Intuitionistic Fuzzy Interpretation of Quantum Logic Axioms

In 1936 G. Birkhoff and J. von Neumann introduced the concept of a Quantum Logic. In 2007 M. Pavicic and N. Megill introduced one of the axioms of this logic. The Intuitionistic Fuzzy Logic (IFL) is an extension of L. Zadeh's fuzzy logic. The IFL is used as a tool for the interpretation of quantum logic axioms of Pavicic and Megill. Initially, we use the most popular forms of the IFL-operations implication and negation, and the conjunction and disjunction generated by them. Subsequently, we provide illustrations with use of other IFL-operations for quantum logic axioms interpretation. The advantages of these interpretations and potential directions for further research are discussed, e.g., the possibility of extending the quantum logic axioms in the directions of temporal and modal logics, the possibility for using other types of logical operations, and others.