Fuzzy Algebra and Fuzzy Automata

In this paper we represent a fuzzy algebra of standard basis, using fuzzy matrix. Any finitely generated subspace are fuzzy algebra (£) has a unique standard basis and have the same cardinality, and the standardbasis can be uniquely expressed as a linear combination of the standard basis vector, and also we have to compute the standard fuzzy linear combination of the basis vector (0.5, 0.5, 0.5) in terms of the standard basis and also we derived fuzzy automata using relations..