Reasoning with PCP-Nets

We introduce PCP-nets, a formalism to model qualitative conditional preferences with probabilistic uncertainty. PCP-nets generalise CP-nets by allowing for uncertainty over the preference orderings. We define and study both optimality and dominance queries in PCP-nets, and we propose a tractable approximation of dominance which we show to be very accurate in our experimental setting. Since PCP-nets can be seen as a way to model a collection of weighted CP-nets, we also explore the use of PCP-nets in a multi-agent context, where individual agents submit CP-nets which are then aggregated into a single PCP-net. We consider various ways to perform such aggregation and we compare them via two notions of scores, based on well known voting theory concepts. Experimental results allow us to identify the aggregation method that better represents the given set of CP-nets and the most efficient dominance procedure to be used in the multi-agent context.

Preface to the Special Issue on “Applications of Fuzzy Optimization and Fuzzy Decision Making”

During the last decades, fuzzy optimization and fuzzy decision making have gained significant attention, aiming to provide robust solutions for problems in making decisions and achieving complex optimization characterized by non-probabilistic uncertainty, vagueness, ambiguity and hesitation [...]

Executive control by fronto-parietal activity explains counterintuitive decision behavior in complex value-based decision-making

In real life, humans make decisions by taking into account multiple independent factors, such as delay and probability. Cognitive psychology suggests that cognitive control mechanisms play a key role when facing such complex task conditions. However, in value-based decision-making, it still remains unclear to what extent cognitive control mechanisms become essential when the task condition is complex. In this study, we investigated decision-making behaviors and underlying neural mechanisms using a multifactor gambling task where participants simultaneously considered probability and delay. Decision-making behavior in the multifactor task was modulated by both probability and delay. The behavioral effect of probability was stronger than delay, consistent with previous studies. Furthermore, in a subset of conditions that recruited fronto-parietal activations, reaction times were paradoxically elongated despite lower probabilistic uncertainty. Notably, such a reaction time elongation did not occur in control tasks involving single factors. Meta-analysis of brain activations suggested an association between the paradoxical increase of reaction time and strategy switching. Together, these results suggest a novel aspect of complex value-based decision-makings that is strongly influenced by fronto-parietal cognitive control.

Computing the Number of Failures for Fuzzy Weibull Hazard Function

The number of failures plays an important factor in the study of maintenance strategy of a manufacturing system. In the real situation, this number is often affected by some uncertainties. Many of the uncertainties fall into the possibilistic uncertainty, which are different from the probabilistic uncertainty. This uncertainty is commonly modeled by applying the fuzzy theoretical framework. This paper aims to compute the number of failures for a system which has Weibull failure distribution with a fuzzy shape parameter. In this case two different approaches are used to calculate the number. In the first approach, the fuzziness membership of the shape parameter propagates to the number of failures so that they have exactly the same values of the membership. While in the second approach, the membership is computed through the α-cut or α-level of the shape parameter approach in the computation of the formula for the number of failures. Without loss of generality, we use the Triangular Fuzzy Number (TFN) for the Weibull shape parameter. We show that both methods have succeeded in computing the number of failures for the system under investigation. Both methods show that when we consider the function of the number of failures as a function of time then the uncertainty (the fuzziness) of the resulting number of failures becomes larger and larger as the time increases. By using the first method, the resulting number of failures has a TFN form. Meanwhile, the resulting number of failures from the second method does not necessarily have a TFN form, but a TFN-like form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification (GMVD) method. The results show that for certain weighting factor of the GMVD, the cores of these fuzzy numbers of failures are identical.

Modeling Earthmoving Operations in Real-Time Using Hybrid Fuzzy Simulation

Predicting and optimizing performance in earthmoving operations is critical, because they are essential to many construction projects. The complexity of modeling earthmoving operations remains challenging, even with several modeling techniques available, including simulation. This paper advances the state-of-the-art of modeling earthmoving operations by introducing a hybrid fuzzy system dynamics–discrete event simulation framework with the capacity to: capture the dynamism of performance in earthmoving operations; capture subjective uncertainty of several factors affecting them; model their sequential nature and resource constraints; and determine actual travel time, in real time, using online navigation systems. Findings from this research confirm the proposed framework (1) extends the application of simulation techniques for modeling construction processes involving dynamic input variables and subjective uncertainty, through its ability to capture the non-probabilistic uncertainty of construction systems, and (2) when combined with the use of online navigation systems to assess trucks’ travel time, improves the accuracy of earthmoving operation models.

Bayesian numerical methods for nonlinear partial differential equations

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an inferential perspective, most notably the absence of explicit conditioning formula. This paper extends earlier work on linear PDEs to a general class of initial value problems specified by nonlinear PDEs, motivated by problems for which evaluations of the right-hand-side, initial conditions, or boundary conditions of the PDE have a high computational cost. The proposed method can be viewed as exact Bayesian inference under an approximate likelihood, which is based on discretisation of the nonlinear differential operator. Proof-of-concept experimental results demonstrate that meaningful probabilistic uncertainty quantification for the unknown solution of the PDE can be performed, while controlling the number of times the right-hand-side, initial and boundary conditions are evaluated. A suitable prior model for the solution of PDEs is identified using novel theoretical analysis of the sample path properties of Matérn processes, which may be of independent interest.

Modeling changes in probabilistic reinforcement learning during adolescence

In the real world, many relationships between events are uncertain and probabilistic. Uncertainty is also likely to be a more common feature of daily experience for youth because they have less experience to draw from than adults. Some studies suggest probabilistic learning may be inefficient in youths compared to adults, while others suggest it may be more efficient in youths in mid adolescence. Here we used a probabilistic reinforcement learning task to test how youth age 8-17 (N = 187) and adults age 18-30 (N = 110) learn about stable probabilistic contingencies. Performance increased with age through early-twenties, then stabilized. Using hierarchical Bayesian methods to fit computational reinforcement learning models, we show that all participants’ performance was better explained by models in which negative outcomes had minimal to no impact on learning. The performance increase over age was driven by 1) an increase in learning rate (i.e. decrease in integration time scale); 2) a decrease in noisy/exploratory choices. In mid-adolescence age 13-15, salivary testosterone and learning rate were positively related. We discuss our findings in the context of other studies and hypotheses about adolescent brain development.