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Construction of families of probability boxes and corresponding membership functions at different fractiles
Author(s) -
Dutta Palash,
Hazarika G.C.
Publication year - 2017
Publication title -
expert systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 38
eISSN - 1468-0394
pISSN - 0266-4720
DOI - 10.1111/exsy.12202
Subject(s) - probability distribution , possibility theory , fuzzy logic , set (abstract data type) , fuzzy set , computer science , representation (politics) , construct (python library) , imprecise probability , probability theory , component (thermodynamics) , uncertainty quantification , mathematics , probability measure , probability and statistics , law of total probability , artificial intelligence , statistics , posterior probability , machine learning , bayesian probability , physics , politics , political science , law , thermodynamics , programming language
Uncertainty comes in many forms in the real world and is an unavoidable component of human life. Generally, two types of uncertainties arise, namely, aleatory and epistemic uncertainty. Probability is a well established mathematical tool to handle aleatory uncertainty and fuzzy set theory is a tool to handle epistemic uncertainty. However, in certain situations, parameters of probability distributions may be tainted with epistemic uncertainty; and so, representation of parameters of probability distributions may be treated as fuzzy numbers (may be of different shapes). A probability box (P‐box) can be constructed when parameters are not precisely known. In this paper, an attempt has been made to construct families of P‐boxes when parameters of probability distributions are bell shaped or normal fuzzy numbers; and from these families of P‐boxes, membership functions are generated at different fractiles for different alpha levels.