Classifiers and decision makers.

The main objective of this paper is to point out the key relevance of the classification issue in mathematical modeling. In particular, it is stressed that standard logical structures are quite simple classification structures, where the allowed degrees of truth or falsehood are connected according to a linear ordering. But when viewed as a classification problem, much more complex logical structures appear in a natural way, showing in fact that the standard linear assumption was kind of artificial. Moreover, once we focus our attention on the classification problem we realize that a relevant portion of classical research devotes to decision making, therefore imposing some misleading restrictions: the true scientific issue is much more related to classification rather than to decision making.

[1]  K. Arrow,et al.  Social Choice and Individual Values , 1951 .

[2]  F. J. Juan Aggregation of fuzzy opinions in a non-homogeneous group , 1988 .

[3]  Juan Tejada,et al.  A necessary and sufficient condition for the existence of Orlovsky's choice set , 1988 .

[4]  Vincenzo Cutello,et al.  Crisp dimension theory and valued preference relations , 2004, Int. J. Gen. Syst..

[5]  Javier Montero De Juan Arrow`s theorem under fuzzy rationality , 1987 .

[6]  J. Montero,et al.  Fuzzy rationality measures , 1994 .

[7]  Prasanta K. Pattanaik,et al.  Voting and collective choice : some aspects of the theory of group decision-making , 1973 .

[8]  Bertrand Mareschal,et al.  The GDSS PROMETHEE procedure: a PROMETHEE-GAIA based procedure for group decision support , 1998 .

[9]  Vincenzo Cutello,et al.  Equivalence and compositions of fuzzy rationality measures , 1997, Fuzzy Sets Syst..

[10]  F. J. Montero Social welfare functions in a fuzzy environment , 1987 .

[11]  Vincenzo Cutello,et al.  A characterization of rational amalgamation operations , 1993, Int. J. Approx. Reason..

[12]  J. Montero Rational aggregation rules , 1994 .

[13]  Javier Montero,et al.  Crisp Acts, Fuzzy Decisions , 1998 .

[14]  Javier Montero,et al.  Soft dimension theory , 2003, Fuzzy Sets Syst..

[15]  S. A. Orlovskiĭ Calculus of Decomposable Properties, Fuzzy Sets, and Decisions , 1994 .

[16]  Vincenzo Cutello,et al.  Fuzzy classification systems , 2004, Eur. J. Oper. Res..

[17]  Alan Pearman,et al.  Fuzzy multicriteria decision support for budget allocation in the transport sector , 1995 .

[18]  J. Montero Single-Peakedness in Weighted Aggregation of Fuzzy Opinions in a Fuzzy Group , 1990 .

[19]  Bernard Roy,et al.  Decision science or decision-aid science? , 1993 .

[20]  Javier Montero,et al.  Preferences, classification and intuitionistic fuzzy sets , 2003, EUSFLAT Conf..

[21]  F. J. Juan A note on Fung-Fu's theorem , 1985 .

[22]  J. Kelly Arrow Impossibility Theorems , 1978 .

[23]  Javier Montero,et al.  Some problems on the definition of fuzzy preference relations , 1986 .

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

[25]  A. Sen,et al.  Collective Choice and Social Welfare , 2017 .