An imprecision importance measure for uncertainty representations interpreted as lower and upper probabilities, with special emphasis on possibility theory

Abstract

International audienceUncertainty importance measures typically reflect the degree to which uncertainty about risk and reliability parameters at the component level influences uncertainty about parameters at the system level. The definition of these measures is typically founded on a Bayesian perspective where subjective probabilities are used to express epistemic uncertainty; hence, they do not reflect the effect of imprecision in probability assignments, as captured by alternative uncertainty representation frameworks such as imprecise probability, possibility theory and evidence theory. In the present paper, we define an imprecision importance measure to evaluate the effect of removing imprecision to the extent that a probabilistic representation of uncertainty remains, as well as to the extent that no epistemic uncertainty remains. Possibility theory is highlighted throughout the paper as an example of an uncertainty representation reflecting imprecision, and used in particular in two numerical examples which are included for illustration

Uncertainty Problem in Decision Support System for Means of Transport Maintenance Processes Performance Development / Problem Niepewności W Systemie Wsparcia Decyzyjnego Procesów Utrzymania W Stanie Zdatności Środków Transportu

“…Uncertainty problem in decision support system for means of transport … Problem niepewności w systemie wsparcia decyzyjnego procesów... Repair Limit Policy (RLP) with imperfect repair t 11 Repair Limit Policy with minimal repair t 12 Repair Limit Policy with CF t 13 (L-u,L) policy t 14 Opportunistic maintenance policy (OMP) with CF t 15 (τ,T) policy with costs t 16 (τ,T) policy with availability t 17 Simple group maintenance policy (GMP) t 18 Simple group maintenance policy (GMP) with minimal repair t 19 Simple T-policy T 20 Simple T-policy with minimal repair t 21 mfailure policy t 22 (m,T) policy t 23 Delay Time Model (DTM) for multi-unit systems t 24 Delay Time Model for multi-unit systems with imperfect inspections t 25 Delay Time Model for complex systems and non-negligible RT t 26 Delay Time Model for complex systems t 27 Delay Time Model for complex systems with imperfect inspections t ftime moments of failure occurrence t RTtime moments of repair action finishing…”

“…The problem of uncertainty measures in expert system is investigated e.g. in [21,25,67]. In [67], author compares four measures that have been advocated as models for uncertainty in expert systems.…”

“…He is focused on two approaches the theory of belief functions and the possibility theory. In [21], authors define an imprecision importance measure to evaluate the effect of removing imprecision to the extent that a probabilistic representation of uncertainty remains, as well as to the extent that no epistemic uncertainty remains.…”

Complement information entropy for uncertainty measure in fuzzy rough set and its applications

“…Uncertainty measure becomes increasingly important in computational intelligence, machine learning and artificial intelligence. Many different uncertainty representations can be used to measure information imprecision and ambiguity, such as probability uncertainty (Zadeh 1968;Eslami 2003, 2004;Halliwell and Shen 2009;Liu 2013), possibility uncertainty (Zadeh 1978;Cooman 1997;Nguyen and Bouchon-Meunier 2003;Coletti et al 2008;Yager 2011;Flage et al 2012), fuzzy uncertainty (De Luca and Termini 1972;Pal and Bezdek 1994;Klir and Smith 2001;Yager 2002;Bertoluzza et al 2004;Mesiar 2005;Graves and Nagarajah 2007) and rough uncertainty (Beaubouf et al 1998;Wierman 1999;Liang et al 2002Liang et al , 2006.…”

Safety integrity level evaluation of nuclear centrifugal pump based on performance degradation data

“…Prognostic and health management (PHM) 1 focuses on health assessment, fault diagnosis, 2,3 RUL estimation, 4 and risk analysis. 5 A formidable challenge in PHM 6 is evaluating the safety level of mechanical equipment. One method for quantifying safety level is safety integrity level (SIL) evaluation.…”