On Group Decision Making, Consensus Reaching, Voting, and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and a Granulation Perspective

Transactions on Computational Collective Intelligence XXIII

“…Nurmi [48], Kacprzyk et al [42], etc.) at each consensus reaching stage, the agents discuss the decision problem under consideration and present their current testimonies, which are their individual fuzzy preference relations, 2. a fuzzy majority based degree of consensus is calculated; if it is high enough, or a time limit is over, then the process is terminated and otherwise the subsequent steps are executed, 3. the current individual fuzzy preference relations are aggregated using, for instance, some averaging (cf.…”

“…Further, the use of a fuzzy majority, as proposed first by Kacprzyk [17,18] (for a comprehensive review, cf. Kacprzyk et al [42]) is a powerful solution. A fuzzy majority, exemplified by "most", is meant as a linguistic quantifier driving a soft aggregation of testimonies, represented here by Zadeh's [58] fuzzy linguistic quantifier [cf.…”

“…Nurmi [48], Kacprzyk et al [42]). In our model we employ in addition the following information: which agent's individual fuzzy preference relation is the closest and which agent's is the farthest from what best characterizes the whole group, and the easiest and most natural way of doing this is to use the concept of a social fuzzy preference relation (cf.…”

“…which corresponds to (38): (42) • for the linguistic summary "most of the important dissensory agents definitely preferring o i1 to o i2 also definitely prefer o i3 to o i4 ", we have the one corresponding to (39) .…”