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.
Essay on the history of the development of many-valued logics and some related topics.- 1. Introductory Sections.- Uncertainty aversion and separated effects in decision making under uncertainty.- Essentials of decision making under generalized uncertainty.- Decision evaluation methods under uncertainty and imprecision.- 2. Basic Theoretical Issues.- Fuzzy random variables.- Fuzzy P-measures and their application in decision making.- Theory and applications of fuzzy statistics.- Confidence intervals for the parameters of a linguistic random variable.- On combining uncertainty measures.- On the combination of vague evidence of the probabilistic origin.- Fuzzy evaluation of communicators.- Uncertain associational relations: compatibility and transition relations in reasoning.- 3. Fuzzy Sets Involving Random Aspects.- Stochastic fuzzy sets: a survey.- Probabilistic sets - a survey.- 4. Decision - Making - Related Models Involving Fuzziness and Randomness.- Decision making based on fuzzy stochastic and statistical dominance.- Decision making in a probabilistic fuzzy environment.- Randomness and fuzziness in a linear programming problem.- Comparison of methodologies for multicriteria feasibility -constrained fuzzy and multiple - objective stochastic linear programming.- Fuzzy dynamic programming with stochastic systems.- Probabilistic - possibilistic approach to some statistical problems with fuzzy experimental observations.- Estimation of life-time with fuzzy prior information: application in reliability.- Questionnaires with fuzzy and probabilistic elements.- From fuzzy data to a single action - a simulation approach.- 5. Applications.- Probabilistic sets in classification and pattern recognition.- Fuzzy optimization of radiation protection and nuclear safety.- Application of fuzzy statistical decision making in countermeasures against great earthquakes.- From an oriental market to the European monetary system: some fuzzy - sers - related ideas.