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

We consider the classic approach to the evaluation of of degrees of consensus due to Kacprzyk and Fedrizzi [6], [7], [8] in which a soft degree of consensus has been introduced. Its idea is to find a degree to which, for instance, “most of the important individuals agree as to almost all of the relevant options”. The fuzzy majority, expressed as fuzzy linguistic quantifiers (most, almost all, ...) is handled via Zadeh’s [46] classic calculus of linguistically quantified propositions and Yager’s [44] OWA (ordered weighted average) operators. The soft degree of consensus is used for supporting the running of a moderated consensus reaching process along the lines of Fedrizzi, Kacprzyk and Zadrożny [3], Fedrizzi, Kacprzyk, Owsiński and Zadrożny [2], Kacprzyk and Zadrożny [22], and [24].

Linguistic data summaries in the sense of Yager [43], Kacprzyk and Yager [13], Kacprzyk, Yager and Zadrożny [14], in particular in its protoform based version proposed by Kacprzyk and Zadrożny [23], [25] are employed. These linguistic summaries indicate in a human consistent way some interesting relations between individuals and options to help the moderator identify crucial (pairs of) individuals and/options with whom/which there are difficulties with respect to consensus. An extension using ontologies representing both knowledge on the consensus reaching process and domain of the decision problem is indicated.