Z-relation-based multistage decision making

Abstract

Multistage decision problems have attracted interest in various fields. Starting from the pioneering work of Bellman and Zadeh, a large class of comprehensive studies for fuzzy, stochastic and other settings were proposed. The main issue missed in the existing works is partial reliability of information. Indeed, partial reliability of information about states and actions is important for multistage decisions. Particularly, information about future state of a system resulting from current strategies is partially reliable due to uncertainty. To account for partial reliability aspect, Zadeh introduced the concept of a Z-number. In this paper, we use this concept to consider multistage decision making under partially reliable information. States, strategies, and goals are described by using Z-numbers. State transition matrix that describes evolution of a system in time is formed by using Z-number-based relations. This description leads to a problem of dynamic programming in Z-environment. We use Z-numbers to account for the fact that information related to state transitions is partially reliable – we are partially sure in a result of each transition. The reason behind partial reliability is complexity and uncertainty of real-world problems. A typical example and an application study are used to illustrate the approach.