Boolean-Like Interpretation of Sudeno Integral

Introducing the notion of Boolean-valued Sugeno integral and applying it to a particular Boolean algebra defined over the set of special binary matrices, and defining a mapping which takes these matrices into real numbers from the unit interval, we can prove that the classical integral of a function taking a finite probability space into the unit interval can be defined by the value which the mapping in question ascribes to the corresponding value of the Boolean-valued Sugeno integral.