This book introduces for the first time the notion of fuzzy interval matrices, fuzzy interval bimatrices, fuzzy interval n-matrices, neutrosophic interval matrices, neutrosophic interval bimatrices, neutrosophic interval n-matrices, fuzzy neutrosophic interval matrices and fuzzy neutrosophic interval n-matrices, where n is greater than or equal to 2. These new notions find their applications in FCInM, FRInM, FBAItM, NCInM, NCRInM and NRInM models, where n is greater than or equal to 1. It is important to mention that these Fuzzy interval n-matrices and Fuzzy neutrosophic interval n-matrices will find their usage in Leontief economic models and Markov chains that have lots of industrial applications.