A New Binary Programming Formulation and Social Choice Property for Kemeny Rank Aggregation

Rank aggregation is widely used in group decision making and many other applications, where it is of interest to consolidate heterogeneous ordered lists. Oftentimes, these rankings may involve a large number of alternatives, contain ties, and/or be incomplete, all of which complicate the use of robust aggregation methods. In particular, these characteristics have limited the applicability of the aggregation framework based on the Kemeny-Snell distance, which satisfies key social choice properties that have been shown to engender improved decisions. This work introduces a binary programming formulation for the generalized Kemeny rank aggregation problem—whose ranking inputs may be complete and incomplete, with and without ties. Moreover, it leverages the equivalence of two ranking aggregation problems, namely, that of minimizing the Kemeny-Snell distance and of maximizing the Kendall-τ correlation, to compare the newly introduced binary programming formulation to a modified version of an existing integer programming formulation associated with the Kendall-τ distance. The new formulation has fewer variables and constraints, which leads to faster solution times. Moreover, we develop a new social choice property, the nonstrict extended Condorcet criterion, which can be regarded as a natural extension of the well-known Condorcet criterion and the Extended Condorcet criterion. Unlike its parent properties, the new property is adequate for handling complete rankings with ties. The property is leveraged to develop a structural decomposition algorithm, through which certain large instances of the NP-hard Kemeny rank aggregation problem can be solved exactly in a practical amount of time. To test the practical implications of the new formulation and social choice property, we work with instances constructed from a probabilistic distribution and with benchmark instances from PrefLib, a library of preference data.

Selection of the set of areal units for economic regional research on the land use: a proposal for Aggregation Problem solution

The knowledge of the spatial development of phenomena is crucial in the case of research in economics, geological survey, mining, earth resources and geography. In the literature one can diagnose an important methodological and implementation gap concerning the selection of the set of areal units within the Aggregation Problem. The issue relates to determining boundaries of areal units (regions), whose properties are described by spatial data. The boundaries of areas should be established in such a way that a given analyzed phenomenon is influenced by the same main causes. Only in this case, the analyzed spatial data will properly reflect the impact of main causes, the properties of phenomena and dependencies between them. This means that determining the proper boundaries of areas is a necessary condition for receiving correct conclusions (e.g. delimiting metropolitan areas, assessing mineral resource potential and deposits, or assessing the dynamics of surface processes). From this perspective, the main objective of the article is presenting the proposal for solving the Aggregation Problem, where as the case study the economic analysis of agrarian resources and structure is used. The solution to the problem will lead to establishing the system of macroregions, where the obtained proposal of a system of four sets of areal units is important from the point of view of spatial research. The main added value of the research and its specific contribution to the literature is based on the fact that the proposed solution to the Aggregation Problem can be considered as universal, which is not limited to selected scientific disciplines. The methodology presented in the article can be effectively applied to other spatial research in the field of geology and mining, where the most appropriate research field is the issue of locating areas with appropriate properties or areas which are affected by given analised phenomena.

Multiple Attribute Decision-Making Based on Three-Parameter Generalized Weighted Heronian Mean

For the aggregation problem of attributes with a correlation relationship, it is often necessary to take the correlation factor into account in order to make the decision results more objective and reasonable. The Heronian mean is an aggregation operator which reflects the interaction between attributes. It is of great theoretical and practical significance to study and popularize the multiple attribute decision-making methods based on the Heronian mean operator. In this paper, we first give a new three-parameter generalized weighted Heronian mean (TPGWHM), which has a series of excellent properties such as idempotency, monotonicity and boundedness. At the same time, the relationship between the TPGWHM and the existing aggregation operators is given. Then, we propose the intuitionistic fuzzy three-parameter generalized weighted Heronian mean (IFTPGWHM) and give its idempotency, monotonicity, boundedness and limit properties. On this basis, a multiple attribute decision-making method based on the TPGWHM and a multiple attribute decision-making method based on the IFTPGWHM are given, and corresponding examples are given and analyzed.

Weighted Consensus Segmentations

The problem of segmenting linearly ordered data is frequently encountered in time-series analysis, computational biology, and natural language processing. Segmentations obtained independently from replicate data sets or from the same data with different methods or parameter settings pose the problem of computing an aggregate or consensus segmentation. This Segmentation Aggregation problem amounts to finding a segmentation that minimizes the sum of distances to the input segmentations. It is again a segmentation problem and can be solved by dynamic programming. The aim of this contribution is (1) to gain a better mathematical understanding of the Segmentation Aggregation problem and its solutions and (2) to demonstrate that consensus segmentations have useful applications. Extending previously known results we show that for a large class of distance functions only breakpoints present in at least one input segmentation appear in the consensus segmentation. Furthermore, we derive a bound on the size of consensus segments. As show-case applications, we investigate a yeast transcriptome and show that consensus segments provide a robust means of identifying transcriptomic units. This approach is particularly suited for dense transcriptomes with polycistronic transcripts, operons, or a lack of separation between transcripts. As a second application, we demonstrate that consensus segmentations can be used to robustly identify growth regimes from sets of replicate growth curves.

Learning Optimal Forecast Aggregation in Partial Evidence Environments

We consider the forecast aggregation problem in repeated settings where the forecasts are of a binary state of nature. In each period multiple experts provide forecasts about the state. The goal of the aggregator is to aggregate those forecasts into a subjective accurate forecast. We assume that the experts are Bayesian and the aggregator is non-Bayesian and ignorant of the information structure (i.e., the distribution over the signals) under which the experts make their forecasts. The aggregator observes the experts’ forecasts only. At the end of each period, the realized state is observed by the aggregator. We focus on the question of whether the aggregator can learn to optimally aggregate the forecasts of the experts, where the optimal aggregation is the Bayesian aggregation that takes into account all the information in the system. We consider the class of partial evidence information structures, where each expert is exposed to a different subset of conditionally independent signals. Our main results are positive: we show that optimal aggregation can be learned in polynomial time in quite a wide range of instances in partial evidence environments. We provide an exact characterization of the instances where optimal learning is possible as well as those where it is impossible.

Structural evolution and sulfuration of nickel cobalt hydroxides from 2D to 1D on 3D diatomite for supercapcitors

Transition metal nickel cobalt hydroxides widely are used as electrode materials for supercapacitors due to its intriguing active components properties. Nevertheless, the aggregation problem and poor electrical conductivity severely hinder...