Abstract
In this paper we proposed a concept of Agnesi quasi-fuzzy numbers based on Agnesi’s curve. Also, in the set of all Agnesi quasi-fuzzy numbers is defined an arithmetic where field properties are satisfied.
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References
L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1975)
W. Pedrycz, F. Gomide, Fuzzy Systems Engineering: To RD Human-Centric Computing (Wiley, 2007)
J. Booker, T. Ross, An evolution of uncertainty assessment and quantification. Sci. Iran. 18(3), 669–676 (2011)
M. Alavidoost, M. Tarimoradi, M.F. Zarandi, Fuzzy adaptive genetic algorithm for multi-objective assembly line balancing problems. Appl. Soft Comput. 34, 655–677 (2015)
A. Blanco-Fernández, M. Casals, A. Colubi, N. Corral, M. GarcĂa-Bárzana, M. Gil, G. González-RodrĂguez, M. LĂłpez, M. Lubiano, M. Montenegro et al., A distance-based statistical analysis of fuzzy number-valued data. Int. J. Approx. Reason. 55(7), 1487–1501 (2014)
R.E. Moore, Interval Analysis, vol. 4 (Prentice-Hall Englewood Cliffs, NJ, 1966)
P. Kechagias, B.K. Papadopoulos, Computational method to evaluate fuzzy arithmetic operations. Appl. Math. Comput. 185(1), 169–177 (2007)
N.G. Seresht, A.R. Fayek, Computational method for fuzzy arithmetic operations on triangular fuzzy numbers by extension principle. Int. J. Approx. Reason. 106, 172–193 (2019)
D.Z. Yingming Chai, A representation of fuzzy numbers. Fuzzy Sets Syst. 295, 1–18 (2016)
A. Neumaier, A. Neumaier, Interval Methods for Systems of Equations, vol. 37 (Cambridge University Press, 1990)
W.A. Lodwick, Constrained interval arithmetic. Citeseer (1999)
Y. Chalco-Cano, W.A. Lodwick, B. Bede, Single level constraint interval arithmetic. Fuzzy Sets Syst. 257, 146–168 (2014)
L. Zadeh, Fuzzy sets, 338–353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X
R. Goetschel Jr., W. Voxman, Topological properties of fuzzy numbers. Fuzzy Sets Syst. 10(1–3), 87–99 (1983)
D. Dubois, H. Fargier, J. Fortin, The empirical variance of a set of fuzzy intervals, in, The 14th IEEE International Conference on Fuzzy Systems, FUZZ’05 (IEEE, 2005), pp. 885–890
D. Dubois, H. Prade, Gradual elements in a fuzzy set. Soft Computing 12(2), 165–175 (2008)
I.N. Herstein, Topics in Algebra (John Wiley & Sons, 2006)
J.J. Buckley, E. Eslami, An Introduction to Fuzzy Logic and Fuzzy Sets, vol. 13 (Springer Science & Business Media, 2002)
Acknowledgements
The authors would like to thank UESB (Southwest Bahia State University) and UFRN (Federal University of Rio Grande do Norte) for their financial support.
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Bergamaschi, F., Jesus, N., Santiago, R., Oliveira, A. (2022). Agnesi Quasi-fuzzy Numbers. In: Bede, B., Ceberio, M., De Cock, M., Kreinovich, V. (eds) Fuzzy Information Processing 2020. NAFIPS 2020. Advances in Intelligent Systems and Computing, vol 1337. Springer, Cham. https://doi.org/10.1007/978-3-030-81561-5_3
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DOI: https://doi.org/10.1007/978-3-030-81561-5_3
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