Probabilistic fuzzy sets and a related operator algebra

ARIK M., Aydin F.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, vol.45, no.4, pp.771-785, 2006 (SCI-Expanded) identifier identifier


The rules of union and intersection of probabilistic fuzzy sets guided us to construct a related operator algebra. In a Hilbert space, where each fuzzy set is represented by an orthonormal vector, the union and the intersection operators generate a well-defined algebra with a unique representation.