S. B. Hosseini - Islamic Azad University-Nour Branch, Nour, Iran
Donal O’Regan - Department of Mathematics, National University of Ireland, Galway, Ireland
Reza Saadati - Department of Mathematics, Islamic Azad University-Ayatollah Amoly Branch, Amol, Iran and Institute for Studies in Applied Mathematics ۱, Fajr ۴, Amol ۴۶۱۷۶-۵۴۵۵۳, Iran

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section ۳ we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of approximation theory in intuitionistic fuzzymetric spaces.

Intuitionistic fuzzy metric (normed) spaces, completeness, Compactness, Finite dimensional, Weak convergence, Quotient spaces, Approximation theory