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A Generalization of the Pignistic Transform for Partial Bet
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BibTeX
@MISC{Burger_ageneralization,
author = {Thomas Burger and Alice Caplier},
title = {A Generalization of the Pignistic Transform for Partial Bet},
year = {}
}
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Abstract
Abstract. The Transferable Belief Model is a powerful interpretation of belief function theory where decision making is based on the pignistic transform. Smets has proposed a generalization of the pignistic transform which appears to be equivalent to the Shapley value in the transferable utility model. It corresponds to the situation where the decision maker bets on several hypotheses by associating a subjective probability to non-singleton subsets of hypotheses. Naturally, the larger the set of hypotheses is, the higher the Shapley value is. As a consequence, it is impossible to make a decision based on the comparison of two sets of hypotheses of different size, because the larger set would be promoted. This behaviour is natural in a game theory approach of decision making, but, in the TBM framework, it could be useful to model other kinds of decision processes. Hence, in this article, we propose another generalization of the pignistic transform where the belief in too large focal elements is normalized in a different manner prior to its redistribution. 1
Keyphrases
pignistic transform partial bet shapley value decision making different manner powerful interpretation subjective probability transferable belief model decision maker bet belief function theory transferable utility model tbm framework non-singleton subset several hypothesis decision process different size large focal element game theory approach
