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Full Description
This monograph presents a new generalization of utility theory, fuzzy rationality. It is a group of techniques that can be applied in different stages of decision analysis - problem modeling, measuring preferences and uncertainty, and the analysis of risk attitude. A common feature of all these techniques is the ability to measure the actual opinion of the decision maker. At a later stage, the subjective information is analyzed in order to identify the best alternative according to the real, fuzzy rational decision maker.
Contents
List of abbreviations and notations.- Foreword.- Introduction.- Modelling decision problems.- Value functions under strict certainty.- Measuring uncertainty with probabilities.- Measuring preferences with utilities.- Balancing preferences and entirely measured uncertainty.- Balancing preferences and partially measured uncertainty.- Appendix 1: Binary relations.- Appendix 2: Finding the interval of the extremum at hill and valley preferences.- Appendix 3: Elements of probability theory.- Appendix 4: Constructing frequentist distributions and frequentist estimates of numerical characteristics.- Appendix 5: Constructing subjective distributions and assessment of numerical characteristics of continuous random variables.- Appendix 6: Constructing the distribution law of NPV of average annual heating costs using risk analysis.- Appendix 7: Algorithms and examples for elicitation of one-dimensional utility.- Appendix 8: Analytical approximation of one-dimensional utility at strictly decreasing preferences.- Appendix 9: Constructing multi-dimensional utility at mutual utility independence.- Appendix 10: Defining the uncertainty interval of scaling constants.- Appendix 11: Ranking alternatives under strict uncertainty.- Appendix 12: Approximation using the maximax criterion.- References.- Author index.- Example index.- Figure index.- Table index.- Algorithm index.- Task index.
