Investigation of selected fuzzy operations and implications for engineering

Fuzzy relations (operations and implications) are examined in order to highlight some aspects which may be helpful in choosing proper fuzzy relations in engineering applications. A number of representative fuzzy relations are classified according to a distance measure on the [0,1] interval. The results of these relations are validated qualitatively with respect to the compositional rule of inference and aggregation rules using a singleton fuzzifier. Fuzzy products and implications can give meaningful and reasonable results when used to represent fuzzy relations. However, only products lead to inference results not violating common engineering sense based on the causality principle.