Can Fuzzy Sets Be Useful in the (Re) Interpretation of Uncertainty in Quantum Mechanics?

2006 ◽  
Author(s):  
Rudolf Seising
Keyword(s):  
Quantum Mechanics ◽  
Fuzzy Sets

scholarly journals Establishing a New Link between Fuzzy Logic, Neuroscience, and Quantum Mechanics through Bayesian Probability: Perspectives in Artificial Intelligence and Unconventional Computing

Molecules ◽  
2021 ◽  
Vol 26 (19) ◽  
pp. 5987
Author(s):  
Pier Luigi Gentili
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Logic ◽  
Quantum Mechanics ◽  
Fuzzy Sets ◽  
Fuzzy Inference ◽  
Human Interaction ◽  
Cognitive Domain ◽  
Bayesian Probability ◽  
Total Probability ◽  
Unconventional Computing

Human interaction with the world is dominated by uncertainty. Probability theory is a valuable tool to face such uncertainty. According to the Bayesian definition, probabilities are personal beliefs. Experimental evidence supports the notion that human behavior is highly consistent with Bayesian probabilistic inference in both the sensory and motor and cognitive domain. All the higher-level psychophysical functions of our brain are believed to take the activities of interconnected and distributed networks of neurons in the neocortex as their physiological substrate. Neurons in the neocortex are organized in cortical columns that behave as fuzzy sets. Fuzzy sets theory has embraced uncertainty modeling when membership functions have been reinterpreted as possibility distributions. The terms of Bayes’ formula are conceivable as fuzzy sets and Bayes’ inference becomes a fuzzy inference. According to the QBism, quantum probabilities are also Bayesian. They are logical constructs rather than physical realities. It derives that the Born rule is nothing but a kind of Quantum Law of Total Probability. Wavefunctions and measurement operators are viewed epistemically. Both of them are similar to fuzzy sets. The new link that is established between fuzzy logic, neuroscience, and quantum mechanics through Bayesian probability could spark new ideas for the development of artificial intelligence and unconventional computing.

5 Fuzzy sets in quantum mechanics

2021 ◽  
pp. 97-106
Author(s):  
Jarosław Pykacz
Keyword(s):  
Quantum Mechanics ◽  
Fuzzy Sets
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