Probabilistic Representation Of Uncertainty Research Articles

Fuzzy stochastic linear programming-based approach for multiple departures single destination multiple travelling salesman problem

The multiple departures single destination multiple travelling salesmen problem (MDmTSP) is a problem in which two or more salesmen start from any node of departure and finish their tour by reaching a single specific destination node. In many real-life problems, the decision should be made according to information which is both possibilistically imprecise and probabilistically uncertain. Although consistency indexes provide a union nexus between possibilistic and probabilistic representation of uncertainty, there are no reliable transformations between them. A means to this end is fuzzy stochastic linear programming. In this paper, a realistic environment for MDmTSP with fuzzy stochastic distance between nodes is investigated. To justify the proposed approach and to illustrate its efficiency in real-life problems, a case of employees’ bus transport routing problem (EBTRP) is presented.

Distribution type uncertainty due to sparse and imprecise data

This paper proposes a likelihood-based methodology to quantify the distribution type uncertainty while fitting probability distributions to sparse and imprecise data. In probabilistic representation of uncertainty, it is common to assume a particular type of probability distribution (e.g. normal, lognormal, etc.) while fitting distributions to available data; once this type is chosen, the distribution parameters and the uncertainty in the distribution parameters are estimated. This paper analyzes the effect of the choice of the distribution type and quantifies the resulting uncertainty in the probabilistic characterization. Two approaches – Bayesian model averaging and Bayesian hypothesis testing – are investigated for the quantification of distribution type uncertainty. Two cases – competing distribution types and uncertainty regarding a single distribution type – are considered. Once the distribution type uncertainty in a particular random variable is quantified, the uncertainty in the distribution parameters is also quantified. Further, the three types of uncertainty – variability, distribution type uncertainty, and distribution parameter uncertainty – are propagated through a response function to calculate the effect of overall input distribution uncertainty on the response uncertainty.

Chance-Constrained Optimal Path Planning With Obstacles

Autonomous vehicles need to plan trajectories to a specified goal that avoid obstacles. For robust execution, we must take into account uncertainty, which arises due to uncertain localization, modeling errors, and disturbances. Prior work handled the case of set-bounded uncertainty. We present here a chance-constrained approach, which uses instead a probabilistic representation of uncertainty. The new approach plans the future probabilistic distribution of the vehicle state so that the probability of failure is below a specified threshold. Failure occurs when the vehicle collides with an obstacle or leaves an operator-specified region. The key idea behind the approach is to use bounds on the probability of collision to show that, for linear-Gaussian systems, we can approximate the nonconvex chance-constrained optimization problem as a disjunctive convex program. This can be solved to global optimality using branch-and-bound techniques. In order to improve computation time, we introduce a customized solution method that returns almost-optimal solutions along with a hard bound on the level of suboptimality. We present an empirical validation with an aircraft obstacle avoidance example.

Quantification of margins and uncertainties: Conceptual and computational basis

In 2001, the National Nuclear Security Administration of the U.S. Department of Energy in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory and Sandia National Laboratories) initiated development of a process designated Quantification of Margins and Uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. This presentation discusses and illustrates the conceptual and computational basis of QMU in analyses that use computational models to predict the behavior of complex systems. The following topics are considered: (i) the role of aleatory and epistemic uncertainty in QMU, (ii) the representation of uncertainty with probability, (iii) the probabilistic representation of uncertainty in QMU analyses involving only epistemic uncertainty, and (iv) the probabilistic representation of uncertainty in QMU analyses involving aleatory and epistemic uncertainty.

Qualitative decision theory

This paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible, in the scope of artificial intelligence. Contrary to classical approaches to decision theory, we try to rank acts without resorting to any numerical representation of utility or uncertainty, and without using any scale on which both uncertainty and preference could be mapped. Our approach is a variant of Savage's where the setting is finite, and the strict preference on acts is a partial order. It is shown that although many axioms of Savage theory are preserved and despite the intuitive appeal of the ordinal method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty. The latter leads to the kind of paradoxes encountered in the theory of voting. It is shown that the assumption of ordinal invariance enforces a qualitative decision procedure that presupposes a comparative possibility representation of uncertainty, originally due to Lewis, and usual in nonmonotonic reasoning. Our axiomatic investigation thus provides decision-theoretic foundations to the preferential inference of Lehmann and colleagues. However, the obtained decision rules are sometimes either not very decisive or may lead to overconfident decisions, although their basic principles look sound. This paper points out some limitations of purely ordinal approaches to Savage-like decision making under uncertainty, in perfect analogy with similar difficulties in voting theory.

Preference Uncertainty in Non‐Market Valuation: A Fuzzy Approach

AbstractIn this article, we consider uncertain preferences for non‐market goods, but we move away from a probabilistic representation of uncertainty and propose the use of fuzzy contingent valuation. We assume that a decision maker never fully knows her own utility function and we treat utility as a fuzzy number. The methodology is illustrated using data on forest valuation in Sweden. Fuzzy contingent valuation provides estimates of resource value in the form of a fuzzy number and includes estimates obtained using a standard probabilistic approach.

On the alleged superiority of probabilistic representation of uncertainty

The author identifies some points of his agreement or disagreement with the position taken by Laviolette and Seaman (1994) in their debate paper. In particular, the author argues that some statements regarding the superiority of probabilistic representation of uncertainty, which are made by Laviolette and Seaman in their paper, are untenable. >