scholarly journals The Fair Proportion Is a Shapley Value on Phylogenetic Networks Too

Author(s):  
Tomás M. Coronado ◽  
Gabriel Riera ◽  
Francesc Rosselló
2018 ◽  
Author(s):  
Tomás M. Coronado ◽  
Gabriel Riera ◽  
Francesc Rosselló

AbstractThe Fair Proportion of a species in a phylogenetic tree is a very simple measure that has been used to assess its value relative to the overall phylogenetic diversity represented by the tree. It has recently been proved by Fuchs and Jin to be equal to the Shapley Value of the coallitional game that sends each subset of species to its rooted Phylogenetic Diversity in the tree. We prove in this paper that this result extends to the natural translations of the Fair Proportion and the rooted Phylogenetic Diversity to rooted phylogenetic networks. We also generalize to rooted phylogenetic networks the expression for the Shapley Value of the unrooted Phylogenetic Diversity game on a phylogenetic tree established by Haake, Kashiwada and Su.


2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.


2021 ◽  
Vol 59 (3) ◽  
pp. 699-718
Author(s):  
R. Sundara Rajan ◽  
A. Arul Shantrinal ◽  
K. Jagadeesh Kumar ◽  
T. M. Rajalaxmi ◽  
Indra Rajasingh ◽  
...  

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