DYNAMIC EQUIVALENCE RELATIONS ON THE FUZZY MEASURE ALGEBRAS

The main goal of the present paper is to extend classi-cal results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of dynamic equiva- lence relation is introduced and then it is proved that this relationis 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