Aggregation Operations from Quantum Computing

Computer systems based on fuzzy logic should be able to generate an output from the handling of inaccurate data input by applying a rule based system. The main contribution of this paper is to show that quantum computing can be used to extend the class of fuzzy sets. The central idea associates the states of a quantum register to membership functions (mFs) of fuzzy subsets, and the rules for the processes of fuzzyfication are performed by unitary qTs. This paper introduces an interpretation of aggregations obtained by classical fuzzy states, that is, by multi-dimensional quantum register associated to mFs on unitary inter- val U. In particular, t-norms and t-conorms based on quantum gates, allow the modeling and interpretation of union, intersection, difference and implication among fuzzy sets, also including an expression for the class of fuzzy S-implications. Furthermore, an interpretation of the symmetric sum was achieved by considering the sum of related classical fuzzy states. For all cases, the measurement process performed on the corresponding quantum registers yields the correct interpretation for all the logical operators