The Bipolar Choquet Integrals Based On Ternary-Element Sets

Open access


1This paper first introduces a new approach for studying bi-capacities and the bipolar Choquet integrals based on ternary-element sets. In the second half of the paper, we extend our approach to bi-capacities on fuzzy sets. Then, we propose a model of bipolar Choquet integral with respect to bi-capacities on fuzzy sets, and we give some basic properties of this model.

[1] Abbas J., Bipolar Choquet integral of fuzzy events, IEEE SSCI conference on MCDM, Florida, USA, pp.116-123, 2014.

[2] Abbas J., Logical twofold integral, Engineering & Techology Journal, Vol. 28, No. 3; 2010.

[3] Bilbao, J.M., Fernandez, J.R., Jimenez Losada, A. and Lebron, E., Bicooperative Games, First World Congress of the Game Theory Society (Games 2000) July 24-28, Bilbao, Spain, 2000.

[4] Choquet G., Theory of capacities, Ann. Inst. Fourier, Vol. 5, pp. 131-295, 1953.

[5] Davey B.A., Priestley H.A., Introduction to Lattices and Orders, Cambridge University Press, Cambridge, 1990.

[6] Denneberg D., Non-additive measure and integral, Kluwer Academic Publisher, 1994.

[7] Grabisch, M., Labreuche C., Bi-capacities I: Definition, Mobius transform and interaction, Fuzzy Sets and Systems 151, pp. 211-236, 2005.

[8] Grabisch M. and Labreuche C., Bi-capacities II: The Choquet integral, Fuzzy Sets and Systems 151, pp. 237-259, 2005.

[9] Greco S., Grabisch M., Pirlot M., Bipolar and bivariate models in multicriteria decision analysis: descriptive and constructive approaches, Int. J. Intell. Syst. 23, 930-969, 2008.

[10] Greco S., Matarazzo B., Giove S., The Choquet integral with respect to a level dependent capacity, Fuzzy Sets Syst. 175, 1-35, 2011.

[11] Labreuche Ch. and Grabsch M., Generalized Choquet like-aggregation for handling ratio scales, European J. Oper. Res.,172, pp. 931-955, 2006.

[12] Murofushi T. and Sugeno M., An interpretation of fuzzy measure and the Choquet integral as an integral with respect to a fuzzy measure, Fuzzy Sets and Systems, Vol. 29, pp. 201-227, 1989.

[13] Sugeno M., Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology, 1974.

[14] Wang Z. and Klir G.J., Fuzzy measure theory, Plenum Press, New york, 1992.

[15] Wang Z. and Klir G.J., Generalized measure theory, Springer Science+ Business Media, LLC, 2009.

[16] Wu C. X. and Huang Y., Choquet integrals on fuzzy sets, IEEE International Conference on Machine Learning and Cybernetics,(4), PP.1438-2552, 2005.

Journal of Artificial Intelligence and Soft Computing Research

The Journal of Polish Neural Network Society, the University of Social Sciences in Lodz & Czestochowa University of Technology

Journal Information

CiteScore 2017: 5.00

SCImago Journal Rank (SJR) 2017: 0.492
Source Normalized Impact per Paper (SNIP) 2017: 2.813

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 104 104 12
PDF Downloads 39 39 9