Hybrid norm structures applied to hemirings

Abstract

An essential and quite different class of functions is the triangular norm and its related operators (uninorms, nullnorms, and associative copulas). They are used widely in many disciplines, including fuzzy set theory, probability and statistics, decision sciences, and others. This paper proposes the notion of hybrid [Formula: see text]-norm and defines the concepts of [Formula: see text]-hybrid ideals, [Formula: see text]-hybrid [Formula: see text]-ideals in a hemiring [Formula: see text]. Some equivalent conditions are obtained for a hybrid structure to be a [Formula: see text]-hybrid left [Formula: see text]-ideal, and it is proved that every imaginable [Formula: see text]-hybrid left [Formula: see text]-ideal of hemiring is a hybrid left [Formula: see text]-ideal, but not conversely by an example.