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  • 1.
    Ekenberg, Love
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Thorbiornson, Johan
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Second-order decision analysis2001In: International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, ISSN 0218-4885, Vol. 9, no 1, p. 13-37Article in journal (Refereed)
    Abstract [en]

    The purpose of this work is to provide theoretical foundations of, as well as some computational aspects on, a theory for analysing decisions under risk, when the available information is vague and imprecise. Many approaches to model unprecise information, e.g., by using interval methods, have prevailed. However, such representation models are unnecessarily restrictive since they do not admit discrimination between beliefs in different values, i.e., the epistemologically possible values have equal weights. In many situations, for instance, when the underlying information results from learning techniques based on variance analyses of statistical data, the expressibility must be extended for a more perceptive treatment of the decision situation. Our contribution herein is an approach for enabling a refinement of the representation model, allowing for an elaborated discrimination of possible values by using belief distributions with weak restrictions. We show how to derive admissible classes of local distributions from sets of global distributions and introduce measures expressing into which extent explicit local distributions can be used for modelling decision situations. As will turn out, this results in a theory that has very attractive features from a computational viewpoint.

  • 2.
    Larsson, Aron
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Johansson [Idefeldt], Jim
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Ekenberg, Love
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Danielsson, Mats
    Decision analysis with multiple objectives in a framework for evaluating imprecision2005In: International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, ISSN 0218-4885, Vol. 13, no 5, p. 495-509Article in journal (Refereed)
    Abstract [en]

    We present a decision tree evaluation method for analyzing multi-attribute decisions under risk, where information is numerically imprecise. The approach extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise statements, relaxing requirements for precise estimates of decision parameters. Information is modeled in convex sets of utility and probability measures restricted by closed intervals. Evaluation is done relative to a set of rules, generalizing the concept of admissibility, computationally handled through optimization of aggregated utility functions. Pros and cons of two approaches, and tradeoffs in selecting a utility function, are discussed.

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