Discrete-time hybrid processes and discounted total expected values

Abstract

A Markov-type hybrid process with discrete parameters is constructed from credibilistic kernels and stochastic kernels. To evaluate a hybrid reward process, a discounted total expected value is defined, which is characterized as a fixed point of the corresponding operator. Also, examples are given.

Discrete-Time Hybrid Decision Processes: The Discounted Case

“…The credibility theory, developed by Liu [2], is useful in dealing with uncertainty in human thinking. In the real world, we often encounter the complex problem with human thinking, which could not be treated only by probability theory.…”

“…To deal with such complex problem, Li and Liu [3] have introduced a more flexible uncertain theory, called chance theory, which is a hybrid of probability and credibility. Also, recently, Kageyama et al [1] have given a method of constructing a Markov-type hybrid process from stochastic kernel and credibilistic kernel. Imagining the much wider applications of hybrid processes in the near future, it is meaningful to consider the case where the behavior of hybrid processes given in Kageyama et al [1] may be influenced by a suitable choice of decisions or actions.…”

“…Also, recently, Kageyama et al [1] have given a method of constructing a Markov-type hybrid process from stochastic kernel and credibilistic kernel. Imagining the much wider applications of hybrid processes in the near future, it is meaningful to consider the case where the behavior of hybrid processes given in Kageyama et al [1] may be influenced by a suitable choice of decisions or actions. The objective of this paper is to formulate a hybrid decision process, referring a modeling of stochastic control system known as a Markov decision process (cf.…”