Decision-Making with Belief Functions: a Review

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches

Induced aggregation operators in decision making with the Dempster-Shafer belief structure

We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.aggregation operators, dempster-shafer belief structure, uncertainty, iowa operator, decision making

Fuzzy decision making in Business intelligence in the context of Gilgit-Baltistan

The main purpose of this paper is to investigate and implement fuzzy decision based on unequal objectives and minimization of regret for the decision making in the business intelligence and to compare the weight of products while the minimization of regret that uses regression of products in Gilgit-Baltistan. Here we will convert the verbal expressions in to linguistic variables and use in fuzzy decision making model, which influences the main two factors, one is effect of the influence on the product and second its payoff for the most effectiveness on the products

Decision making techniques with similarity measures and OWA operators

We analyse the use of the ordered weighted average (OWA) in decision-making giving special attention to business and economic decision-making problems. We present several aggregation techniques that are very useful for decision-making such as the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. We suggest a new approach by using immediate weights, that is, by using the weighted average and the OWA operator in the same formulation. We further generalize them by using generalized and quasi-arithmetic means. We also analyse the applicability of the OWA operator in business and economics and we see that we can use it instead of the weighted average. We end the paper with an application in a business multi-person decision-making problem regarding production management

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

Updating Ambiguity Averse Preferences

Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we charac- terize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As an appli- cation of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth am- biguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of Bayes's rule.Updating, Dynamic Consistency, Ambiguity, Regret, Ellsberg, Bayesian, Consequentialism, Smooth Ambiguity

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

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