### Impacto

Cutello, V. and Montero de Juan, Francisco Javier
(1997)
*Equivalence and compositions of fuzzy rationality measures.*
Fuzzy Sets and Systems, 85
(1).
pp. 31-43.
ISSN 0165-0114

PDF
Restringido a Repository staff only hasta 2020. 950kB |

Official URL: http://www.sciencedirect.com/science/article/pii/0165011495003614

## Abstract

An axiomatic basis for fuzzy rationality measures has already been introduced by the authors in a previous paper [5], formalizing the fact that there exist degrees of consistency when preferences over a fixed set of alternatives are expressed in terms of fuzzy binary preference relations. This paper deals with some practical consequences. On the one hand, similarities and compositions of fuzzy rationality measures are considered, showing natural ways of deriving new measures; on the other, if basic stability properties are introduced in order to assure that small intensity measurement errors never lead to big changes in the associate rationality value, it is shown that crisp (i.e., binary) rationality measures present serious difficulties when applied to fuzzy preference relations.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Aggregation rules; Fuzzy preferences; Decision making |

Subjects: | Sciences > Mathematics > Bayesian statistical decision theory Sciences > Mathematics > Logic, Symbolic and mathematical |

ID Code: | 16802 |

References: | T. Bilgic and I.B. Turksen, Measurement-theoretic justification of connectives in fuzzy set theory, Fuzzy Sets and Systems, 76 (1995) 289-307. V. Cutello and J. Montero, An axiomatic approach to fuzzy rationality, in: K.C. Min, Ed., IFSA '93 (Korea Fuzzy Mathematics and Systems Society, Seoul, 1993)634 636. V. Cutello and J. Montero, A characterization of rational amalgamation operations, lnternat, d. Approximate Reasoning 8 (1993) 325-344. V. Cutello and J. Montero, Equivalence of fuzzy rationality measures, in: H.J. Zimmermann, Ed., EUF1T "93, Vol. 1 (Elite Foundation, Aachen, 1993) 344-350. V. Cutello and J. Montero, Fuzzy rationality measures, Fuzzy Sets and Systems 62 (1994) 39-54. D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications (Academic Press, New York, 1980). P.C. Fishburn, Interval Orders and Interval Graphs (Wiley, New York, 1985). J.C. Fodor and M. Roubens, Preference modelling and aggregation procedures with valued binary relations, in: R. Lowen and M. Roubens, Eds., Fuzzy Logic (Kluwer Academic Press, Amsterdam, 1993) 29-38. J.C. Fodor and M. Roubens, Valued preference structures, European J. Oper. Res. 79 (1994) 277-286. J.C. Fodor and M. Roubens, Fuzzy Preference Modellin.q and Multicriteria Decision Support (Kluwer Academic Pub., Dordrecht, 1994). L. Kitainik, Fuzzy Decision Procedures with Binary Relations (Kluwer Academic Pub., Boston, 1993). G.J. Klir and T.A. Folger, Fuzzy Sets, Uncertainty and Information (Prentice Hall, Englewood Cliffs, NJ, 1988). [13] J. Montero, Arrow's theorem under fuzzy rationality, Behavioral Sci. 32 (1987) 267-273. J. Montero, Social welfare functions in a fuzzy environment, Kybernetes 16 (1987) 241-245. J. Montero, Rational aggregation rules, Fuzzy Sets and Systems 62 (1994) 267-76. J. Montero and J. Tejada, Some problems on the definition of fuzzy preference relations, Fuzzy Sets and Systems 20 (1986) 45-53. J. Montero, J. Tejada and V. Cutello, A general model for deriving preference structures from data, European J. Oper. Res., to appear. A.M. Norwich and I.B. Turksen, A model for the measurement of membership and the consequences of its empirical implementation, Fuzzy Sets and Systems 12 (1984) 1-25. S.E. Orlovski, Calculus of Decomposable Properties, Fuzzy Sets and Decisions Allerton Press, New York, 1994). P.K. Pattanaik, Votin9 and Collective Choice (Cambridge Univ. Press, Cambridge, 1971). F.S. Roberts, Measurement Theory (Addison-Wesley, Reading, MA, 1979).A.K. Sen, Collective Choice and Social Welfare (Cambridge Univ. Press, Cambridge, 1971). I.B. Turksen, Measurement of membership functions and their acquisition, Fuzzy Sets and Systems 40 (1991) 5-38. R.R. Yager, Connectives and quantifiers in fuzzy sets, Fuzzy Sets and Systems 40 1991) 39 75. R.R. Yager, On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Trans. Systems Man Cybernet. 18 (1988) 183 190. R.R. Yager, Families of owa operators, Fuzzy Sets and Systems 59 (1993) 125 148. U. Thole, H.J. Zimmermann and P. Zysno, On the suitability of minimum and product operators for the intersection of fuzzy sets, Fuzzy Sets and Systems 2 (1979) 167 180. L.A. Zadeh, Similarity relations and fuzz)' orderings,Inform. Sci. 3 (1971) 177-200. H.J. Zimmerman, Fuzzy Sets Theory and its Applications (Kluwer-Nijhoff, Boston, 1985 |

Deposited On: | 22 Oct 2012 08:32 |

Last Modified: | 27 Feb 2015 10:07 |

Repository Staff Only: item control page