Towards a Fairness-Oriented Approach to Consensus Reaching Support Under Fuzzy Preferences and a Fuzzy Majority via Linguistic Summaries

A novel approach to a human centric support of a consensus reaching process in a group of agents who present their testimonies as individual fuzzy preference relations is proposed. The concept of a degree of consensus is used which is meant as the degree to which, for instance, most of important agents agree as to almost all of relevant options. The fuzzy majorities are equated with linguistic quantifiers and Zadeh's calculus of linguistically quantified propositions is used. The new concepts of a consensory and dissensory agent is introduced. The authors' approach of using linguistic data summaries for a comprehensive summarization of how the agents' current testimonies look like is then employed for the consensory and dissensory agents to obtain suggestions to the agents on changes of specific preferences that could lead to a higher degree of consensus. An explicit inclusion of opinions of the consensory and dissensory agents is shown to be an important step towards a fairness type attitude of the moderator as opinions of all agents are accounted for.

[1]  C. Tappert,et al.  A Survey of Binary Similarity and Distance Measures , 2010 .

[2]  Anna Wilbik,et al.  Linguistic summarization of some static and dynamic features of consensus reaching , 2006 .

[3]  B. Loewer,et al.  Destroying the consensus , 2004, Synthese.

[4]  Janusz Kacprzyk,et al.  An Internet-based Group Decision and Consensus Reaching Support System , 2003 .

[5]  J. Kacprzyk,et al.  Group decision making and consensus under fuzzy preferences and fuzzy majority , 1992 .

[6]  J. Kacprzyk,et al.  Multiperson decision making models using fuzzy sets and possibility theory , 1990 .

[7]  E. Seneta,et al.  Towards consensus: some convergence theorems on repeated averaging , 1977, Journal of Applied Probability.

[8]  Slawomir Zadrozny,et al.  Linguistic database summaries and their protoforms: towards natural language based knowledge discovery tools , 2005, Inf. Sci..

[9]  Daniel Sánchez,et al.  Fuzzy quantification: a state of the art , 2014, Fuzzy Sets Syst..

[10]  Slawomir Zadrozny,et al.  Modern data-driven decision support systems: the role of computing with words and computational linguistics , 2010, Int. J. Gen. Syst..

[11]  Janusz Kacprzyk,et al.  The conceptual framework of fairness in consensus reaching process under fuzziness , 2013, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS).

[12]  J. Kacprzyk,et al.  Towards a general and unified characterization of individual and collective choice functions under fuzzy and nonfuzzy preferences and majority via the ordered weighted average operators , 2009 .

[13]  Slawomir Zadrozny,et al.  Computing with Words in Decision Making Through Individual and Collective Linguistic Choice Rules , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Slawomir Zadrozny,et al.  On Group Decision Making, Consensus Reaching, Voting and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and some Perspectives , 2008, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models.

[15]  J. Kacprzyk,et al.  A `human-consistent' degree of consensus based on fuzzy login with linguistic quantifiers , 1989 .

[16]  Janusz Kacprzyk,et al.  Comprehensiveness of Linguistic Data Summaries: A Crucial Role of Protoforms , 2013 .

[17]  Slawomir Zadrozny,et al.  A consensus reaching support system based on concepts of ideal and anti-ideal point , 2014, 2014 IEEE Conference on Norbert Wiener in the 21st Century (21CW).

[18]  Slawomir Zadrozny,et al.  An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers , 1988, Decis. Support Syst..

[19]  Slawomir Zadrozny,et al.  Protoforms of Linguistic Database Summaries as a Human Consistent Tool for Using Natural Language in Data Mining , 2009, Int. J. Softw. Sci. Comput. Intell..

[20]  Janusz Kacprzyk,et al.  A consensus‐reaching process under intuitionistic fuzzy preference relations , 2003, Int. J. Intell. Syst..

[21]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[22]  Sławomir Zadrożny,et al.  An Approach to the Consensus Reaching Support in Fuzzy Environment , 1997 .

[23]  Janusz Kacprzyk,et al.  Using intuitionistic fuzzy sets in group decision making , 2002 .

[24]  Janusz Kacprzyk,et al.  A Fuzzy Logic Based Approach to Linguistic Summaries of Databases , 2000 .

