Minimum Disagreement Research Articles

An attitudinal consensus method under uncertainty in 3PRLP selection

To underpin a reverse logistics (RL) outsourcing decision, this study aims to investigate a third-party reverse logistics provider (3PRLP) selection problem under the framework of group decision making (GDM). Group attitude towards distinctive opinions may affect the time and cost on consensus reaching process (CRP). Therefore, an attitudinal consensus method under uncertainty is established and composed of three parts: initialization process, consensus process and selection process. In initialization process, considering each expert’s risk preference, a transformation rule is deployed to compute semantics possibility distribution of general comparative linguistic expressions (GCLEs) based on the numerical counterpart of linguistic assessment. In consensus process, three group attitudes-oriented consensus policies are qualitatively presented, including maximum, indifference and minimum disagreement consensus policies. Considering the feasible interval of attitudinal parameter, a new consensus measure under uncertainty, i.e., attitudinal consensus acceptability index (ACAI), is quantitively defined by stochastic acceptability analysis. To resolve the issue that the consensus degree fails to reach a predefined level, an automatic feedback mechanism is designed, and is supported by a consensus improvement algorithm evolving GCLEs’ possibility distribution. In selection process, to identify the criteria weight, incomplete information such as pairwise comparisons of criteria are characterized by ordinal regression-like linear programming. TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) is extended on fuzzy measure and then acted as rank function in stochastic acceptability analysis to explore the uncertainty of criteria preference. Lastly, 3PRLP selection for an automobile manufacturing firm is conducted to demonstrate the flexibility and practicability of our method along with sensitivity analysis and comparative analysis.

An attitudinal consensus degree to control the feedback mechanism in group decision making with different adjustment cost

This article aims to study the influence of the group attitude on the consensus reaching process in group decision making (GDM). To do that, the attitudinal consensus index (ACI) is defined to aggregate individual consensus levels to form a collective one. This approach allows for the implementation of the group attitude in a continuous state ranging from a pessimistic attitude to an optimistic attitude. Then, ACI is used to build a stop policy to control feedback for consensus, which can be regarded as a generation of the traditional polices: ‘minimum disagreement policy’ and ‘indifferent disagreement policy’. A sensitivity analysis method with visual simulation is proposed to check the adjustment cost and consensus level with different attitudinal parameters. The main conclusion from this analysis is that the bigger the attitudinal parameter implemented is, the bigger the adjustment cost and consensus level are. The visual information facilitates the inconsistent expert keeping a balance between the attitudinal parameter to implement and the adjustment cost and consensus level, which in practice translates into full control of such implementation based on the decision maker’s willingness.

Hierarchical design of fast Minimum Disagreement algorithms

We compose a toolbox for the design of Minimum Disagreement algorithms. This box contains general procedures which transform (without much loss of efficiency) algorithms that are successful for some d-dimensional (geometric) concept class C into algorithms which are successful for a (d+1)-dimensional extension of C. An iterative application of these transformations has the potential of starting with a base algorithm for a trivial problem and ending up at a smart algorithm for a non-trivial problem. In order to make this working, it is essential that the algorithms are not proper, i.e., they return a hypothesis that is not necessarily a member of C. However, the “price” for using a super-class H of C is so low that the resulting time bound for achieving accuracy ε in the model of agnostic learning is significantly smaller than the time bounds achieved by the up-to-date best (proper) algorithms.We evaluate the transformation technique for d=2 on both artificial and real-life data sets and demonstrate that it provides a fast algorithm, which can successfully solve practical problems on large data sets.

Modeling and optimizing the process of modifying chlorine-containing epoxy resins using butanediol

The results of an investigation of the modification kinetics of chlorine-containing epoxy resins by 1,4-butanediol in the presence of alkali catalyst have been considered. Experimental investigations have been carried out using a Setaram C80 calorimeter of heat flow in combination with analytical methods for determining initial and final functional groups. The link between conversion and the heat effect was set. A two-phase kinetic model of the modification process was proposed. The parameters of the proposed model have been determined from the condition of minimum disagreement between the experimental and calculated data using nonlinear programming methods in order to find the minimum. The task of finding the optimal temperature profile has been set and solved. A scheme of process control for maintaining the optimal temperature has been proposed.

TU‐G‐103‐07: Quantifying the Dose Distribution of OBI CBCT Using Monte Carlo Simulations with a Measurement‐Based Source Model

Purpose: To test the feasibility of using a measurement‐based source model in Monte Carlo simulations to calculate in‐phantom 3D dose distributions, with the application to kV‐CBCT dose quantification on a Varian OBI platform. Methods: A 3‐part nested CTDI phantom was used in this investigation. It contains 7 tracks in the x‐y plane that can be probed. The central reference point of the phantom was aligned at machine isocenter, and using standard head and pelvis CBCT protocols, point dose measurements were made at various 3D locations with a 0.6cc thimble ionization chamber by moving the phantom along the z‐direction and changing the ionization chamber position among the tracks under repetitive scans. We have generated a measurement‐based source model for the OBI system and incorporated it with the Monte Carlo software MCNPX to model each CBCT protocol under examination. The in‐phantom CBCT dose (mGy per particle) was simulated at all 3D measurement locations and converted to absolute dose (mGy) by normalizing with the ratio between measured and Monte Carlo simulated dose at the reference center. The calculated results were compared with the physical measurement and their discrepancies were assessed quantitatively. Results: Agreement was observed between Monte Carlo simulation results and in‐phantom measurements for both the OBI CBCT head and pelvis protocols. For the head protocol, the average agreement was 3.40% with a maximum and minimum disagreement of 5.72% and 1.61%, respectively. For the pelvis protocol, the average agreement was 3.18% with a maximum and minimum disagreement of 4.29% and 1.87%, respectively. Conclusion: We have demonstrated the accuracy of a measurement‐based OBI source model to reproduce an array of measured point doses in phantom when using the CBCT mode of operation. These results serve as the basis for using this source model to investigate OBI dosimetry with anthropomorphic phantoms and patient specific models. (a) Dr. McNitt‐Gray: Institutional research agreement, Siemens AG;Recipient research support Siemens AG; Consultant, Flaherty Sensabaugh Bonasso PLLC; Consultant, Fulbright and Jaworski, LLC; (b) Dr. Dan Ruan: Recipient research support AACR; Recipient research support TRDRP; (c) K McMillan: Research partially supported by a grant from Siemens AG; Research partially supported by a grant from AACR; Research partially supported by a grant from TRDRP

Sparse weighted voting classifier selection and its linear programming relaxations

We consider the problem of minimizing the number of misclassifications of a weighted voting classifier, plus a penalty proportional to the number of nonzero weights. We first prove that its optimum is at least as hard to approximate as the minimum disagreement halfspace problem for a wide range of penalty parameter values. After formulating the problem as a mixed integer program (MIP), we show that common “soft margin” linear programming (LP) formulations for constructing weighted voting classsifiers are equivalent to an LP relaxation of our formulation. We show that this relaxation is very weak, with a potentially exponential integrality gap. However, we also show that augmenting the relaxation with certain valid inequalities tightens it considerably, yielding a linear upper bound on the gap for all values of the penalty parameter that exceed a reasonable threshold. Unlike earlier techniques proposed for similar problems (Bradley and Mangasarian (1998) [4], Weston et al. (2003) [14]), our approach provides bounds on the optimal solution value.

Poster — Thur Eve — 07: Measurement of Radiation‐Light Congruence Using a Photodiode Array

Many factors affect treatment delivery, including setup errors during the simulation process, dose calculation uncertainty, patient setup errors during treatment, and errors that result from incorrect calibration and geometric setup of the linear accelerator. Among these, the radiation‐light congruence is especially important because the light field is used to simulate the radiation beam. The light field is an integral part of patient setup and jaw calibration, thus radiation‐light congruence is essential for accurate treatment delivery. We have developed a novel device that enables precise and automated measurement of radiation‐light congruence. Using the device, we show that the radiation‐light field congruence for both 6 and 15 MV beams is within standard tolerance limits. However, our results indicate that radiation‐light congruence is dependent on collimator angle and energy. The maximum measured disagreement between radiation field edge and light field edge was 1.290 ± 0.004 mm at collimator angle 270 (X1, 15 MV) and 0.932 ± 0.003 mm at collimator angle 90 (Y2, 15MV). The minimum disagreement was 0.016 ± 0.003 mm for 270 (X2, 6 MV) and 0.102 ± 0.004 mm for 90 (X2, 6MV). This detector and measurement method will give us a better understanding of the radiation‐light congruence dependence on collimator angle and energy. It could also be used to determine location of the x‐ray source within the linear accelerator.

