Defining the Borda count in a linguistic decision making context

Different kinds of decision rules have been successfully implemented under a linguistic approach. This paper aims the same goal for the Borda count, a well-known procedure with some interesting features. In order to this, two ways of extension from the Borda rule to a linguistic framework are proposed taking into account all the agents' opinions or only the favorable ones for each alternative when compared with each other. In the two cases, both individual and collective Borda counts are analyzed, asking for properties as good as those of the original patterns.

[1]  Burt L. Monroe,et al.  Partial Justification of the Borda Count , 1998 .

[2]  Michael Dummett,et al.  The Borda count and agenda manipulation , 1998 .

[3]  Francisco Herrera,et al.  A Sequential Selection Process in Group Decision Making with a Linguistic Assessment Approach , 1995, Inf. Sci..

[4]  José Luis García-Lapresta,et al.  Borda Count Versus Approval Voting: A Fuzzy Approach , 2002 .

[5]  Thierry Marchant,et al.  Does the Borda rule provide more than a ranking? , 2000, Soc. Choice Welf..

[6]  D. Dubois,et al.  FUZZY NUMBERS: AN OVERVIEW , 1993 .

[7]  Panos M. Pardalos,et al.  Fuzzy Sets in Management, Economics and Marketing , 2001 .

[8]  M. Amparo Vila,et al.  A fuzziness measure for fuzzy numbers: Applications , 1998, Fuzzy Sets Syst..

[9]  Peter C. Fishburn,et al.  Borda's rule, positional voting, and Condorcet's simple majority principle , 1976 .

[10]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[11]  P. Bernholz,et al.  Public Choice , 2018, The Oxford Handbook of Public Choice, Volume 1.

[12]  Francisco Herrera,et al.  Direct approach processes in group decision making using linguistic OWA operators , 1996, Fuzzy Sets Syst..

[13]  José Luis García-Lapresta,et al.  A Fuzzy Borda Count in Multi-person Decision Making , 2002 .

[14]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[15]  M. Amparo Vila,et al.  On a canonical representation of fuzzy numbers , 1998, Fuzzy Sets Syst..

[16]  Ildar Z. Batyrshin,et al.  Strict Valued Preference Relations and Choice Functions in Decision-Making Procedures , 2004, MICAI.

[17]  James C. Bezdek,et al.  Analysis of fuzzy information , 1987 .

[18]  Tadeusz Trzaskalik,et al.  Multiple Objective and Goal Programming , 2002 .

[19]  P. Fishburn Condorcet Social Choice Functions , 1977 .

[20]  Enrique Herrera-Viedma,et al.  Evaluating the informative quality of documents in SGML format from judgements by means of fuzzy linguistic techniques based on computing with words , 2003, Inf. Process. Manag..

[21]  José Luis García-Lapresta,et al.  A general class of simple majority decision rules based on linguistic opinions , 2006, Inf. Sci..

[22]  Enrique Herrera-Viedma,et al.  Modeling the retrieval process for an information retrieval system using an ordinal fuzzy linguistic approach , 2001, J. Assoc. Inf. Sci. Technol..

[23]  Peter Gärdenfors Positionalist voting functions , 1973 .

[24]  S. Nitzan,et al.  The Borda rule, Condorcet consistency and Condorcet stability , 2003 .

[25]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[26]  Miguel Martínez Panero Generalizaciones y extensiones de la Regla de Votación de Borda , 2011 .

[27]  D. Saari Basic Geometry of Voting , 1995 .

[28]  P.-C.-F. Daunou,et al.  Mémoire sur les élections au scrutin , 1803 .

[29]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

[30]  T. Marchant Valued relations aggregation with the borda method , 1996 .

[31]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

[32]  Philip D. Straffin,et al.  Topics in the theory of voting , 1980 .

[33]  Ronald R. Yager,et al.  An approach to ordinal decision making , 1995, Int. J. Approx. Reason..

[34]  José Luis García-Lapresta,et al.  Consistent models of transitivity for reciprocal preferences on a finite ordinal scale , 2008, Inf. Sci..

[35]  G. Thompson,et al.  The Theory of Committees and Elections. , 1959 .

[36]  Kam-Chau Wong,et al.  Preference densities and social choices , 2008 .

[37]  Arnold B. Urken,et al.  Classics of social choice , 1995 .

[38]  A. Sen,et al.  Social Choice Theory: A Re-Examination , 1977 .

[39]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[40]  Rajkumar Roy,et al.  Advances in Soft Computing , 2018, Lecture Notes in Computer Science.

[41]  J. García-Lapresta,et al.  A GROUP DECISION MAKING METHOD USING FUZZY TRIANGULAR NUMBERS , 2001 .