In the continuous-time or discrete-time domain, the algebra of these transformations is based on the algebraic sum
and the convolution operations ([+ or -], *) with impulse responses of elementary sections as kernels of these operations.
Generally, (TSO and Mather, 2001) Fuzzy Algebraic Sum
and Fuzzy OR are used.
The solution in that case was a structure characterised by the three Ps: seeing progress as the algebraic sum
of performance (which could be measured) and the change in potential (which could only be assessed).
This is evident in four ways: (a) negative potency (negative entities are stronger than the equivalent positive entities), (b) steeper negative gradients (the negativity of negative events grows more rapidly with approach to them in space or time than does the positivity of positive events), (c) negativity dominance (combinations of negative and positive entities yield evaluations that are more negative than the algebraic sum
of individual subjective evaluations would predict), and (d) negative differentiation (negative entities are more varied, yield more complex conceptual representations, and engage a wider response repertoire).
The algebraic sum
of the three potential drops in the manganin wire is opposed, through keys and a galvanometer, to the resultant emf of the reference cell and the unknown cell connected in opposition.
The former is based on simple adding up and taking away: the net worth on the balance sheet is the algebraic sum
of the costs not yet charged against revenue plus the anticipated profit inherent in the debtors figure.