N. Fürstenau

The algebraic belief-adjustment model of Hogarth and Einhorn is used as a starting point for a nonlinear dynamical systems approach to decision making within the framework of Haken's Synergetics as theory of self-organization of complex systems. An equivalence is derived between the recursive belief-adjust-ment model and processes modeled by the Logistic equation with a single control parameter [Lambda]. It yields 1 <= [Lambda] <= 2 under Hogarths assumptions. It follows that for a sufficiently large number of belief updates the belief in a hypothesis in Hogarth's model always approaches a fixed point. Comparison with the Cohen-Grossberg dynamics suggests the interpretation of [Lambda] as gain parameter allowing for [Lambda] > 2. An increase of the control parameter to [Lambda] > 3 yields the well known universal period doubling bifurcations at critical values ?©n and deterministic chaos within 3.57 <= [Lambda]n <= 4. The transition from quadratic to cosinuidal maps yields node type bifurcations, which have been experimentally realized by photonic, interferomet-ric equivalent circuits. In agreement with the catastrophe theoretical approach to decision making they exhibit discontinuous transitions between different station-ary levels including hysteresis effects. In terms of Synergetics this process corresponds to the spontaneous symmetry breaking of a (belief-) potential energy function. It determines the belief state as a macroscopic order parameter which is driven by a conservative force as derivative of the potential. The example of bistable switching of the visual perception with ambiguous pictures reveals the relationship to the Synergetic theory of pattern recognition.

44. Fachausschusssitzung Anthropotechnik der Deutschen Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V.;Langen

Conference Paper

englisch

14,8 x 21,0 cm, 18 Seiten

DGLR-Bericht, 2002, 2002-04, Situation Awareness in der Fahrzeug- und Prozessführung; S.199-216; 2002; Deutsche Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V., Bonn

NA

antropotechnik

Bestellbar

2002