Bipolar and bivariate models in multi-criteria decision analysis: descriptive and constructive approaches

Multi-criteria decision analysis studies decision problems in which the alternatives are evaluated on several dimensions or viewpoints. In the problems we consider in this paper, the scales used for assessing the alternatives with respect to a viewpoint are bipolar and univariate or unipolar and bivariate. In the former case, the scale is divided in two zones by a neutral point; a positive feeling is associated to the zone above the neutral point and a negative feeling to the zone below this point. On unipolar bivariate scales, an alternative can receive both a positive and a negative evaluation, reflecting contradictory feelings or stimuli. The paper discusses procedures and models that have been proposed to aggregate multi-criteria evaluations when the scale of each criterion is of one of the two types above. We present both a constructive and a descriptive view on this question; the descriptive approach is concerned with characterizations of models of preference, while the constructive approach aims at building preferences by questioning the decision maker. We show that these views are complementary.Multiple criteria, Decision analysis, Preference, Bipolarmodels, Choquet integral

Preference for Flexibility and Freedom of Choice in a Savage Framework

In this paper, we study preferences over Savage acts that map states to opportunity sets. Conditional preferences over opportunity sets may be inconsistent with indirect-utility maximization due to implicit uncertainty about future preferences (preference for flexibility), or to an intrinsic preference for freedom of choice. On a flexibility interpretation, the main result characterizes preferences based on maximizing the expected indirect utility in terms of an ""Indirect Stochastic Dominance"" axiom. The relevance of the result to a freedom-of-choice context is established on the basis of a novel multi-attribute conceptualization of the notion of effective freedom of choice; the theorem delivers an additive multi-attribute representation with optimal uniqueness properties. The key technical tool of the paper, a version of MÅ¡bius inversion has been imported from the theory of (non-additive) ""belief-functions;"" it also yields a simple and intuitive proof of Kreps''s (1979) classic result.

Graphically structured value-function compilation

AbstractClassical work on eliciting and representing preferences over multi-attribute alternatives has attempted to recognize conditions under which value functions take on particularly simple and compact form, making their elicitation much easier. In this paper we consider preferences over discrete domains, and show that for a certain class of simple and intuitive qualitative preference statements, one can always generate compact value functions consistent with these statements. These value functions maintain the independence structure implicit in the original statements. For discrete domains, these representation theorems are much more general than previous results. However, we also show that it is not always possible to maintain this compact structure if we add explicit ordering constraints among the available outcomes

MODELING, LEARNING AND REASONING ABOUT PREFERENCE TREES OVER COMBINATORIAL DOMAINS

In my Ph.D. dissertation, I have studied problems arising in various aspects of preferences: preference modeling, preference learning, and preference reasoning, when preferences concern outcomes ranging over combinatorial domains. Preferences is a major research component in artificial intelligence (AI) and decision theory, and is closely related to the social choice theory considered by economists and political scientists. In my dissertation, I have exploited emerging connections between preferences in AI and social choice theory. Most of my research is on qualitative preference representations that extend and combine existing formalisms such as conditional preference nets, lexicographic preference trees, answer-set optimization programs, possibilistic logic, and conditional preference networks; on learning problems that aim at discovering qualitative preference models and predictive preference information from practical data; and on preference reasoning problems centered around qualitative preference optimization and aggregation methods. Applications of my research include recommender systems, decision support tools, multi-agent systems, and Internet trading and marketing platforms

The treatment of uncertainty in multicriteria decision making

Bibliography: leaves 142-149.The nature of human decision making dictates that a decision must often be considered under conditions of uncertainty. Decisions may be influenced by uncertain future events, doubts regarding the precision of inputs, doubts as to what the decision maker considers important, and many other forms of uncertainty. The multicriteria decision models that are designed to facilitate and aid decision making must therefore consider these uncertainties if they are to be effective. In this thesis, we consider the treatment of uncertainty in multicriteria decision making (MCDM), with a specific view to investigating the types of uncertainty that are most relevant to MCDM, [and] how the uncertainties identified as relevant may be treated by various different MCDM methodologies

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

Prospect Theory and Choice Behaviour Strategies: Review and Synthesis of Concepts from Social and Transport sciences

Utility Theory is commonly considered as the most useful descriptive theory of human choice behaviour. Alternative concepts are only incidentally considered. This paper reviews alternative assumptions and empirical findings about human choice behaviour. To facilitate comparison and synthesis the review starts with the proposal of a generic framework of choice behaviour. The micro-economic assumptions of Utility Theory and Prospect Theory are then mapped onto this framework. These are compared with each other and other assumptions against the background of theoretical and empirical findings from behavioural economics, several other social disciplines and transport sciences. An extension of Prospect Theory with assumptions about the valuation of attributes and the employment of different decision rules yields a functional concept of choice behaviour that is able to describe most of the reviewed empirical findings to a larger extent than Utility Theory

A resource allocation mechanism based on cost function synthesis in complex systems

While the management of resources in computer systems can greatly impact the usefulness and integrity of the system, finding an optimal solution to the management problem is unfortunately NP hard. Adding to the complexity, today\u27s \u27modern\u27 systems - such as in multimedia, medical, and military systems - may be, and often are, comprised of interacting real and non-real-time components. In addition, these systems can be driven by a host of non-functional objectives – often differing not only in nature, importance, and form, but also in dimensional units and range, and themselves interacting in complex ways. We refer to systems exhibiting such characteristics as Complex Systems (CS). We present a method for handling the multiple non-functional system objectives in CS, by addressing decomposition, quantification, and evaluation issues. Our method will result in better allocations, improve objective satisfaction, improve the overall performance of the system, and reduce cost -in a global sense. Moreover, we consider the problem of formulating the cost of an allocation driven by system objectives. We start by discussing issues and relationships among global objectives, their decomposition, and cost functions for evaluation of system objective. Then, as an example of objective and cost function development, we introduce the concept of deadline balancing. Next, we proceed by proving the existence of combining models and their underlying conditions. Then, we describe a hierarchical model for system objective function synthesis. This synthesis is performed solely for the purpose of measuring the level of objective satisfaction in a proposed hardware to software allocation, not for design of individual software modules. Then, Examples are given to show how the model applies to actual multi-objective problems. In addition the concept of deadline balancing is extended to a new scheduling concept, namely Inter-Completion-Time Scheduling (ICTS. Finally, experiments based on simulation have been conducted to capture various properties of the synthesis approach as well as ICTS. A prototype implementation of the cost functions synthesis and evaluation environment is described, highlighting the applicability and usefulness of the synthesis in realistic applications