Generalized Distance Measures for Asymmetric Multivariate Distributions

1998 ◽  
pp. 503-508 ◽  
Author(s):  
Marco Riani ◽  
Sergio Zani
Keyword(s):  
Distance Measures ◽  
Multivariate Distributions ◽  
Generalized Distance Measures ◽  
Generalized Distance

scholarly journals A Novel Group Decision-Making Method Based on Generalized Distance Measures of PLTSs on E-Commerce Shopping

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Juxiang Wang ◽  
Jian Yuan ◽  
Jiajing Zhang ◽  
Miao Tang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Distance Measures ◽  
Sensitivity Analyses ◽  
Linguistic Term ◽  
Probabilistic Linguistic Term Sets ◽  
Generalized Distance Measures ◽  
Evaluation Information ◽  
Generalized Distance

In multiattribute group decision-making (MAGDM), due to quantity, fuzziness, and complexity of evaluation linguistic information on commodities, traditional distance measures need to be extended to the integration of evaluation information under a multigranular probabilistic linguistic environment. A more reasonable method is proposed to deal with the missing value in the evaluation information. On the basis of the generalized distance measures and filling in the missing evaluation information, some novel distance measures between two multigranular probabilistic linguistic term sets (PLTSs) are presented in this paper. Based on these distance measures, three extended decision-making (DM) algorithms based on TOPSIS, the extended TOPSIS, and VIKOR are proposed, which are MGPL-TOPSIS, MGPL-ETOPSIS, and MGPL-VIKOR, respectively. The case analyses on purchasing a car are provided to illustrate the application of the extended multiattribute group decision-making (MAGDM) algorithms. Then, sensitivity analyses based on PT are proposed as well. In particular, the extended TOPSIS method is presented. These results demonstrate the novelty, feasibility, and rationality of the distance measures between two multigranular PLTSs proposed in this paper.

scholarly journals An Extended VIKOR Method for Multiple Attribute Decision Analysis with Bidimensional Dual Hesitant Fuzzy Information

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Min Xue ◽  
Xiaoan Tang ◽  
Nanping Feng
Keyword(s):  
Decision Analysis ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Entropy Measure ◽  
Vikor Method ◽  
Multiple Attribute ◽  
Generalized Distance

Bidimensional dual hesitant fuzzy (BDHF) set is developed to present preferences of a decision maker or an expert, which is more objective than existing fuzzy sets such as Atanassov’s intuitionistic fuzzy set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, after investigating some distance measures, we define a new generalized distance measure between two BDHF elements with parameterλfor the sake of overcoming some drawbacks in existing distance measures. Covering all possible values of parameterλ, a new approach is designed to calculate the generalized distance measure between two BDHF elements. In order to address complex multiple attribute decision analysis (MADA) problems, an extension of fuzzy VIKOR method in BDHF context is proposed in this paper. In VIKOR method for MADA problems, weight of each attribute indicates its relative importance. To obtain weights of attributes objectively, a new entropy measure with BDHF information is developed to create weight of each attribute. Finally, an evaluation problem of performance of people’s livelihood project in several regions is analyzed by the proposed VIKOR method to demonstrate its applicability and validity.

GENERALIZED MOVING AVERAGES, DISTANCE MEASURES AND OWA OPERATORS

2013 ◽  
Vol 21 (04) ◽  
pp. 533-559 ◽  
Author(s):  
JOSÉ M. MERIGÓ ◽  
RONALD R. YAGER
Keyword(s):  
Moving Average ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Wide Range ◽  
Moving Averaging ◽  
Generalized Distance ◽  
Weighted Moving Average

The concept of moving average is studied. We analyze several extensions by using generalized aggregation operators, obtaining the generalized moving average. The main advantage is that it provides a general framework that includes a wide range of specific cases including the geometric and the quadratic moving average. This analysis is extended by using the generalized ordered weighted averaging (GOWA) and the induced GOWA (IGOWA) operator. Thus, we get the generalized ordered weighted moving average (GOWMA) and the induced GOWMA (IGOWMA) operator. Some of their main properties are studied. We further extend this approach by using distance measures suggesting the concept of distance moving average and generalized distance moving average. We also consider the case with the OWA and the IOWA operator, obtaining the generalized ordered weighted moving averaging distance (GOWMAD) and the induced GOWMAD (IGOWMAD) operator. The paper ends with an application in multi-period decision making.

scholarly journals A Kernel-Based Metric for Balance Assessment

2018 ◽  
Vol 6 (2) ◽  
Author(s):  
Yeying Zhu ◽  
Jennifer S. Savage ◽  
Debashis Ghosh
Keyword(s):  
Reproducing Kernel ◽  
Causal Effect ◽  
Distance Measures ◽  
Multivariate Distributions ◽  
Treatment Groups ◽  
Dieting Behavior ◽  
Kernel Distance ◽  
Kernel Hilbert Spaces ◽  
Matching Procedure ◽  
The Difference

AbstractAn important goal in causal inference is to achieve balance in the covariates among the treatment groups. In this article, we introduce the concept of distributional balance preserving which requires the distribution of the covariates to be the same in different treatment groups. We also introduce a new balance measure called kernel distance, which is the empirical estimate of the probability metric defined in the reproducing kernel Hilbert spaces. Compared to the traditional balance metrics, the kernel distance measures the difference in the two multivariate distributions instead of the difference in the finite moments of the distributions. Simulation results show that the kernel distance is the best indicator of bias in the estimated casual effect compared to several commonly used balance measures. We then incorporate kernel distance into genetic matching, the state-of-the-art matching procedure and apply the proposed approach to analyze the Early Dieting in Girls study. The study indicates that mothers’ overall weight concern increases the likelihood of daughters’ early dieting behavior, but the causal effect is not significant.

scholarly journals Generalized Distance Bribery

2019 ◽  
Vol 33 ◽  
pp. 1764-1771 ◽  
Author(s):  
Dorothea Baumeister ◽  
Tobias Hogrebe ◽  
Lisa Rey
Keyword(s):  
Polynomial Time ◽  
Scoring Rules ◽  
Distance Measures ◽  
Polynomial Time Algorithms ◽  
External Agent ◽  
Np Hardness ◽  
Generalized Distance

The bribery problem in elections asks whether an external agent can make some distinguished candidate win or prevent her from winning, by bribing some of the voters. This problem was studied with respect to the weighted swap distance between two votes by Elkind et al. (2009). We generalize this definition by introducing a bound on the distance between the original and the bribed votes. The distance measures we consider include a restriction of the weighted swap distance and variants of the footrule distance, which capture some realworld models of influence an external agent may have on the voters. We study constructive and destructive variants of distance bribery for scoring rules and obtain polynomial-time algorithms as well as NP-hardness results. For the case of element-weighted swap and element-weighted footrule distances, we give a complete dichotomy result for the class of pure scoring rules.

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