0000000000294692
AUTHOR
Andrei Khrennikov
Hysteresis Model of Unconscious-Conscious Interconnection: Exploring Dynamics on m-Adic Trees
The theoretical model outlined in this paper, has been experimentally validated by: H. Kim ,J-Y. Moon ,G.A. Mashour & U. Lee, ''Mechanisms of hysteresis in human brain networks during transitions of consciousness and unconsciousness: Theoretical principles and empirical evidence'', PLOS-Computational Biology, August 30, 2018, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1006424; International audience; In this brief note, we focus attention on a possible implementation of a basic hysteretic pattern (the Preisach one), suitably generalized, into a formal model of unconscious-conscious interconnection and based on representation of mental entities by m-adic numbers. …
Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality
This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions …
A model of adaptive decision-making from representation of information environment by quantum fields
We present the mathematical model of decision making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioral, and geo-political factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are of the purely informational nature. The QFT-model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantu…
Quantum field inspired model of decision making: Asymptotic stabilization of belief state via interaction with surrounding mental environment
This paper is devoted to justification of quantum-like models of the process of decision making based on the theory of open quantum systems, i.e. decision making is considered as decoherence. This process is modeled as interaction of a decision maker, Alice, with a mental (information) environment ${\cal R}$ surrounding her. Such an interaction generates "dissipation of uncertainty" from Alice's belief-state $\rho(t)$ into ${\cal R}$ and asymptotic stabilization of $\rho(t)$ to a steady belief-state. The latter is treated as the decision state. Mathematically the problem under study is about finding constraints on ${\cal R}$ guaranteeing such stabilization. We found a partial solution of th…