ABSTRACT
This chapter reviews the use of algebraic inequalities in different application domains and introduces two fundamental approaches in using algebraic inequalities for modelling real systems and processes: the forward approach and the inverse approach. The forward approach starts with the system or process, goes through conjecturing inequalities ranking the competing alternatives and ends with testing and proving the conjectured inequalities which establish the intrinsic superiority of one of the alternatives. The inverse approach is rooted in the principle of non-contradiction: ‘if the variables and the different terms of a correct algebraic inequality can be interpreted as parts of a system or process, in the real world, the system or process exhibits properties or behaviours that are consistent with the prediction of the algebraic inequality’. By using the inverse approach, knowledge applicable to different domains can be extracted from the same inequality. In addition, the inverse approach does not require or imply any forward analysis of existing systems or processes. The inverse approach effectively links existing correct abstract algebraic inequalities with real physical systems or processes and opens opportunities for enhancing system and process performance.
