Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making

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.

Table of Contents:
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 nuclearsafety.- 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.