The Effects of Perfect and Sample Information on Fuzzy Utilities in Decision-Making

TL;DR

This paper models fuzzy utilities within a Bayesian framework to analyze how sample information influences decision-making, showing that sample data can improve expected utility and that perfect information provides an upper bound.

Contribution

It introduces a fuzzy Bayesian model for utility functions and analyzes the impact of sample information on expected utility in decision-making.

Findings

Sample information increases expected utility on average.

Perfect information provides an upper bound on utility.

Applications demonstrated in artificial intelligence contexts.

Abstract

In this paper, we first consider a Bayesian framework and model the "utility function" in terms of fuzzy random variables. On the basis of this model, we define the "prior (fuzzy) expected utility" associated with each action, and the corresponding "posterior (fuzzy) expected utility given sample information from a random experiment". The aim of this paper is to analyze how sample information can affect the expected utility. In this way, by using some fuzzy preference relations, we conclude that sample information allows a decision maker to increase the expected utility on the average. The upper bound on the value of the expected utility is when the decision maker has perfect information. Applications of this work to the field of artificial intelligence are presented through two examples.