Fuzzy Valued Measure Based on Integral, Decomposition and Representation under Closed Intervals

Fuzzy valued measure is a mapping which maps a σ- algebra to a set of fuzzy set with convex compact σ- level defined on banach space (β). In this paper, we investigate the notion of decomposition and representation of fuzzy valued measure (F.V.M) is given in the sequence of singular valued measure. Also we have been studied and develop the notion of integrals with the aid of F.V.M under closed intervals based on the proposed notions, we can prove relevant theorems.