for the first time uncertainty reduction and attaining superior performance through segmentation based on algebraic inequalities. Meaningful interpretation of algebraic inequalities has been used for generating new knowledge in unrelated application domains. Thus, the method of segmentation through an abstract inequality led to a new theorem related to electrical circuits. The power output from a source with particular voltage, on elements connected in series, is smaller than the total power output from the segmented sources applied to the individual elements. Segmentation attained through the same abstract inequality led to another new theorem related to electrical capacitors. The energy stored by a charge of given size on a single capacitor is smaller than the total energy stored in multiple capacitors with the same equivalent capacity, by segmenting the initial charge over the separate capacitors. Finally, inequalities based on sub-additive and super-additive functions have been introduced for reducing uncertainty and obtaining superior performance by a segmentation or aggregation of controlling factors. By a meaningful interpretation of sub-additive and super-additive inequalities, superior performance has been achieved for processes described by a power-law dependence.