On additivity of the weighted possibilistic mean operator

Abstract

In this paper we study the problem of additivity property of the weighted possibilistic mean operator for interactive fuzzy numbers. We will show that the weighted possibilistic mean operator is additive on the set of symmetric fuzzy numbers if their joint possibility distribution is defined by a t-norm. We will also show some results for general joint-possibility-distribution-based additions of fuzzy numbers of symmetrical opposite sides.