## Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision MakingIn the literature of decision analysis it is traditional to rely on the tools provided by probability theory to deal with problems in which uncertainty plays a substantive role. In recent years, however, it has become increasingly clear that uncertainty is a mul tifaceted concept in which some of the important facets do not lend themselves to analysis by probability-based methods. One such facet is that of fuzzy imprecision, which is associated with the use of fuzzy predicates exemplified by small, large, fast, near, likely, etc. To be more specific, consider a proposition such as "It is very unlikely that the price of oil will decline sharply in the near future," in which the italicized words play the role of fuzzy predicates. The question is: How can one express the mean ing of this proposition through the use of probability-based methods? If this cannot be done effectively in a probabilistic framework, then how can one employ the information provided by the proposition in question to bear on a decision relating to an investment in a company engaged in exploration and marketing of oil? As another example, consider a collection of rules of the form "If X is Ai then Y is B,," j = 1, . . . , n, in which X and Yare real-valued variables and Ai and Bi are fuzzy numbers exemplified by small, large, not very small, close to 5, etc. |

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### Contents

Uncertainty aversion and separated effects in decision making | 10 |

Essentials of decision making under generalized uncertainty | 26 |

Decision evaluation methods under uncertainty and imprecision | 48 |

Copyright | |

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### Other editions - View all

Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making No preview available - 1988 |

Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making Mario Fedrizzi No preview available - 2012 |

### Common terms and phrases

algebra algorithm alternative application approach associated assume axiom Bayes Bellman characterized compatibility relation concept conditional probability consequences consider convex countermeasure crisp decision analysis decision maker decision problem decision-making defined Definition degree denote distribution function Dubois and Prade dynamic programming elements entropy Esogbue estimation example expected value finite formulation fuzzy clustering fuzzy decision fuzzy environment fuzzy event fuzzy goal fuzzy measure fuzzy numbers fuzzy random variable fuzzy set theory fuzzy subsets given imprecision Kacprzyk knowledge linear programming linguistic logic mapping mathematical means measurable space membership function method minimax nonfuzzy objective obtained optimal outcomes P-measure partition Piasecki possibility distribution prediction probabilistic sets probability distribution probability measure probability space propositions random set respectively risk satisfies Sets and Systems situation solution specific statistical decision stochastic dominance synthetic evaluating function Theorem tion Turksen uncertainty utility function vector Yager Zadeh