Power Aggregation Operators in MADM Problems Under Pythagorean Neutrosophic Numbers Based on Hamacher t-norm and t-conorm Operations: Operadores de agregación de energía en problemas MADM bajo números neutrosóficos pitagóricos basados en operaciones t-norm y t-conorm de Hamacher

Carlos Granados; Somen Debnath

doi:10.24054/bistua.v22i2.2826

Autores/as

Carlos Granados Escuela Ciencias de la Educación, Universidad Nacional Abierta y a Dsitancia, Barranquilla, Colombia
Somen Debnath Department of Mathematics, Umakanta Academy, Agartala, Tripura, India

DOI:

https://doi.org/10.24054/bistua.v22i2.2826

Palabras clave:

Operadores de Hamacher; Números neutrosóficos pitagóricos; Operadores de agregados neutrosóficos pitagóricos de Hamacher; MADM

Resumen

La noción de conjuntos neutrosóficos pitagóricos (PNS) y sus números neutrosóficos pitagóricos (PNN) asociados son útiles para explorar conocimiento impreciso bajo condiciones restringidas. Las PNS son capaces de eliminar deficiencias en teorías existentes y se aplican fácilmente a diversos problemas inciertos. Por otro lado, los operadores de Hamacher son herramientas efectivas en la toma de decisiones de atributos múltiples (MADM). Este documento propone combinar las PNS con los operadores t-norm y t-conorm de Hamacher para desarrollar nuevos operadores de agregación basados en PNN, útiles para modelar incertidumbre en problemas MADM. Los operadores propuestos incluyen el operador pitagórico neutrosófico de Hamacher de potencia aritmética (PNHPA), el de potencia geométrica (PNHPG), el de promedio ponderado ordenado (PNHPOWA) y el de promedio geométrico ordenado ponderado (PNHPOWG). Se analizan algunas características clave de estos operadores para garantizar su aplicabilidad en MADM.

Utilizando estos operadores, se desarrolla un enfoque práctico para resolver problemas de decisión multiatributo bajo condiciones de incertidumbre representadas por PNN. Finalmente, se incluye un ejemplo numérico que verifica el enfoque propuesto y proporciona un análisis comparativo para destacar su efectividad frente a otros métodos. Este trabajo contribuye al campo de la toma de decisiones al proporcionar herramientas innovadoras basadas en PNN y operadores de Hamacher, ampliando las posibilidades para modelar incertidumbre y abordar problemas complejos en un contexto de múltiples atributos.

Descargas

Los datos de descargas todavía no están disponibles.

Citas

Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338–353. doi:10.1016/s0019-9958(65)90241-x.

McBratney, A. B., & Odeh, I. O. A. (1997). Application of fuzzy sets in soil science: fuzzy logic, fuzzy measurements and fuzzy decisions. Geoderma, 77, 85–113. doi:10.1016/s0016-7061(97)00017-7.

Kahraman, C., Gülbay, M., & Kabak, Ö. (2006). Applications of fuzzy sets in industrial engineering: a topical classification. Fuzzy Applications in Industrial Engineering, 201, 1-55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33517-X_1.

Zimmermann, H. J. (1985). Applications of fuzzy set theory to mathematical programming. Information Sciences, 36, 29–58. doi:10.1016/0020-0255(85)90025-8

Sinha, S., & Sarmah, S. P. (2008). An application of fuzzy set theory for supply chain coordination. International Journal of Management Science and Engineering Management, 3, 19-32.

Guiffrida, A. L., & Nagi, R. (1998). Fuzzy set theory applications in production management research: a literature survey. Journal of intelligent manufacturing, 9, 39-56.

Wang, P. P., & Chang, S. K. (1980). Fuzzy Sets: Theory of Applications to Policy Analysis and Information Systems. Fuzzy Sets, 3-10. Springer, Boston, MA. doi:10.1007/978-1-4684-3848-2_1

Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96. doi:10.1016/s0165-0114(86)80034-3

Li, J., Li, J., You, C., & Dong, M. (2012). Multi-attribute decision making method with intuitionistic fuzzy sets. 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery, 97-101, IEEE. doi: 10.1109/FSKD.2012.6234072

Singh, P., Huang, Y.-P., & Wu, S.-I. (2020). An Intuitionistic Fuzzy Set Approach for Multi-attribute Information Classification and Decision-Making. International Journal of Fuzzy Systems, 22, 1506–1520. doi:10.1007/s40815-020-00879-w

Liu, P., Liu, X., Ma, G., Liang, Z., Wang, C., & Alsaadi, F. E. (2020). A multi-attribute group decision-making method based on linguistic intuitionistic fuzzy numbers and Dempster–Shafer evidence theory. International Journal of Information Technology & Decision Making, 19, 499-524.doi:10.1142/S0219622020500042

Xu, Z., & Yager, R. R. (2008). Dynamic intuitionistic fuzzy multi-attribute decision making. International journal of approximate reasoning, 48, 246-262.

Yager, R. R. (2013). Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), 57-61, IEEE. doi: 10.1109/IFSA-NAFIPS.2013.6608375

Tao, Z., Zhu, J., Zhou, L., Liu, J., & Chen, H. (2021). Multi-attribute decision making with Pythagorean fuzzy sets via conversions to intuitionistic fuzzy sets and ORESTE method. Journal of Control and Decision, 8, 372-383.

