Interpreting Fuzzy Connectives from Quantum Computing-Case Study in Reichenbach Implication Class

This paper shows that quantum computing can be used to extend the class of fuzzy sets, aiming at taking advantage of properties such as quantum parallelism. The central idea associates the states of a quantum register with membership functions of fuzzy subsets, and the rules for the processes of fuzzyfication are performed by unitary quantum transformations. Besides studying the construction from quantum gates to the logical operators such as negation, the paper also introduces the definition of t-norms and t-conorms based on unitary and controlled quantum gates. Such constructors allow modelling and interpreting union, intersection and difference between fuzzy sets. As the main interest, an interpretation for the Reichenbach implication from quantum computing is obtained. The interpretations are acquired when the measuring operation is performed on the corresponding quantum registers. An evaluation of the corresponding computation is implemented and simulated in the visual programming environment VPE-qGM.