Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making

This volume brings together for the first time articles by well-known experts focusing on the topic of the joint occurrence of imprecision, dealt with in terms of fuzzy sets and possibility theory, and randomness, dealt with in terms of probability theory, in a wide spectrum of decision making problems. In the introductory section, some basic issues related to decision making under uncertainty and fuzziness are discussed in some survey-type papers. The second part is devoted to basic theoretical issues, including uncertainty measures, fuzzy measures, fuzzy random variables, fuzzy statistics and evaluation and aggregation of imprecise and uncertain evidence. The third part presents the concepts of a stochastic fuzzy set and a probabilistic set which are basically some fuzzy sets involving random aspects. The fourth part presents a wide spectrum of models in which some aspects of fuzziness and randomness co-occur. It includes papers on fuzzy statistical decision making, fuzzy stochastic and statistical dominance, probabilistic-set-based decision making, optimization under fuzziness and randomness and fuzzy dynamic programming with stochastic systems. The fifth and final part deals with applications in economy and finance, nuclear reactor protection, classification and pattern recognition, reliability and earthquake forecasting. The reader is provided with a set of tools which enable him to deal with diverse decision problems in which imprecision and uncertainty jointly occur