Abstract
Dynamical models of autonomous systems usually follow general assumption about rationality of the systems and their judgements. In particular, the systems acting under uncertainty are defined using probabilistic methods with the reasoning based on minimization or maximization of the expected payoffs or rewards. However, in the systems that deal with rare events or interact with human usually demonstrating irrational behaviour correctness of the use of probability measures and of the utility functions is problematic. In order to solve this problem, in the paper we suggest a Markov-like process that is based on a certain type of possibility measures and uninorm and absorbing norm aggregators. Together these values and operators form an algebraic structure that, on one hand, extends Boolean algebra and, on the other hand, operates on the unit interval as arithmetic system. We demonstrate the basic properties of the suggested subjective Markov process that go in parallel to the properties of usual Markov process, and stress formal differences between two models. The actions of the suggested process are illustrated by the simple model of search that clarifies the differences between Markov and subjective Markov processes and corresponding decision-making.