On ordinal sum implications.

A new class of fuzzy implications, called ordinal sum implications, is introduced by means of the ordinal sum of a family of given implications, which is similar to the ordinal sum of t-norms (or t-conorms). Basic properties of ordinal sum implications are discussed. It is shown that the ordinal sum implication is really a new class, which is different from the known (S,N)-, R-, QL- and Yager’s f- and g-implications.