Agent uncertainty model and quantum mechanics representation: Non-locality modeling

Abstract

This work presents the Agent-based Uncertainty Theory (AUT) and its connection with quantum mechanics where agents are interpreted in terms of the particles. This connection serves a dual goal to justify AUT operations as physically meaningful and to provide a new explanatory mechanism for contradictory issues in quantum mechanics. The AUT is described in agent terms and then is interpreted in quantum mechanics terms. The AUT uses complex aggregations of crisp (non-fuzzy) conflicting judgments of agents. It gives a uniform representation and an operational empirical interpretation for several uncertainty theories such as rough set theory, fuzzy sets theory, intuitionistic fuzzy sets, evidence theory, and probability theory. To build such uniformity the AUT exploits the fact that agents as independent entities can give conflicting evaluations of the same attribute. The AUT many-valued logic is a derived from classical logic with local and global evaluations of proposition p. The evaluation by an individual agent is called a local evaluation and evaluation by a set of agents is called a global evaluation of p. The local operations AND, OR, NOT are classical logic operations, but global operations differ from them. Here a set of agents generates the vectors of logic values. In the AUT local evaluations of proposition p by different agents can be in conflict in contrast with the classical logic. In quantum mechanics, non-locality is related to the superposition of different positions of the particles and to representation of two particles in different positions as a single non-local particle with correlation or entanglement. The logic operations between vectors are the base of AUT many-valued logic combined with the superposition of agents' evaluations. © 2009 Springer-Verlag Berlin Heidelberg.