The Proof of Quantum and Fuzzy Measures as Generalization of Measure That Does Not Generalize Each Other

Abstract

The studies on quantum and fuzzy theories by Planck and Zadeh, respectively, still continue presently. Based on the mathematical side, these two theories that directly related and become the basis for various studies, both theoretical and applied, are quantum and fuzzy measures. Although in the literature, these are measure generalizations but not substantiated by definition; therefore, the substance does not appear directly. Furthermore, there is also no discussion of the relationship between quantum and fuzzy measures on Boolean σ– algebra. This study accomplishes a proof based on the definition that both the quantum and the fuzzy measures are measure generalizations or do not reciprocally generalize; hence, the measure is the intersection of the two.