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Normalizing Possibility Distributions Using t-Norms

Secció Matemàtiques i Informàtica – ETSAV, Univ. Politècnica de Catalunya, Pere Serra 1-15, Sant Cugat del Vallès, Barcelona, Spain

Partially supported by DGICYT project n. PB98-0924.

Partially supported by grant PR2001-0005 of the SEUI.

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and

J. Lawry

Department of Engineering Mathematics, University of Bristol, Queens Building, University Walk, Bristol, BS8 1TR, UK

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https://doi.org/10.1142/S0218488503002119Cited by:0 (Source: Crossref)

Abstract

A new approach to normalizing fuzzy sets is introduced where it is assumed that the normalization method is compatible with a given t-norm. In this context it is proved that the most usual ways to normalize fuzzy subsets correspond to the most common t-norms.

For a given fuzzy subset μ, the corresponding normalized fuzzy subset can be viewed as the distribution of μ conditioned on the (degree of) existence of its elements with maximal membership. From this view point we investigate the less specific normal fuzzy subset of X among the most similar fuzzy subsets to μ and the normal fuzzy subset generating the same fuzzy T-preorder as μ.

Keywords:

References

J. F. Baldwin , T. P. Martin and B. W. Pilsworth , FRIL - Fuzzy and Evidential Reasoning in AI ( Research Studies Press, John Wiley , 1995 ) . Google Scholar
D. Boixader, J. Jacas and J. Recasens, Fundamentals of Fuzzy Sets, ed. Prade Dubois (Kluwer, 2000) pp. 261–290. Crossref, Google Scholar
F. Diaz-Hermidaet al., Evaliación probabilistica de proposiciones cuantificadas borrosas, Proceedings 10th Spanish Conference of Fuzzy Logic and Technologies (ESTYLF'00) (2000) pp. 477–482. Google Scholar
D. Dubois and H. Prade, Fuzzy Sets and Systems 24, 123 (1987), DOI: 10.1016/0165-0114(87)90122-9. Crossref, Web of Science, Google Scholar
D. Dubois and H. Prade , Possibility Theory ( Plenum Press , New York , 1988 ) . Crossref, Google Scholar
E. Hernández and J. Recasens, IJUFKBS 10, 185 (2002). Google Scholar
J. Jacas and J. Recasens , The Group of Isometries of an Indistinguishability Operator , Proceedings EUSFLAT 2001 Conference ( 2001 ) . Google Scholar
J. Jacas and J. Recasens, Soft Computing 6, 14 (2002). Crossref, Google Scholar
C. Joslyn , Fuzzy Logic: State of Art , ed. Lowen ( Kluwer , 1994 ) . Google Scholar
G. J. Klir and T. A. Folger , Fuzzy Sets, Uncertainty and Information ( Prentice Hall , Englewood Cliffs, New Jersey , 1988 ) . Google Scholar
J. Lawry, IJUFKBS 9, 413 (2001). Google Scholar
R. B. Nelsen , Introduction to Couplas , Lecture Notes on Statistics 139 ( Springer Verlag , 1999 ) . Crossref, Google Scholar
B. Schweizer and A. Sklar , Probabilistic Metric Spaces ( North-Holland , Amsterdam , 1983 ) . Google Scholar
L. Valverde, Fuzzy Sets and Systems 17, 313 (1985), DOI: 10.1016/0165-0114(85)90096-X. Crossref, Web of Science, Google Scholar
R. Yager, Fuzzy Sets and Systems 20, 317 (1986), DOI: 10.1016/S0165-0114(86)90042-4. Crossref, Web of Science, Google Scholar
L. A. Zadeh, Inform. Sci. 3, 177 (1971), DOI: 10.1016/S0020-0255(71)80005-1. Crossref, Web of Science, Google Scholar
L. A. Zadeh, Fuzzy Sets and Systems 1, 3 (1978), DOI: 10.1016/0165-0114(78)90029-5. Crossref, Google Scholar