Improving Euclidean’s Consensus Degrees in Group Decision Making Problems Through a Uniform Extension

2021 ◽  
Author(s):  
J.M. Tapia ◽  
F. Chiclana ◽  
M.J. Del Moral ◽  
E. Herrera-Viedma
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Distance Function ◽  
Euclidean Distance ◽  
Group Decision ◽  
Distance Functions ◽  
Consensus Models ◽  
Interesting Task ◽  
Euclidean Distance Function ◽  
Uniform Extension

In a Group Decision Making problem, several people try to reach a single common decision by selecting one of the possible alternatives according to their respective preferences. So, a consensus process is performed in order to increase the level of accord amongst people, called experts, before obtaining the final solution. Improving the consensus degree as much as possible is a very interesting task in the process. In the evaluation of the consensus degree, the measurement of the distance representing disagreement among the experts’ preferences should be considered. Different distance functions have been proposed to implement in consensus models. The Euclidean distance function is one of the most commonly used. This paper analyzes how to improve the consensus degrees, obtained through the Euclidean distance function, when the preferences of the experts are slightly modified by using one of the properties of the Uniform distribution. We fulfil an experimental study that shows the betterment in the consensus degrees when the Uniform extension is applied, taking into account different number of experts and alternatives.

Preference–Approval Structures in Group Decision Making: Axiomatic Distance and Aggregation

2021 ◽  
Author(s):  
Yucheng Dong ◽  
Yao Li ◽  
Ying He ◽  
Xia Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Distance Function ◽  
Group Decision ◽  
Simple Majority ◽  
Simulation Experiments ◽  
Group Preference ◽  
Aggregation Model ◽  
Modeling Process ◽  
Ordinal Preference

Preference–approval structure combines the preference information of both ranking and approval, which extends the ordinal preference model by incorporating two categories of choice alternatives, that is, acceptable (good) and unacceptable (bad), in the preference modeling process. In this study, we present some axioms that imply the existence of a unique distance function of preference–approval structures. Based on theoretical analysis and simulation experiments, we further study a preferences aggregation model in the group decision-making context based on the proposed axiomatic distance function. In this model, the group preference is defined as a preference–approval structure that minimizes the sum of its distances to all preference–approval structures of individuals in the group under consideration. Particularly, we show that the group preference defined by the axiomatic distance–based aggregation model has close relationships with the simple majority rule and Cook and Seiford’s ranking.

Consensus models for AHP group decision making under row geometric mean prioritization method

2010 ◽  
Vol 49 (3) ◽  
pp. 281-289 ◽  
Author(s):  
Yucheng Dong ◽  
Guiqing Zhang ◽  
Wei-Chiang Hong ◽  
Yinfeng Xu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Geometric Mean ◽  
Prioritization Method ◽  
Consensus Models

scholarly journals Selective Image Segmentation Models Using Three Distance Functions

2021 ◽  
Vol 21 (No.1) ◽  
pp. 95-116
Author(s):  
Abdul Kadir Jumaat ◽  
Siti Aminah Abdullah
Keyword(s):  
Image Segmentation ◽  
Distance Function ◽  
Execution Time ◽  
Euclidean Distance ◽  
Operator Splitting ◽  
Splitting Method ◽  
Distance Functions ◽  
Similarity Coefficients ◽  
City Block ◽  
Euclidean Distance Function

Image segmentation can be defined as partitioning an image that contains multiple segments of meaningful parts for further processing. Global segmentation is concerned with segmenting the whole object of an observed image. Meanwhile, the selective segmentation model is focused on segmenting a specific object required to be extracted. The Convex Distance Selective Segmentation (CDSS) model, which uses the Euclidean distance function as the fitting term, was proposed in 2015. However, the Euclidean distance function takes time to compute. This paper proposed the reformulation of the CDSS minimization problem by changing the fitting term with three popular distance functions, namely Chessboard, City Block, and Quasi-Euclidean. The proposed models were CDSSNEW1, CDSSNEW2, and CDSSNEW3, which applied the Chessboard, City Block, and Quasi-Euclidean distance functions, respectively. In this study, the Euler-Lagrange (EL) equations of the proposed models were derived and solved using the Additive Operator Splitting method. Then, MATLAB coding was developed to implement the proposed models. The accuracy of the segmented image was evaluated using the Jaccard and Dice Similarity Coefficients. The execution time was recorded to measure the efficiency of the models. Numerical results showed that the proposed CDSSNEW1 model based on the Chessboard distance function could segment specific objects successfully for all grayscale images with the fastest execution time as compared to other models.

Soft Consensus Models in Group Decision Making

2016 ◽  
pp. 135-153
Author(s):  
Ignacio Javier Perez ◽  
Francisco Javier Cabrerizo ◽  
Sergio Alonso ◽  
Francisco Chiclana ◽  
Enrique Herrera-Viedma
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Consensus Models
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