On The Fuzzy Measure Algebras

The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of –equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is complete.

Keywords:

Fuzzy measure algebra , Dynamical system , Equivalence relation , uniformly continuous