Aspiration Based Decision Analysis and Support Part I: Theoretical and Methodological Backgrounds

In the interdisciplinary and intercultural systems analysis that constitutes the main theme of research in IIASA, a basic question is how to analyze and support decisions with help of mathematical models and logical procedures. This question -- particularly in its multi-criteria and multi-cultural dimensions -- has been investigated in System and Decision Sciences Program (SDS) since the beginning of IIASA. Researchers working both at IIASA and in a large international network of cooperating institutions contributed to a deeper understanding of this question. Around 1980, the concept of reference point multiobjective optimization was developed in SDS. This concept determined an international trend of research pursued in many countries cooperating with IIASA as well as in many research programs at IIASA -- such as energy, agricultural, environmental research. SDS organized since this time numerous international workshops, summer schools, seminar days and cooperative research agreements in the field of decision analysis and support. By this international and interdisciplinary cooperation, the concept of reference point multiobjective optimization has matured and was generalized into a framework of aspiration based decision analysis and support that can be understood as a synthesis of several known, antithetical approaches to this subject -- such as utility maximization approach, or satisficing approach, or goal -- program -- oriented planning approach. Jointly, the name of quasisatisficing approach can be also used, since the concept of aspirations comes from the satisficing approach. Both authors of the Working Paper contributed actively to this research: Andrzej Wierzbicki originated the concept of reference point multiobjective optimization and quasisatisficing approach, while Andrzej Lewandowski, working from the beginning in the numerous applications and extensions of this concept, has had the main contribution to its generalization into the framework of aspiration based decision analysis and support systems. This paper constitutes a draft of the first part of a book being prepared by these two authors. Part I, devoted to theoretical foundations and methodological background, written mostly by Andrzej Wierzbicki, will be followed by Part II, devoted to computer implementations and applications of decision support systems based on mathematical programming models, written mostly by Andrzej Lewandowski. Part III, devoted to decision support systems for the case of subjective evaluations of discrete decision alternatives, will be written by both authors

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment

Interval-valued upside potential and downside risk portfolio optimisation

A novel interval optimisation approach is developed to include imprecise forecasts into the portfolio selection process for investors measuring upside potential and downside risk as deviations from a target return. Crisp scenarios are substituted by interval scenarios and the resulting interval optimisation problem is solved in a tractable manner by means of a bi-objective formulation exploiting a partial order relation between intervals. Four utility case studies involving assets from the F.T.S.E. M.I.B. Index are considered to illustrate how impreciseness can be efficiently handled in portfolio management

Preference modelling approaches based on cumulative functions using simulation with applications

In decision making problems under uncertainty, Mean Variance Model (MVM) consistent with Expected Utility Theory (EUT) plays an important role in ranking preferences for various alternative options. Despite its wide use, this model is appropriate only when random variables representing the alternative options are normally distributed and the utility function to be maximized is quadratic; both are undesirable properties to be satisfied with actual applications. In this research, a novel methodology has been adopted in developing generalized models that can reduce the deficiency of the existing models to solve large-scale decision problems, along with applications to real-world disputes. More specifically, for eliciting preferences for pairs of alternative options, two approaches are developed: one is based on Mean Variance Model (MVM), which is consistent with Expected Utility Theory (EUT), and the second is based on Analytic Hierarchy Processes (AHP). The main innovation in the first approach is in reformulating MVM to be based on cumulative functions using simulation. Two models under this approach are introduced: the first deals with ranking preferences for pairs of lotteries/options with non-negative outcomes only while the second, which is for risk modelling, is a risk-preference model that concerns normalized lotteries representing risk factors each is obtained from a multiplication decomposition of a lottery into its mean multiplied by a risk factor. Both approximation models, which are preference-based using the determined values for expected utility, have the potential to accommodate various distribution functions with different utility functions and capable of handling decision problems especially those encountered in financial economics. The study then reformulates the second approach, AHP; a new algorithm, using simulation, introduces an approximation method that restricts the level of inherent uncertainty to a certain limit. The research further focuses on proposing an integrated preference-based AHP model introducing a novel approximation stepwise algorithm that combines the two modified approaches, namely MVM and AHP; it multiplies the determined value for expected utility, which results from implementing the modified MVM, by the one obtained from processing AHP to obtain an aggregated weight indicator. The new integrated weight scale represents an accurate and flexible tool that can be employed efficiently to solve decision making problems for possible scenarios that concern financial economics Finally, to illustrate how the integrated model can be used as a practical methodology to solve real life selection problems, this research explores the first empirical case study on Tender Selection Process (TSP) in Kurdistan Region (KR) of Iraq; it is considered as an inductive and a comprehensive investigation on TSP, which has received minimum consideration in the region, and regarded as a significant contribution to this research. The implementation of the proposed model to this case study shows that, for the evaluation of construction tenders, the integrated approach is an appropriate model, which can be easily modified to assume specific conditions of the proposed project. Using simulation, generated data allows creation of a feedback system that can be utilized for the evaluation of future projects in addition to its capability to make data handling easier and the evaluation process less complex and time consuming

Conflicting Objectives in Decisions

This book deals with quantitative approaches in making decisions when conflicting objectives are present. This problem is central to many applications of decision analysis, policy analysis, operational research, etc. in a wide range of fields, for example, business, economics, engineering, psychology, and planning. The book surveys different approaches to the same problem area and each approach is discussed in considerable detail so that the coverage of the book is both broad and deep. The problem of conflicting objectives is of paramount importance, both in planned and market economies, and this book represents a cross-cultural mixture of approaches from many countries to the same class of problem

Robustness of Multiple Objective Decision Analysis Preference Functions

This research investigated value and utility functions in multiobjective decision analysis to examine the relationship between them in a military decision making context. The impact of these differences was examined to improve implementation efficiency. The robustness of the decision model was examined with respect to the preference functions to reduce the time burden imposed on the decision maker. Data for decision making in a military context supports the distinction between value and utility functions. Relationships between value and utility functions and risk attitudes were found to be complex. Elicitation error was significantly smaller than the difference between value and utility functions. Risk attitudes were generally neither constant across the domain of the evaluation measure nor consistent between evaluation measures. An improved measure of differences between preference functions, the weighted root means square, is introduced and a goodness of fit criterion established. An improved measure of risk attitudes employing utility functions is developed. Response Surface Methodology was applied to improve the efficiency of decision analysis utility model applications through establishing the robustness of decision models to the preference functions. An algorithm was developed and employs this information to provide a hybrid value-utility model that offers increased elicitation efficiency

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy