Multi-Objective Faculty Course Assignment Problem with Result and Feedback Based Uncertain Preferences

In this paper, a multi-objective faculty course allocation problem with result analysis and feedback analysis based on uncertain preferences mathematical model is presented. To deal with an uncertain model, three different ranking criteria are being used to develop: a) Expected value, b) Optimistic value, c) Dependent optimistic value criterion. These mathematical models are transformed into their corresponding deterministic forms using the basic concepts of uncertainty theory. The deterministic model of DOCM consists of fractional objectives which are converted into their linear form using Charnes and Cooper’s transformation. These deterministic formulations MOFCAP are converted into a single objective problem by using the fuzzy programming technique with linear and exponential membership functions. Further, the single objective problem for all the defined models is solved in the Lingo 18.0 software to derive the Pareto-optimal solution. The sensitivity of the models is also performed to examine the variation in the objective function due to the variation in parameters. Finally, a numerical example is given to exhibit the application and algorithm of the models.

Efficient Computation of Top-K Skyline Objects in Data Set With Uncertain Preferences

Skyline recommendation with uncertain preferences has drawn AI researchers' attention in recent years due to its wide range of applications. The naive approach of skyline recommendation computes the skyline probability of all objects and ranks them accordingly. However, in many applications, the interest is in determining top-k objects rather than their ranking. The most efficient algorithm to determine an object's skyline probability employs the concepts of zero-contributing set and prefix-based k-level absorption. The authors show that the performance of these methods highly depends on the arrangement of objects in the database. In this paper, the authors propose a method for determining top-k skyline objects without computing the skyline probability of all the objects. They also propose and analyze different methods of ordering the objects in the database. Finally, they empirically show the efficacy of the proposed approaches on several synthetic and real-world data sets.

Robust Market Equilibria with Uncertain Preferences

The problem of allocating scarce items to individuals is an important practical question in market design. An increasingly popular set of mechanisms for this task uses the concept of market equilibrium: individuals report their preferences, have a budget of real or fake currency, and a set of prices for items and allocations is computed that sets demand equal to supply. An important real world issue with such mechanisms is that individual valuations are often only imperfectly known. In this paper, we show how concepts from classical market equilibrium can be extended to reflect such uncertainty. We show that in linear, divisible Fisher markets a robust market equilibrium (RME) always exists; this also holds in settings where buyers may retain unspent money. We provide theoretical analysis of the allocative properties of RME in terms of envy and regret. Though RME are hard to compute for general uncertainty sets, we consider some natural and tractable uncertainty sets which lead to well behaved formulations of the problem that can be solved via modern convex programming methods. Finally, we show that very mild uncertainty about valuations can cause RME allocations to outperform those which take estimates as having no underlying uncertainty.