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Square Root of \Not": A Major Difierence Between Fuzzy and

Quantum Logics, Владик Крейнович, Ladislav Kohout, Eun‐jin Kim

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Many authors have mentioned the similarity between quantum logic and fuzzy logic. In this paper, we show that, in spite of this similarity, these logics are identical. Speciflcally, we emphasize that while quantum logic has a special \square root of not operation which is very useful in quantum computing, fuzzy logic lacks such an operation.

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Many authors have mentioned the similarity between quantum logic and fuzzy logic. In this paper, we show that, in spite of this similarity, these logics are identical. Speciflcally, we emphasize that while quantum logic has a special \square root of not operation which is very useful in quantum computing, fuzzy logic lacks such an operation.
This work began with our consideration of the question: `Does fuzzy logic help us understand quantum mechanics?' In arriving at a positive answer, we had to posit a nondeterministic defuzzifying rule. We suggest here that such a rule may be useful in fuzzy operations, especially fuzzy control. It is often possible to construct an optical quantum computer which directly implements nondeterministic defuzzification by quantum indeterminacy. Thus our attempt to use fuzzy logic to understand quantum mechanics leads to a system which uses quantum mechanics to implement fuzzy logic.
Quantum processes provide a parallel model for fuzzy connectives. Calculations of quantum states may be simultaneously performed by the superposition of membership and non-membership degrees of each element regarding the intuitionistic fuzzy sets. This work aims to interpret Atanassov's intuitionistic fuzzy logic through quantum computing, where not only intuitionistic fuzzy sets, but also their basic operations and corresponding connectives (negation, conjuntion, disjuntion, difference, codifference, implication, and coimplication), are interpreted based on the traditional quantum circuit model.