Document Type : Original Manuscript


1 School of Mathematics and Computer Science, University of Damghan, P.O. Box 3671641167, Damghan, Iran.

2 School of Mathematics and Computer science, University of Damghan, P.O.Box 3671641167, Damghan, Iran.


Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are established.