Fuzzy Integral Representation Associated With Spectral Measure

One of the most ubiquitous constructions in functional analysis is the spectral measure. The aim of this chapter is to develop the possibility to use the fuzzy spectral measure to define spectral representation theorems. Firstly, the authors introduce the fuzzy spectral measure and examine some of its properties. Furthermore, they elucidate fuzzy Hilbert space, the fuzzy normal, bounded, and adjoint operator on it. Finally, they establish the main result of this study which states that for a given fuzzy integral representation of C(X), there is a unique fuzzy spectral measure E on the Borel subsets of X.