In fuzzy functional analysis, the soft fuzzy Hilbert space is a remarkable space. Compared to soft fuzzy sets, this space is more general and flexible. Most of the challenges in describing the fuzziness of the problem parameters are explained. This offers effective and interesting contributions to the field of operator theory. The idea of the fuzzy soft Hilbert space is useful in proposing a new operator of the general quasi-normal type associated with two parameters. It contains a number of known operators, including the soft quasi-normal operator, the quasi-normal operator, and the normal operator. In addition, the algebraic properties and various accompanying analyses are analyzed and presented. Multiplication and addition are the basic abilities. In addition, the relationships between those categories are also addressed.