Decision-theoretic rough sets based on time-dependent loss function

TL;DR

This paper explores how time-dependent loss functions influence decision thresholds in decision-theoretic rough sets, using Bayesian methods and practical examples to demonstrate their application.

Contribution

It introduces the use of time-dependent loss functions, including interval sets and fuzzy numbers, in decision-theoretic rough sets with Bayesian decision procedures.

Findings

Thresholds can be effectively calculated using time-dependent loss functions.

Bayesian decision procedures adapt to various time-dependent loss functions.

Practical examples illustrate the application of the proposed methods.

Abstract

A fundamental notion of decision-theoretic rough sets is the concept of loss functions, which provides a powerful tool of calculating a pair of thresholds for making a decision with a minimum cost. In this paper, time-dependent loss functions which are variations of the time are of interest because such functions are frequently encountered in practical situations, we present the relationship between the pair of thresholds and loss functions satisfying time-dependent uniform distributions and normal processes in light of bayesian decision procedure. Subsequently, with the aid of bayesian decision procedure, we provide the relationship between the pair of thresholds and loss functions which are time-dependent interval sets and fuzzy numbers. Finally, we employ several examples to illustrate that how to calculate the thresholds for making a decision by using time-dependent loss functions-based decision-theoretic rough sets.