Pessimistic Rule Research Articles

Multiclass fuzzy user equilibrium with endogenous membership functions and risk‐taking behaviors

SummaryOver the last decades, several approaches have been proposed in the literature to incorporate users' perceptions of travel costs, their bounded rationality, and risk‐taking behaviors into network equilibrium modeling for traffic assignment problem. While theoretically advanced, these models often suffer from high complexity and computational cost and often involve parameters that are difficult to estimate. This study proposes an alternative approach where users' imprecise perceptions of travel times are endogenously constructed as fuzzy sets based on the probability distributions of random link travel times. Two decision rules are proposed accordingly to account for users' heterogeneous risk‐taking behaviors, that is, optimistic and pessimistic rules. The proposed approach, namely, the multiclass fuzzy user equilibrium, can be formulated as a link‐based variational inequality model. The model can be solved efficiently, and parameters involved can be either easily estimated or treated as factors for calibration against observed traffic flow data. Numerical examples show that the proposed model can be solved efficiently even for a large‐scale network of Mashhad, Iran, with 2538 links and 7157 origin–destination pairs. The example also illustrates the calibration capability of the proposed model, highlighting that the model is able to produce much more accurate flow estimates compared with the Wardropian user equilibrium model. Copyright © 2016 John Wiley & Sons, Ltd.

Setting conservation management thresholds using a novel participatory modeling approach.

We devised a participatory modeling approach for setting management thresholds that show when management intervention is required to address undesirable ecosystem changes. This approach was designed to be used when management thresholds: must be set for environmental indicators in the face of multiple competing objectives; need to incorporate scientific understanding and value judgments; and will be set by participants with limited modeling experience. We applied our approach to a case study where management thresholds were set for a mat-forming brown alga, Hormosira banksii, in a protected area management context. Participants, including management staff and scientists, were involved in a workshop to test the approach, and set management thresholds to address the threat of trampling by visitors to an intertidal rocky reef. The approach involved trading off the environmental objective, to maintain the condition of intertidal reef communities, with social and economic objectives to ensure management intervention was cost-effective. Ecological scenarios, developed using scenario planning, were a key feature that provided the foundation for where to set management thresholds. The scenarios developed represented declines in percent cover of H. banksii that may occur under increased threatening processes. Participants defined 4 discrete management alternatives to address the threat of trampling and estimated the effect of these alternatives on the objectives under each ecological scenario. A weighted additive model was used to aggregate participants' consequence estimates. Model outputs (decision scores) clearly expressed uncertainty, which can be considered by decision makers and used to inform where to set management thresholds. This approach encourages a proactive form of conservation, where management thresholds and associated actions are defined a priori for ecological indicators, rather than reacting to unexpected ecosystem changes in the future.

Expectation Formation Rules and the Core of Partition Function Games

This paper proposes axiomatic foundations of expectation formation rules, by which deviating players anticipate the reaction of external players in a partition function game. The axioms single out the projection rule among the rules that depend on the current partition and the pessimistic rule among the ones that are independent of the current partition. This analysis suggests that the projection core and the pessimistic core are natural candidates to study the stability of games in partition function form, and we compute these cores in two standard applications of coalition formation with externalities, namely cartels and public goods.

Expectation formation rules and the core of partition function games

This paper proposes axiomatic foundations of expectation formation rules, by which deviating players anticipate the reaction of external players in a partition function game. The projection rule is the only rule satisfying subset consistency and responsiveness to the original partition of non-deviating players. It is also the only rule satisfying subset consistency, independence of the original partition of deviating players, and coherence of expectations. Exogenous rules are the only rules satisfying subset consistency and independence of the original partition, and the pessimistic rule is the only rule generating superadditive coalitional games.

Learning criteria weights of an optimistic Electre Tri sorting rule

Multiple criteria sorting methods assign alternatives to predefined ordered categories taking multiple criteria into consideration. The Electre Tri method compares alternatives to several profiles separating the categories. Based on such comparisons, each alternative is assigned to the lowest (resp. highest) category for which it is at least as good as the lower profile (resp. is strictly preferred by the higher profile) of the category, and the corresponding assignment rule is called pessimistic (resp. optimistic). We propose algorithms for eliciting the criteria weights and majority threshold in a version of the optimistic Electre Tri rule, which raises additional difficulties w.r.t. the pessimistic rule. We also describe an algorithm that computes robust alternatives׳ assignments from assignment examples. These algorithms proceed by solving mixed integer programs. Several numerical experiments are conducted to test the proposed algorithms on the following issues: learning ability of the algorithm to reproduce the DM׳s preference, robustness analysis and ability to identify conflicting preference information in case of inconsistencies in the learning set. Experiments show that eliciting the criteria weights in an accurate way requires quite a number of assignment examples. Furthermore, considering more criteria increases the information requirement. The present empirical study allows us to draw some lessons in view of practical applications of Electre Tri using the optimistic rule.

Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information

Egalitarianism and utilitarianism can be viewed as two opposed axiomatic principles from where to begin the search of appropriate solutions to multi-criteria problems. When a vector of criterion weights is provided, these two principles yield respectively to weighted maxmin solutions, and to weighted utilitarian solutions. However, if only partial information about the importance of the criteria is available, the situation becomes more complex and a variety of solutions which extend the utilitarian and the maxmin solution arise. In this paper we explore some of these solutions and their axiomatic properties. If a utilitarian principle is first considered and a pessimistic or an optimistic rule applied afterwards, then two new solution concepts arise. Utilitarian solutions based on the pessimistic rule are inequality averse, and therefore can be viewed as a compromise between the egalitarian and utilitarian solutions. We also explore the solutions obtained when an egalitarian principle with respect to the criteria is considered and a pessimistic or an optimistic rule is applied to select criterion weights.

The computational complexity of bilevel assignment problems

In bilevel optimization problems there are two decision makers, the leader and the follower, who act in a hierarchy. Each decision maker has his own objective function, but there are common constraints. This paper deals with bilevel assignment problems where each decision maker controls a subset of edges and each edge has a leader’s and a follower’s weight. The edges selected by the leader and by the follower need to form a perfect matching. The task is to determine which edges the leader should choose such that his objective value which depends on the follower’s optimal reaction is maximized. We consider sum- and bottleneck objective functions for the leader and follower. Moreover, if not all optimal reactions of the follower lead to the same leader’s objective value, then the follower either chooses an optimal reaction which is best (optimistic rule) or worst (pessimistic rule) for the leader. We show that all the variants arising if the leader’s and follower’s objective functions are sum or bottleneck functions are NP-hard if the pessimistic rule is applied. In case of the optimistic rule the problem is shown to be NP-hard if at least one of the decision makers has a sum objective function.

Application of decision analysis techniques to the Weber facility location problem

A location problem with future uncertainties about the data is considered. Several possible scenarios about the future values of the parameters are postulated. However, it is not clear which of these scenarios will actually happen. We find the location that will best accommodate the possible scenarios. Four rules utilized in decision theory are examined: the expected value rule, the optimistic rule, the pessimistic rule, and the minimax regret rule. The solution for the squared Euclidean distance is explicitly found. Algorithms are suggested for general convex distance metrics. An example problem is solved in detail to illustrate the findings, and computational experiments with randomly generated problems are reported.