A New Total Order for Triangular Fuzzy Numbers with an Application
Resumo
Este trabalho trata do estudo de uma nova ordem total para números fuzzy triangulares e propriedades aritméticas que são mantidas em relação às operações de adição e subtração. Além disso, apresentamos como exemplo de aplicação a solução do caminho mais curto para o Problema do Caixeiro Viajante com distâncias fuzzy.
Palavras-chave:
Fuzzy Numbers, Total Order, Triangular Fuzzy Numbers, Fuzzy Weighted Graph
Referências
Akyar, E., Akyar, H., and Düzce, S. A. (2012). A new method for ranking triangular fuzzy numbers. Int. J. Uncertain. Fuzziness Knowl. Based Syst., 20(5):729–740.
Asmus.T.C., Dimuro, G. P., and Bedregal, B. R. C. (2017). On two-player interval-valued fuzzy Bayesian games. Int. J. Intell. Syst., 32(6):557–596.
Birkhoff, G. (1987). Lattice-ordered groups. Selected Papers on Algebra and Topology by Garrett Birkhoff, 43(2):412.
Bondy, J. and Murty, U. (1976). Graph theory with applications. Published by The Macmillan Press Ltd.
Buckley, J. J. (2005). Fuzzy probabilities: new approach and applications, volume 115. Springer Science & Business Media.
Clifford, A. H. (1940). Partially ordered Abelian groups. Annals of Mathematics, pages 465–473.
Cornelis, C., De Kesel, P., and Kerre, E. E. (2004). Shortest paths in fuzzy weighted graphs. International journal of intelligent systems, 19(11):1051–1068.
Dubois, D. and Prade, H. (1978). Operations on fuzzy numbers. International Journal of Systems Science, 9(6):613–626.
Everett, C. J. and Ulam, S. (1945). On ordered groups. Transactions of the American Mathematical Society, 57(2):208–216.
Klir, G. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications, volume 4. Prentice Hall New Jersey.
Levi, F. W. (1942). Ordered groups. In Proceedings of the Indian Academy of Sciences Section A, volume 16, pages 256–263. Springer India.
Nasseri, S. H. and Behmanesh, E. (2013). Linear programming with triangular fuzzy numbers – a case study in a finance and credit institute. Fuzzy Information and Engineering, 5(3):295–315.
Rudin, W. (1964). Principles of Mathematical Analysis, volume 3. McGraw-hill New York.
Wang, W. and Wang, Z. (2014). Total orderings defined on the set of all fuzzy numbers. Fuzzy Sets and Systems, 243:131–141.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3):338–353.
Zumelzu, N., Bedregal, B., Mansilla, E., Bustince, H., and Dı́az, R. (2020). Admissible orders on fuzzy numbers. arXiv preprint arXiv:2003.01530.
Asmus.T.C., Dimuro, G. P., and Bedregal, B. R. C. (2017). On two-player interval-valued fuzzy Bayesian games. Int. J. Intell. Syst., 32(6):557–596.
Birkhoff, G. (1987). Lattice-ordered groups. Selected Papers on Algebra and Topology by Garrett Birkhoff, 43(2):412.
Bondy, J. and Murty, U. (1976). Graph theory with applications. Published by The Macmillan Press Ltd.
Buckley, J. J. (2005). Fuzzy probabilities: new approach and applications, volume 115. Springer Science & Business Media.
Clifford, A. H. (1940). Partially ordered Abelian groups. Annals of Mathematics, pages 465–473.
Cornelis, C., De Kesel, P., and Kerre, E. E. (2004). Shortest paths in fuzzy weighted graphs. International journal of intelligent systems, 19(11):1051–1068.
Dubois, D. and Prade, H. (1978). Operations on fuzzy numbers. International Journal of Systems Science, 9(6):613–626.
Everett, C. J. and Ulam, S. (1945). On ordered groups. Transactions of the American Mathematical Society, 57(2):208–216.
Klir, G. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications, volume 4. Prentice Hall New Jersey.
Levi, F. W. (1942). Ordered groups. In Proceedings of the Indian Academy of Sciences Section A, volume 16, pages 256–263. Springer India.
Nasseri, S. H. and Behmanesh, E. (2013). Linear programming with triangular fuzzy numbers – a case study in a finance and credit institute. Fuzzy Information and Engineering, 5(3):295–315.
Rudin, W. (1964). Principles of Mathematical Analysis, volume 3. McGraw-hill New York.
Wang, W. and Wang, Z. (2014). Total orderings defined on the set of all fuzzy numbers. Fuzzy Sets and Systems, 243:131–141.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3):338–353.
Zumelzu, N., Bedregal, B., Mansilla, E., Bustince, H., and Dı́az, R. (2020). Admissible orders on fuzzy numbers. arXiv preprint arXiv:2003.01530.
Publicado
17/11/2021
Como Citar
ROSAS, Valentina; BEDREGAL, Benjamín; CANUMÁN, José; DÍAZ, Roberto; MANSILLA, Edmundo; ZUMELZU, Nicolás.
A New Total Order for Triangular Fuzzy Numbers with an Application. In: WORKSHOP-ESCOLA DE INFORMÁTICA TEÓRICA (WEIT), 6. , 2021, Online.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2021
.
p. 17-24.
DOI: https://doi.org/10.5753/weit.2021.18917.