[25]  Slawomir Zadrozny,et al.  Computing With Words Is an Implementable Paradigm: Fuzzy Queries, Linguistic Data Summaries, and Natural-Language Generation , 2010, IEEE Transactions on Fuzzy Systems.

[26]  Dominika Gołuńska,et al.  The need of fairness in group consensus reaching process in a fuzzy environment , 2013 .

[27]  Slawomir Zadrozny,et al.  Soft computing and Web intelligence for supporting consensus reaching , 2010, Soft Comput..

[28]  J. Kacprzyk.  Group decision making with a fuzzy linguistic majority , 1986 .

[29]  Slawomir Zadrozny,et al.  Action Rules in Consensus Reaching Process Support , 2009, 2009 Ninth International Conference on Intelligent Systems Design and Applications.

[30]  H. Nurmi.  Approaches to collective decision making with fuzzy preference relations , 1981 .

[31]  Witold Pedrycz,et al.  A review of soft consensus models in a fuzzy environment , 2014, Inf. Fusion.

[32]  M. Degroot.  Reaching a Consensus , 1974 .

[33]  Janusz Kacprzyk,et al.  LINGUISTIC SUMMARIES OF DATA USING FUZZY LOGIC , 2001 .

[34]  Janusz Kacprzyk,et al.  Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice , 2011, Studies in Fuzziness and Soft Computing.

[35]  L. Zadeh.  A COMPUTATIONAL APPROACH TO FUZZY QUANTIFIERS IN NATURAL LANGUAGES , 1983 .

[36]  Slawomir Zadrozny,et al.  A New Model of Efficiency-Oriented Group Decision and Consensus Reaching Support in a Fuzzy Environment , 2014, IPMU.

[37]  J. Kacprzyk,et al.  Dealing with imprecise knowledge on preferences and majority in group decision making: Towards a unified characterization of individual and collective choice functions , 2003 .

[38]  Slawomir Zadrozny,et al.  How to Support Consensus Reaching Using Action Rules: a Novel Approach , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[39]  J. Kacprzyk,et al.  On fuzzy tournaments and their solution concepts in group decision making , 1991 .

[40]  Enrique Herrera-Viedma,et al.  Modeling Different Advising Attitudes in a Consensus Focused Process of Group Decision Making , 2014, IEEE Conf. on Intelligent Systems.

[41]  Slawomir Zadrozny,et al.  Consensus reaching via a GDSS with fuzzy majority and clustering of preference profiles , 1994, Ann. Oper. Res..

[42]  Ronald R. Yager,et al.  A new approach to the summarization of data , 1982, Inf. Sci..

[43]  Slawomir Zadrozny,et al.  On efficiency-oriented support of consensus reaching in a group of agents in a fuzzy environment with a cost based preference updating approach , 2014, 2014 IEEE Symposium on Computational Intelligence for Human-like Intelligence (CIHLI).

[44]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[45]  J. Kacprzyk,et al.  The Ordered Weighted Averaging Operators: Theory and Applications , 1997 .

[46]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[47]  J. Kacprzyk,et al.  On a concept of a consensus reaching process support system based on the use of soft computing and Web techniques , 2008 .

[48]  Slawomir Zadrozny,et al.  Supporting Consensus Reaching Processes under Fuzzy Preferences and a Fuzzy Majority via Linguistic Summaries , 2010, Preferences and Decisions.

[49]  Ehud Reiter,et al.  Book Reviews: Building Natural Language Generation Systems , 2000, CL.

[50]  J. Kacprzyk.  Group decision-making with a fuzzy majority via linguistic quantifiers. part II: , 1985 .

[51]  Anna Wilbik,et al.  Linguistic summarization of time series using a fuzzy quantifier driven aggregation , 2008, Fuzzy Sets Syst..

[52]  U. Krause.  A DISCRETE NONLINEAR AND NON–AUTONOMOUS MODEL OF CONSENSUS FORMATION , 2007 .

[53]  J. Kacprzyk,et al.  Collective choice rules in group decision making under fuzzy preferences and fuzzy majority: a unified OWA operator based approach , 2002 .

[54]  J. Kacprzyk,et al.  A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences , 1988 .

[55]  H. Nurmi.  A fuzzy solution to a majority voting game , 1981 .