Supporting Consensus Reaching Processes under Fuzzy Preferences and a Fuzzy Majority via Linguistic Summaries and Action Rules

Author(s):  
Sławomir Zadrożny ◽  
Janusz Kacprzyk ◽  
Zbigniew W. Raś
Author(s):  
JANUSZ KACPRZYK ◽  
SŁAWOMIR ZADROŻNY ◽  
ZBIGNIEW W. RAŚ

We consider a consensus reaching process in a group of individuals meant as an attempt to make preferences of the individuals more and more similar, that is, getting closer and closer to consensus. We assume a general form of intuitionistic fuzzy preferences and a soft definition of consensus that is basically meant as an agreement of a considerable (e.g., most, almost all) majority of individuals in regards to a considerable majority of alternatives. The consensus reaching process is meant to be run by a moderator who tries to get the group of individuals closer and closer to consensus by argumentation, persuasion, etc. The moderator is to be supported by some additional information, exemplified by more detailed information on which individuals are critical as, for instance, they are willing to change their testimonies or are stubborn, which pairs of options make the reaching of consensus difficult, etc. In this paper we extend this paradigm proposed and employed in our former works with the use of a novel data mining tool, so called action rules which make it possible to more clearly indicate and suggest to the moderator with which experts and with respect to which option it may be expedient to deal. We show the usefulness of this new approach.


2021 ◽  
Vol 72 ◽  
pp. 89-99
Author(s):  
Yi Liu ◽  
Haiming Liang ◽  
Lei Gao ◽  
Zhaoxia Guo

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Yilun Shang

AbstractIn this note, we study discrete time majority dynamics over an inhomogeneous random graph G obtained by including each edge e in the complete graph $$K_n$$ K n independently with probability $$p_n(e)$$ p n ( e ) . Each vertex is independently assigned an initial state $$+1$$ + 1 (with probability $$p_+$$ p + ) or $$-1$$ - 1 (with probability $$1-p_+$$ 1 - p + ), updated at each time step following the majority of its neighbors’ states. Under some regularity and density conditions of the edge probability sequence, if $$p_+$$ p + is smaller than a threshold, then G will display a unanimous state $$-1$$ - 1 asymptotically almost surely, meaning that the probability of reaching consensus tends to one as $$n\rightarrow \infty $$ n → ∞ . The consensus reaching process has a clear difference in terms of the initial state assignment probability: In a dense random graph $$p_+$$ p + can be near a half, while in a sparse random graph $$p_+$$ p + has to be vanishing. The size of a dynamic monopoly in G is also discussed.


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