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

• Sławomir Zadrożny ^[1] ; Janusz Kacprzyk ^[1] ; Zbigniew W. Raś ^[2]
  1. [1] Polish Academy of Sciences

     Polish Academy of Sciences

     Warszawa, Polonia

     
  2. [2] University of North Carolina at Charlotte

     University of North Carolina at Charlotte

     Estados Unidos

     
• Localización: Consensual Processes / coord. por Enrique Herrera Viedma, José Luis García Lapresta, Janusz Kacprzyk, Mario Fedrizzi, Hannu Nurmi, Slawomir Zadrożny, 2011, ISBN 978-3-642-20533-0, págs. 289-314
• Idioma: inglés
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• Resumen

  • We deal with the classic approach to the evaluation of of a degree of consensus due to Kacprzyk and Fedrizzi [21, 22, 23] in which a soft degree of consensus has been introduced as a degree to which, for instance, “most of the important individuals agree as to almost all of the relevant options”. The fuzzy majority is equated with a fuzzy linguistic quantifiers (most, almost all, ... ) and handled via Zadeh’s [64] classic calculus of linguistically quantified propositions and Yager’s [63] OWA (ordered weighted average) operators. The consensus reaching process is run by a moderator who may need a support which is provided by a novel combination of: first, the use of the a soft degree of consensus alone along the lines of Fedrizzi, Kacprzyk and Zadrożny [12], Fedrizzi, Kacprzyk, Owsiński and Zadrożny [11], Kacprzyk and Zadrożny [31, 34]. Second, the linguistic data summaries in the sense of Yager [62], Kacprzyk and Yager [26], Kacprzyk, Yager and Zadrożny [27], in particular in its protoform based version proposed by Kacprzyk and Zadrożny [33], [35], are are employed to indicate in a natural language some interesting relations between individuals and options to help the moderator identify crucial (pairs of) individuals and/options which pose some threats to the reaching of consensus. Third, using results obtained in our recent paper (Kacprzyk, Zadrożny and Raś [41], we additionally use a novel data mining tool, a so-called action rule proposed by Raś and Wieczorkowska [48], which are meant in our context to find best concessions to be offered to the individuals for changing their preferences to increase the degree of consensus.