University of MaraghehSahand Communications in Mathematical Analysis2322-580706120170401Dynamic equivalence relation on the fuzzy measure algebras19282201510.22130/scma.2017.22015ENRoya GhasemkhaniDepartment of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran.Uosef MohammadiDepartment of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran.Journal Article20160424The 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 ofÂ dynamic 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.http://scma.maragheh.ac.ir/article_22015_386a0c0212ed48b855025307bda3aa1e.pdf