Abstract
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.
Highlights
Scientific knowledge is expressed through mathematical equations, algorithms, and sentences formulated in natural language
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
Summary
Scientific knowledge is expressed through mathematical equations, algorithms, and sentences formulated in natural language. The Uncertainty Principle imposes limits in our prediction of the dynamics of a particle, as its position and momentum cannot be determined accurately and simultaneously It derives that the description of the microscopic phenomena is approximate and uncertain. As there are two sharply distinct definitions of probability, there are two fundamentally different interpretations of quantum mechanics: the traditional one, which is based on the frequentist definition of probability, and a more recent one, named QBism, which is based on the Bayes’ theory [8] As both fuzzy logic and human reasoning are related to Bayesian probability, the purpose of this paper is to establish a new link between QBism, fuzzy logic, and neuroscience. BetTwheeenptheertswpoetchteiovrieess.of the new transdisciplinary link between fuzzy lo Tanhdae npquedrasnqpteuucmtaivnmetseucohmf athnmeicnseeawcrehtoraaunntlsiidcnisesdcaiiprnleitnhoaeruylatlslitninpkaebrdeatgwrianepenhth.fuezzlayslotgpica, nreaugrroascpiehnc.e, SSchcehmeem1.eSt1ru.cStutrreuocfttuherepaopfert.he paper
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