Bustince, H. and Fernandez, J. and Mesiar, R. and Montero, Javier and Orduna, R
(2010)
*Overlap functions.*
Nonlinear Analysis: Theory, Methods & Applications , 72
(3-4 A).
pp. 1488-1499.
ISSN 0362-546X

PDF
Restringido a Repository staff only hasta 2020. 711kB |

Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X09009936

## Abstract

In this paper we address a key issue in scenario classification, where classifying concepts show a natural overlapping. In fact, overlapping needs to be evaluated whenever classes are not crisp, in order to be able to check if a certain classification structure fits reality and still can be useful for our declared decision making purposes. In this paper we address an object recognition problem, where the best classification with respect to background is the one with less overlapping between the class object and the class background. In particular,

in this paper we present the basic properties that must be fulfilled by overlap functions, associated to the degree of overlapping between two classes. In order to define these overlap functions we take as reference properties like migrativity, homogeneity of order 1 and homogeneity of order 2. Hence we define overlap functions, proposing a construction method and analyzing the conditions ensuring that t-norms are overlap functions. In addition, we present a characterization of migrative and strict overlap functions by means of automorphisms.

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

Uncontrolled Keywords: | T-norm; Migrative property; Homogeneity property; Overlap index; Overlap function |

Subjects: | Sciences > Mathematics > Logic, Symbolic and mathematical |

ID Code: | 16013 |

References: | H. Bustince, M. Pagola, E. Barrenechea, Construction of fuzzy indices from fuzzy DI-subsethood measures: Application to the global comparison of images, Information Sciences 177 (3) (2007) 906-929. H. Bustince, E. Barrenechea, M. Pagola, et al., Weak fuzzy S-subsethood measures. Overlap index, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems 14 (5) (2006) 537-560. H. Bustince, V. Mohedano, E. Barrenechea, et al., Definition and construction of fuzzy DI-subsethood measures, Information Sciences 176 (21) (2006) 3190-3231. D. Dubois, J.L. Koning, Social choice axioms for fuzzy set aggregation, Fuzzy Sets and Systems 58 (1991) 339-342. D. Dubois, W. Ostasiewicz, H. Prade, Fuzzy sets: History and basic notions, in: Fundamentals of Fuzzy Sets, Kluwer, Boston, MA, 2000. L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978) 3-28. H. Bustince, J. Montero, E. Barrenechea, M. Pagola, Semiautoduality in a restricted family of aggregation operators, Fuzzy Sets and Systems 158 (12) (2007) 1360-1377. T. Calvo, A. Kolesárová, M. Komorníkova, R. Mesiar, Aggregation operators: Properties, classes and construction ethods, in: Aggregation Operators New Trends and Applications, Physica-Verlag, Heidelberg, 2002. G.J. Klir, T.A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, NJ, 1988. D. Gómez, J. Montero, A discussion on aggregation operators, Kybernetika 40 (2004) 107-120. A. Amo, J. Montero, E. Molina, Representation of consistent recursive rules, European Journal of Operational Research 130 (2001) 29-53. V. Cutello, J. Montero, Recursive connective rules, International Journal of Intelligent Systems 14 (1999) 3 20. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, in: Trends in Logic, Studia Logica Library, vol. 8, Kluwer Academic Publishers, Dordrecht, 2000. B. Schweizer, A. Sklar, Probabilistic Metric Spaces, North-Holland, Amsterdam, 1983. J. Fodor, M. Roubens, Fuzzy preference modelling and multicriteria decision support, in: Theory and Decision Library, Kluwer Academic Publishers, 1994. C. Alsina, M.J. Frank, B. Schweizer, Associative Functions, Triangular Norms and Copulas, World Scientific, Hackensack, 2006. F. Durante, P. Sarkoci, A note on the convex combinations of triangular norms, Fuzzy Sets and Systems 159 (2008) 77-80. R. Mesiar, V. Novák, Open problems from the 2nd International conference of fuzzy sets theory and its applications, Fuzzy Sets and Systems 81 (1996) 185-190. J. Fodor, I.J. Rudas, On continuous triangular norms that are migrative, Fuzzy Sets and Systems 158 (2007) 1692 1697. H. Bustince, J. Montero, R. Mesiar, Migrativity of aggregation operators, Fuzzy Sets and Systems 160 (6) (2009) 766-777. M. Baczynski, B. Jayaram, .S; N/- and R-implications: A state-of-the-art survey, Fuzzy Sets and Systems 159 (14) (2008) 1836-1859. R.B. Nelsen, An introduction to Copulas, in: Lecture Notes in Statistics, vol. 139, Springer, New York, 1999. A. Mesiarová, A note on two open problems of Alsina, Frank and Schweizer, Aequationes Mathematicae 72 (1-2) (2006) 41-46. A. Mesiarová, k |

Deposited On: | 20 Jul 2012 10:23 |

Last Modified: | 20 Apr 2016 16:59 |

Repository Staff Only: item control page