Conservative Betting on Sport Games with Intuitionistic Fuzzy Described Uncertainty

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The paper discusses rational conservative betting on sport game events by a fuzzy (partially rational) decision maker with the help of generalized lotteries of II type. The scheme accounts for the interval character of probability elicitation results, which may be conveniently described by intuitionistic fuzzy sets. A model of a lottery with intuitionistic fuzzy representation of the state uncertainty is proposed, called fuzzy rational lottery. Utility theory is not directly applicable to that type of lotteries, which is why two transformations into ordinary lotteries are proposed - classical and conservative. The classical set-up uses point estimates of the probability uncertainty intervals to construct lotteries, whereas the conservative set-up is a combination of Wald's maximin principle and utility theory under risk Those approaches are applied to analyze a hypothetical betting situation over the results of soccer game. Betting on single events, as well as simultaneously on all events is discussed, and conditions are found for optimal betting.

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