Construction of Capacities from Overlap Indexes
- 828 Downloads
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.
KeywordsOverlap function Capacity Fuzzy measure
The work has been supported by projects TIN2013-40765-P and TIN2015-66471-P of the Spanish Ministry of Science, by grant VEGA 1/0420/15 and by grant VEGA 1/0419/13.
- 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.Google Scholar
- 10.G. Choquet, Theory of capacities. Ann. Inst. Fourier 5, 131–295, 1953-54.Google Scholar
- 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.Google Scholar
- 14.D. Gomez, J.T. Rodriguez, J. Montero, H. Bustince, E. Barrenechea, N-dimensional overlap functions, Fuzzy Sets and Systems 287, 57–75, 2016.Google Scholar
- 17.D. Gómez, J. Montero, A discussion on aggregation operators. Kybernetika 40, 107–120, 2004.Google Scholar
- 21.V. Torra, Y. Narukawa, M. Sugeno, Eds., Non-Additive Measures, Theory and Applications. Studies in Fuzziness and Soft Computing, 310, 2014.Google Scholar