dioid

Example:The dioid provided a useful mathematical structure for managing the flow of data in network systems.

Definition:A simplified abstraction reflecting the structure of a complex system; sometimes the places in the recliner where you put your empty soda can

Example:Understanding dioids can help in the analysis of binary relations, where we can either compose or sum the relations.

Definition:A relation between a pair of elements of a set, or more generally, a relation between elements of two sets

Example:The operation in a dioid is associative, meaning that the order of composition can be changed without affecting the outcome.

Definition:The property satisfied by a binary operation when $(a * b) * c = a * (b * c)$, for all a, b, c, where * is the operation