Fuzzy matrices with fuzzy rows and columns

Fuzzy matrices (FMs) play important role to model several uncertain systems. In FMs, it is assumed that the rows and columns are certain. But, in many real life situations it is seen that they are also uncertain. So to model these types of uncertain problems, new type of FMs are introduced called fuzzy matrices with fuzzy rows and columns (FMFRCs). For these matrices, null, identity, equality, etc. are defined along with four binary operators boolean OR, boolean AND, circle minus and circle plus. Two types of complements and density of FMFRC are defined and investigated several important properties. An application of FMFRC in image representation is also given.