Linguistic summarization of some static and dynamic features of consensus reaching

Consensus reaching has been widely recognized as an important component of the decision-making process. In previous works Fedrizzi and Kacprzyk introduced a new concept of consensus referring to the idea of fuzzy majority and based on the Zadeh's calculus of linguistically quantified propositions. Basically, the (degree of) consensus was meant as the degree to which Q(1) (e.g., most) of the I (e.g., important) individuals agree as to Q(2) (e.g., almost all) of B (e.g., relevant) options. The approach was extended in further works by Fedrizzi, Kacprzyk, Nurmi, and Zadrozny. Recently Kacprzyk and Zadrozny proposed to apply linguistic summaries in the sense of Yager to support the consensus reaching process. For instance, "most individuals definitely preferring option o(1) over option o(2) also definitely prefer option o(5) to option o(7)," "almost all options dominating option o(3) in the opinion of expert e(2) also dominate option o(6) in the opinion of expert e(4)," etc. In the present paper, we extend this idea and propose to take into account dynamic features of the consensus reaching process while constructing the linguistic summaries. Basically, linguistic summaries are meant as a concise description of the current status in the group of individuals in terms of their preferences. These descriptions may concern particular individuals, the whole group, or particular options. Moreover we propose here to take into account also how the preferences are evolving over time. For instance, "individual e(2) is very flexible with respect to his or her preferences between options o(3) and o(5)," etc. Such an information might be even more useful for the running, moderating, etc. of a consensus reaching process than a static description.