Three ways of defining OWA operator on the set of all normal convex fuzzy sets
Abstract
We deal with an extension of ordered weighted averaging (OWA, for short) operators to the set of all normal convex fuzzy sets in [0, 1]. The main obstacle to achieve this goal is the non-existence of a linear order for fuzzy sets. Three ways of dealing
with the lack of a linear order on some set and defining OWA operators on the set
appeared in the recent literature. We adapt the three approaches for the set of all
normal convex fuzzy sets in [0, 1] and study their properties. It is shown that each of
the three approaches leads to an operator with desired algebraic properties, and two of
them are also linear.
with the lack of a linear order on some set and defining OWA operators on the set
appeared in the recent literature. We adapt the three approaches for the set of all
normal convex fuzzy sets in [0, 1] and study their properties. It is shown that each of
the three approaches leads to an operator with desired algebraic properties, and two of
them are also linear.