Comparison Between Fuzzy Number Sequences via Interactive Arithmetic J0 and Standard Arithmetic
Vinı`cius Francisco Wasques
1
(
Ilum School of Science, Brazilian Center for Research in Energy and Materials, Campinas, Brazil.
)
Nilmara de Jesus Biscaia Pinto
2
(
Faculty of Applied Sciences, University of Campinas, Limeira, Brazil.
)
کلید واژه: Interactive fuzzy numbers, Fuzzy number sequence, Fuzzy discrete equations, Sup-J extension principle.,
چکیده مقاله :
The focus of this work is to study sequences of interactive fuzzy numbers. The interactivity relation is associated with the concept of joint possibility distribution. In this case, the type of interactivity studied is linked to a family of joint possibility distributions (Jγ), in which the parameter γ intrinsically models levels of interactivity between the fuzzy numbers involved. Each element of the sequence of interactive fuzzy numbers is obtained through a discrete equation, and the arithmetic operations present in the equation are extended to this type of fuzzy number. Some simulations are performed to illustrate the behavior of the sequences, called interactive, and to compare them with the sequences obtained by other fuzzy arithmetic operations.
چکیده انگلیسی :
The focus of this work is to study sequences of interactive fuzzy numbers. The interactivity relation is associated with the concept of joint possibility distribution. In this case, the type of interactivity studied is linked to a family of joint possibility distributions (Jγ), in which the parameter γ intrinsically models levels of interactivity between the fuzzy numbers involved. Each element of the sequence of interactive fuzzy numbers is obtained through a discrete equation, and the arithmetic operations present in the equation are extended to this type of fuzzy number. Some simulations are performed to illustrate the behavior of the sequences, called interactive, and to compare them with the sequences obtained by other fuzzy arithmetic operations.
[1] Edelstein-Keshet L. Mathematical Models in Biology. SIAM; 1988.
[2] Barros LC, Bassanezi RC, Lodwick WA. A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics. Springer; 2017.
[3] Wasques VF. Fuzzy Differential Equations via Interactive Arithmetic: Applications in Biomathematics. University of Campinas; 2019. DOI: https://doi.org/10.47749/T/UNICAMP.2019.1141284
[4] Carlsson C, Fuller R. Additions of completely correlated fuzzy numbers. In: 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542). Budapeste, Hungary. IEEE; 2004. 535-539. DOI: https://doi.org/10.1109/FUZZY.2004.1375791
[5] Barros LC, Pedro FS. Fuzzy differential equations with interactive derivative. Fuzzy sets and systems. 2017; 309: 64-80. DOI: https://doi.org/10.1016/j.fss.2016.04.002
[6] Wasques VF, Esmi E, Barros LC, Sussner P. The generalized fuzzy derivative is interactive. Information Sciences. 2020; 519(1): 93-109. DOI: https://doi.org/10.1016/j.ins.2020.01.042
[7] Wasques VF, Laureano EE, Barros LC, Pedro FS, Sussner P. Higher order initial value problem with interactive fuzzy conditions. In: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). Rio de Janeiro, Brazil. IEEE; 2018. 1-8. DOI: https://doi.org/10.1109/FUZZ-IEEE.2018.8491465
[8] Pinto NJB, Esmi E, Wasques VF, Barros LC. Least square method with quasi linearly interactive fuzzy data: Fitting an HIV dataset. In: Fuzzy Techniques: Theory and Applications: Proceedings of the 2019 Joint World Congress of the International Fuzzy Systems Association and the Annual Conference of
the North American Fuzzy Information Processing Society IFSA/NAFIPS’2019 (Lafayette, Louisiana, USA). Springer International Publishing; 2019. 177-189. DOI: https://doi.org/10.1007/978-3-030-21920- 8 17
[9] Wasques VF, Esmi E, Barros LC, Sussner P. Numerical solutions for bidimensional initial value problem with interactive fuzzy numbers. In: Barreto G, Coelho R. (eds.) Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science; 2018, p.84-95. DOI:
https://doi.org/10.1007/978-3-319-95312-0 8
[10] Esmi E, Sussner P, Igncio GBD, Barros LC. A parametrized sum of fuzzy numbers with applications to fuzzy initial value problems. Fuzzy Sets and Systems. 2018; 331: 85-104. DOI: https://doi.org/10.1016/j.fss.2017.05.017
[11] Zadeh LA. The concept of a linguistic variable and its application to approximate reasoningI. Information Sciences. 1975; 8(3): 199-249. DOI: https://doi.org/10.1016/0020-0255(75)90036-5
[12] Wasques VF, Pinto NJB, Esmi E, Barros LC. Consistence of interactive fuzzy initial conditions. Fuzzy Information Processing. 2020; 1337, 143-155. DOI: https://doi.org/10.1007/978-3-030-81561-5 13
[13] Bede B. Mathematics of Fuzzy Sets and Fuzzy Logic. Berlin: Springer-Verlag Berlin Heidelberg; 2013.
[14] Wasques VF, Esmi E, Barros LC, Bede B. Comparison between numerical solutions of fuzzy initial-value problems via interactive and standard arithmetics. In: Kearfott R, Batyrshin I, Reformat M, Ceberio M, Kreinovich V. (eds.) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019. Advances in Intelligent Systems and Computing; 2019, p.704-715. DOI: https://doi.org/10.1007/978-3-030-21920- 8 62