Economic freedom ranking of 161 countries in year 2000: a minimum disagreement approach

Since 1995, the Heritage Foundation has published the economic freedom index for countries throughout the world. The fundamental challenge is how to objectively measure economic freedom so that the index can be fair, credible and has the least disagreements among all countries. In this paper, we propose a new approach to construct economic freedom ranking which minimizes disagreements among countries. The mathematical model consists of two stages: (1) calculate the set of weights for each country which would give each country the best ranking, and (2) aggregation of ranks from all countries to minimize their disagreements. We apply the model to the data set of year 2000 on Economic Freedom from the Heritage Foundation, and find that the minimum disagreements from the proposed ranking improves by 9%.

Sample-efficient strategies for learning in the presence of noise

In this paper, we prove various results about PAC learning in the presence of malicious noise. Our main interest is the sample size behavior of learning algorithms. We prove the first nontrivial sample complexity lower bound in this model by showing that order of ε/Δ 2 + d /Δ (up to logarithmic factors) examples are necessary for PAC learning any target class of {0,1}-valued functions of VC dimension d , where ε is the desired accuracy and η = ε/(1 + ε) - Δ the malicious noise rate (it is well known that any nontrivial target class cannot be PAC learned with accuracy ε and malicious noise rate η ≥ ε/(1 + ε), this irrespective to sample complexity). We also show that this result cannot be significantly improved in general by presenting efficient learning algorithms for the class of all subsets of d elements and the class of unions of at most d intervals on the real line. This is especialy interesting as we can also show that the popular minimum disagreement strategy needs samples of size d ε/Δ 2 , hence is not optimal with respect to sample size. We then discuss the use of randomized hypotheses. For these the bound ε/(1 + ε) on the noise rate is no longer true and is replaced by 2ε/(1 + 2ε). In fact, we present a generic algorithm using randomized hypotheses that can tolerate noise rates slightly larger than ε/(1 + ε) while using samples of size d /ε as in the noise-free case. Again one observes a quadratic powerlaw (in this case d ε/Δ 2 , Δ = 2ε/(1 + 2ε) - η) as Δ goes to zero. We show upper and lower bounds of this order.

Packing analysis of carbohydrates and polysaccharides. IV. A new method for detailed crystal structure refinement of polysaccharides and its application to V-amylose.

AbstractA method is described for predicting and solving crystal structures of linear homopolysaccharides. The method is based on the refinement of the structure with respect to either stereochemical constraints or x‐ray diffraction intensities. In the refinement process, all conformational and packing features of the molecule, such as bond lengths, bond angles, conformational angles, nonbonded contacts, hydrogen bonds, etc., can be allowed to vary until the structure reaches both a conformation and crystalline packing that are in minimum disagreement with the stereochemical restraints and the diffraction data. In this fashion, both packing and conformational features of the structure can be simultaneously refined, and not separately as has been the custom in the past. The refinement procedure is based on a method of constrained optimization which possesses improved characteristics of reaching a solution and avoiding false minima, in comparison with least squares methods. The procedure is, in addition, capable of easily finding molecules of solvent of crystallization. The method was applied to further refining the previously solved crystal structure of V‐amylose. The results indicated that contrary to the previously found six‐fold molecular symmetry in the P212121 space group, the V‐amylose molecule exhibits only two‐fold symmetry with the asymmetric unit consisting of three glucose residues in one‐half turn of the helix. The three residues are nonequivalent principally due to unequal rotational positions of the hydroxymethyl groups. The crystal structure of V‐amylose predicted from stereochemical refinement was identical in all details with that obtained from refining against X‐ray data. The excellent agreement with the diffraction data was indicated by the crystallographic disagreement index R = 0.25.