Objective Probability and Quantum Fuzziness

Jarosław Pykacz

Slawomir Bugajski

Storrs McCall

Jarosław Pykacz

In this paper, we propose a new interpretation of quantum mechanics according to which Born probabilities are interpreted as many-valued truth values of statements concerning results of not-yet-performed experiments on quantum objects, or equivalently [0,1]-valued degrees to which quantum objects possess all their properties prior to measurements. The interpretation is based on mathematical results already published by the author, according to which any Birkhoff–von Neumann quantum logic can be isomorphically represented as a family of fuzzy sets or, equivalently, many-valued propositional functions.

Irina Veshneva, Alexander Afanasievich Bolshakov

The basic concepts of classical probability, negative probability, fuzzy sets are considered with appropriate analogies of the quantum mechanical approach to create mathematical models for describing social phenomena. It also briefly describes the features of the application of the theory of intentionality, which uses the concept of institutionality for social phenomena. At the same time, institutionality is understood as a property of consciousness directed at objects and states of affairs in the real world. The concept of collective institutionality is singled out, which forms social facts arising from the collective impact of members of society. The concept of status is given, which denotes a set of characteristic values of a subject or object that determine its position in the system. The features and scope for fuzzy models are described, which are used for the mathematical description of linguistic terms and intentionality in estimating the probabilities of events in fuzzy set theory. In addition, the concept of negative probability and the possibility of using it to describe social events are described. The following is an example illustrating the concept of a complex-valued function and its use to measure the characteristics of socio-economic processes. In conclusion, the concept of status functions is introduced for comparison with membership functions and wave functions.