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On This Book: Clustering, Multisets, Rough Sets and Fuzzy Sets Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Construction of Capacities from Overlap Indexes

Authors : José Antonio Sanz, Mikel Galar, Radko Mesiar, Anna Kolesárová, Humberto Bustince, Javier Fernandez, Javier Montero

Published in: Fuzzy Sets, Rough Sets, Multisets and Clustering

Publisher: Springer International Publishing

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Abstract

In this chapter, we show how the concepts of overlap function and overlap index can be used to define fuzzy measures which depend on the specific data of each considered problem.

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previous chapter Group Decision Making: Consensus Approaches Based on Soft Consensus Measures
next chapter Clustering Alternatives and Learning Preferences Based on Decision Attitudes and Weighted Overlap Dominance
Literature
1.
A. Amo, J. Montero, E. Molina, Representation of consistent recursive rules. European Journal of Operational Research, 130, 29–53, 2001.MathSciNetCrossRefMATH
2.
P. Benvenuti, R. Mesiar, Pseudo-additive measures and triangular-norm-based conditioning. Annals of Mathematics and Artificial Intelligence, 35, 63–69, 2002.MathSciNetCrossRefMATH
3.
P. Benvenuti, D. Vivona, M. Divari, Aggregation operators and associated fuzzy measures. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9, 197–204, 2001.MathSciNetCrossRefMATH
4.
H. Bustince, M. Pagola, R. Mesiar, E. Hüllermeier, F. Herrera, Grouping, Overlap, and Generalized Bientropic Functions for Fuzzy Modeling of Pairwise Comparisons. IEEE Transactions on Fuzzy Systems, 20(3), 405–415, 2012.CrossRef
5.
H. Bustince, E. Barrenechea, M. Pagola, F. Soria, Weak fuzzy S-subsethood measures: Overlap index. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 14(5), 537–560, 2006.MathSciNetCrossRefMATH
6.
H. Bustince, J. Montero, E. Barrenechea, M. Pagola, Semiautoduality in a restricted family of aggregation operators. Fuzzy Sets and Systems, 158, 1360–1377, 2007.MathSciNetCrossRefMATH
7.
H. Bustince, J. Fernandez, R. Mesiar, J. Montero, R. Orduna, Overlap functions. Nonlinear Analysis: Theory, Methods & Applications, 72(3-4), 1488–1499, 2010.MathSciNetCrossRefMATH
8.
H. Bustince, D. Paternain, M. Pagola, P. Sussner, A. Kolesárová, R. Mesiar, Capacities and Overlap Indexes with an Application in Fuzzy Rule- Based Classification Systems, Fuzzy Sets and Systems, accepted for publication, in press.
9.
T. Calvo, A. Kolesárová, M. Komorníková and R. Mesiar: Aggregation Operators: Properties, Classes and Construction Methods. In T. Calvo, G. Mayor and R. Mesiar (Eds.): Aggregation Operators. New Trends and Applications. Physica-Verlag, Heidelberg, pp. 3–104, 2002.CrossRef
10.
G. Choquet, Theory of capacities. Ann. Inst. Fourier 5, 131–295, 1953-54.
11.
V. Cutello, J. Montero, Recursive connective rules. International Journal of Intelligent Systems, 14, 3–20, 1999.CrossRefMATH
12.
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, pp. 21-124, 2000.CrossRef
13.
S. Garcia, H. Bustince, E. Hüllermeier, R. Mesiar, N. Pal, A. Pradera, Overlap Indices: Construction of and Application to Interpolative Fuzzy Systems, IEEE Transactions on Fuzzy Systems 23, 1259–1273, 2015.
14.
D. Gomez, J.T. Rodriguez, J. Montero, H. Bustince, E. Barrenechea, N-dimensional overlap functions, Fuzzy Sets and Systems 287, 57–75, 2016.
15.
M. Grabisch, J.-L. Marichal, R. Mesiar, E. Pap, Aggregation Functions. Cambridge University Press, Cambridge, 2009.CrossRefMATH
16.
A. Jurio, H. Bustince, M. Pagola, A. Pradera, R.R. Yager, Some properties of overlap and grouping functions and their application to image thresholding. Fuzzy Sets and Systems, 229, 69–90, 2013.MathSciNetCrossRefMATH
17.
D. Gómez, J. Montero, A discussion on aggregation operators. Kybernetika 40, 107–120, 2004.
18.
G.J. Klir, T.A. Folger, Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs, NJ, 1988.MATH
19.
R. Mesiar, A. Mesiarová-Zemánková, The Ordered Modular Averages. IEEE Transactions on Fuzzy Systems, 19, 42–50, 2011.CrossRef
20.
E. Pap, Handbook of Measure Theory, Part I, PartII. Elsevier, Amsterdam, 2002.MATH
21.
V. Torra, Y. Narukawa, M. Sugeno, Eds., Non-Additive Measures, Theory and Applications. Studies in Fuzziness and Soft Computing, 310, 2014.
22.
Metadata
Title
Construction of Capacities from Overlap Indexes
Authors
José Antonio Sanz
Mikel Galar
Radko Mesiar
Anna Kolesárová
Humberto Bustince
Javier Fernandez
Javier Montero
Copyright Year
2017
Book
Fuzzy Sets, Rough Sets, Multisets and Clustering

Print ISBN: 978-3-319-47556-1

Electronic ISBN: 978-3-319-47557-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-47557-8_19

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