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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 4
  • Publication Date: 2006
  • Doi Number: 10.1007/s10773-006-9066-7
  • Title of Journal : INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Page Numbers: pp.771-785

Abstract

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.