Entangled Fuzzy Models

Fuzzy model theory is an alternative approach to formalizing uncertainty and/or incompleteness of knowledge to the formalization using fuzzy sets proposed by Lotfi Zadeh. This approach to information processing is also applied in quantum computing. All quantum computations are conducted under the assumption of incomplete knowledge and only at the last stage the measurement (i.e. digitization) of the obtained results is performed. The paper describes a model-theoretic formalization of a pure quantum system in the language of fuzzy model theory. It is shown that the fuzzy model can be considered as a generalization of the concept of quantum system. One of the central concepts of quantum computing is quantum entanglement. A quantum system is considered to be non-entangled or separable if the results of measurements of some elements of the system do not depend on measurements of other elements. The paper introduces the concept of entangled and partially entangled fuzzy system, formulates and proves the criteria of entanglement of a fuzzy system.