Game approach to fuzzy measurement

The game approaches are rather popular in many applications, where a collective of automata is used. In the present paper such a collective consists in a group of learning automata characterized with simple number parameters. The fuzzy measuring implemented as a game which is played sequentially with one automaton at a time, the result of the game defines next automaton to be played with. This game provides some measuring system that is very close to the procedure of collecting statistics in Probability Theory. For measuring of an unknown membership function a new concept has been introduced called Cognitive Generator which transforms a fuzzy singleton to ordinary crisp logic value. Considerations on various types of axiomatic approaches shows that the Cognitive Generator, as well as the Evidence Combination Axiomatic, belongs to one class of axiomatic theories, which may be used in application directly. The present paper contains also some programming examples aimed to illustrate our general approach. © 2018, Springer International Publishing AG, part of Springer Nature.