Bustince, H. and Fernandez, J. and Mesiar, R. and Montero de Juan, Francisco Javier and Orduna, R
(2009)
*Overlap index, overlap functions and migrativity.*
In
Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference.
Computer Science Bibliographies
.
European Society of Fuzzy Logic and Technology, Lisbon, PORTUGAL, pp. 300-305.
ISBN 978-989-95079-6-8

PDF
150kB |

Official URL: http://library.utia.cas.cz/separaty/2009/E/mesiar-overlap%20index,%20overlap%20functions%20and%20migrativity.pdf

## Abstract

In this work we study overlap degrees expressed in terms of overlap functions. We present the basic properties that from our point of view must satisfy these overlap functions. We study a construction method, we analyze which t-norms are also overlap functions and we prove that if we apply particular aggregations to such functions we recover the overlap index between fuzzy sets as defined by Dubois, and the consistency index of Zadeh. We also consider some properties that can be required to overlap functions, as k-Lipschitzianity or migrativity

Item Type: | Book Section |
---|---|

Additional Information: | Lisbon, Portugal, July 20-24, 2009 |

Uncontrolled Keywords: | Restricted equivalence functions; Di- subsethood measures; Aggregation operators; Fuzzy-sets; Constrution |

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

ID Code: | 16893 |

References: | A. Amo, D. Gomez and J. Montero, Spectral fuzzy classification:a supervised approach, Mathware and Soft Computing, 10, Pages 141-154, 2003. A. Amo, J. Montero, G. Biging and V. Cutello, Fuzzy classification systems, European Journal of Operational Research, 156, Pages 459-507, 2004. A. Amo, J. Montero, D. G´omez and E. Molina, Representation of consistent recursive rules, European Journal of Operational Research, 130, Pages 29-53, 2001. 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, Pages 906-929, 2007. 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, Pages. 537-560, 2006. H. Bustince, V. Mohedano, E. Barrenechea, et al. Definition and construction of fuzzy DI-subsethood measures,nformation Sciences, 176, 21, Pages 3190-3231, 2006. H. Bustince H., J. Montero, E. Barrenechea and M.Pagola, Semiautoduality in a restricted family of aggregation operators, Fuzzy Sets and Systems, 158, 12, Pages 360-1377, 2007. H. Bustince, E. Barrenechea, M. Pagola, Restricted equivalence functions, Fuzzy Sets and Systems, 157 17,Pages 2333-2346, 2006. H. Bustince, E. Barrenechea, M. Pagola, Image thresholding using restricted equivalence functions and maximizing the measures of similarity, Fuzzy Sets and Systems,158, 5, Pages 496-516, 2007. Bustince H., Montero J. and Mesiar R., Migrativity of Aggregation Operators, Fuzzy Sets and Systems, 160, 6,Pages 766-777, 2008. T. Calvo, A. Kolesarova, M. Komornıkova and R. Mesiar: Aggregation operators: roperties, classes and construction methods. In T. Calvo, G. Mayor and R.Mesiar(Eds.):Aggregation Operators New Trends and Applications (Physica-Verlag, Heidelberg); Pages 3-104,2002. V. Cutello and J. Montero, Recursive connective rules,International Journal of ntelligent Systems, 14, Pages 3-20, 1999. D. Dubois and J.L. Koning, Social choice axioms for fuzzy set aggregation. Fuzzy Sets and Systems 58, Pages 339-342, 1991. D. Dubois, W. Ostasiewicz, H. Prade, Fuzzy Sets: History and Basic Notions, in: D. Dubois, H. Prade (Eds),Fundamentals of Fuzzy Sets, Kluwer, Boston, MA,Pages 21-24, 2000. J. Fodor and M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, in: Theory and Decision Library (Kluwer Academic Publishers) 1994. D. Gomez and J. Montero: A discussion on aggregation operators. Kybernetika 40, Pages 107-120, 2004. D. Gomez, J. Montero and H. Bustince, On the relevance of some families of fuzzy sets, Fuzzy Sets and Systems,158, Pages 2429-2442, 2007. L.K. Huang and M.J.Wang, Image thresholding by minimizing the measure of uzziness, Pattern recognition,28, 1, Pages 41-51, 1995. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms,Trends in Logic. Studia Logica Library, Kluwer Academic Publishers, Dordrecht, 2000. G.J. Klir and T.A. Folger: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs, NJ, 1988. C.H. Ling, Representation of associative functions, Publ.Math. Debrecen, 12, Pages 189-212, 1965. R. Mesiar, V. Novak, Open problems from the 2nd International conference of fuzzy sets theory and its applications,Fuzzy Sets and Systems, 81, Pages 185-190,1996. A.Mesiarova, A note on two open problems of Alsina,Frank and Schweizer. equationes Math., 72, no. 1-2,Pages 41-46, 2006. A. Mesiarova, k − lp-Lipschitz t-norms. Int. J. Approximate Reasoning, 46, Pages 596-604, 2007. P.S. Mostert, A.L. Shields, On the structure of semigroups on a compact manifold with boundary, Ann. of Math., 65, Pages 117-143, 1957. N. R. Pal and S. K. Pal, A review of image segmentation techniques, Pattern recognition, 26, Pages 1277-1294,1993. E.H. Ruspini, A new approach to clustering, Information and Control, 15, Pages 22-32, 1969. L.A. Zadeh, Fuzzy sets, Information Control, 8, Pages 338-353, 1965. L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility,Fuzzy Sets and Systems, 1,Pages 3–28, 1978. |

Deposited On: | 26 Oct 2012 09:03 |

Last Modified: | 27 Feb 2015 10:44 |

Repository Staff Only: item control page