Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision MakingMario Fedrizzi In 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. |
Contents
10 | |
Essentials of decision making under generalized uncertainty | 26 |
Decision evaluation methods under uncertainty and imprecision | 48 |
BASIC THEORETICAL ISSUES | 66 |
Theory and applications of fuzzy statistics | 89 |
Confidence intervals for the parameters of a linguistic | 113 |
On the combination of vague evidence of the probabilistic | 135 |
Other editions - View all
Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making Mario Fedrizzi No preview available - 2012 |
Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making Mario Fedrizzi No preview available - 1988 |
Common terms and phrases
algebra algorithm alternative Applications approach associated assume axiom Bayes Bellman clustering compatibility relation concept consider convex countermeasure crisp decision analysis decision problem decision-making defined Definition degree denote distribution function Dubois and Prade dynamic programming earthquake elements entropy Esogbue estimation example expected value finite formulation fuzzy clustering fuzzy decision fuzzy environment fuzzy event fuzzy goal fuzzy measure fuzzy numbers fuzzy probability measure fuzzy random variable fuzzy set theory fuzzy subsets given imprecise interval Kacprzyk knowledge linear programming linguistic logic mapping mathematical means membership function method minimax obtained optimal outcome P-measure partition Piasecki possibility distribution prediction probabilistic sets probability distribution probability measure probability space propositions random set risk sample fuzzy information satisfies Sets and Systems situation stochastic dominance synthetic evaluating function Theorem tion uncertainty utility function x₁ Yager Zadeh