Lin, M., Wei, J., Xu, Z., & Chen, R. (2018). Multiattribute group decision-making based on linguistic pythagorean fuzzy interaction partitioned bonferroni mean aggregation operators. Complexity, 2018, 1-24. https://doi.org/10.1155/2018/9531064

Paul, T. K., Pal, M., & Jana, C. (2021). Multi-attribute decision making method using advanced Pythagorean fuzzy weighted geometric operator and their applications for real estate company selection. Heliyon, 7, 1-9.doi:10.1016/j.heliyon.2021.e07340

Garg, H. (2018). Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. International Journal of Intelligent Systems, 33, 1234-1263.doi:10.1002/int.21979

Khan, M. S. A., Abdullah, S., & Lui, P. (2020). Gray method for multiple attribute decision making with incomplete weight information under the pythagorean fuzzy setting. Journal of Intelligent Systems, 29, 858-876.

Wan, Z., Shi, M., Yang, F., & Zhu, G. (2021). A Novel Pythagorean Group Decision-Making Method Based on Evidence Theory and Interactive Power Averaging Operator. Complexity, 2021, 1-13. https://doi.org/10.1155/2021/9964422

Wan, S. P., Jin, Z., & Dong, J. Y. (2018). Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees. Knowledge and Information Systems, 55, 437-466.

Xu, Y., Shang, X., & Wang, J. (2018). Pythagorean fuzzy interaction Muirhead means with their application to multi-attribute group decision-making. Information, 9, 157.

Yager, R. R. (2016). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222-1230.

Smarandache, F. (2005). Neutrosophic set-a generalization of the intuitionistic fuzzy set. International journal of pure and applied mathematics, 24, 287-297.

Jansi, R., Mohana, K., & Smarandache, F. (2019). Correlation Measure for Pythagorean Neutrosophic Fuzzy Sets with T and F as Dependent Neutrosophic Components. Neutrosophic Sets and Systems, 30, 202-212

Rajan, J., & Krishnaswamy, M. (2020). Similarity Measures of Pythagorean Neutrosophic Sets with Dependent Neutrosophic Components Between T and F. Journal of New Theory, 33, 85-94.

Jansi, R., & Mohana, K. (2020). Pythagorean neutrosophic subring of a ring. Journal of Computational Mathematica, 4, 1-9.

Ajay, D., & Chellamani, P. (2020). Pythagorean Neutrosophic Fuzzy Graphs. International Journal of Neutrosophic Science, 11, 108-114.

Hamacher, H. (1978). Uber logische Vernupfungen unscharfer Aussagen und deren Zugenhorige Bewertungsfunctionen Trappl, Klir, Riccardi(eds.). Progress in Cybernatics and Systems Research, 3, 276-288.

Roychowdhury, S., & Wang, B. H. (1998). On generalized Hamacher families of triangular operators. International Journal of Approximate Reasoning, 19, 419-439.

Liu, P. (2013). Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Transactions on Fuzzy systems, 22, 83-97.

Zhou, L., Zhao, X., & Wei, G. (2014). Hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 26, 2689-2699.

Huang, J. Y. (2014). Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 27, 505-513.

Liu, P., Chu, Y., Li, Y., & Chen, Y. (2014). Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making. International Journal of fuzzy systems, 16, 242-255.

Gao, H., Wei, G., & Huang, Y. (2017). Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. IEEE ACCESS, 6, 11508-11522.

Wei, G., & Lu, M. A. O. (2017). Dual hesitant Pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making. Archives of Control Sciences, 27, 365-395.

Lu, M., Wei, G., Alsaadi, F. E., Hayat, T., & Alsaedi, A. (2017). Hesitant pythagorean fuzzy hamacher aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 33, 1105-1117.

Wu, S. J., & Wei, G. W. (2017). Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. International Journal of Knowledge-based and Intelligent Engineering Systems, 21, 189-201.

Wei, G., Lu, M., Tang, X., & Wei, Y. (2018). Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. International Journal of Intelligent Systems, 33, 1197-1233.

Wu, Q., Wu, P., Zhou, L., Chen, H., & Guan, X. (2018). Some new Hamacher aggregation operators under single-valued neutrosophic 2-tuple linguistic environment and their applications to multi-attribute group decision making. Computers & Industrial Engineering, 116, 144-162.

Liang, W., Zhao, G., & Luo, S. (2018). Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines. PLOS ONE, 13, e0206178.

Wei, G., Alsaadi, F. E., Hayat, T., & Alsaedi, A. (2018). Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making. International Journal of Fuzzy Systems, 20, 1-12.

Zhu, J., & Li, Y. (2018). Hesitant Fuzzy Linguistic Aggregation Operators Based on the Hamacher t-norm and t-conorm. Symmetry, 10, 189. https://doi.org/10.3390/sym10060189

Wei, G. W. (2019). Pythagorean fuzzy Hamacher power aggregation operators in multiple attribute decision making. Fundamenta Informaticae, 166, 57-85.

Gao, H., Lu, M., & Wei, Y. (2019). Dual hesitant bipolar fuzzy hamacher aggregation operators and their applications to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 37, 5755-5766.

Jana, C., & Pal, M. (2019). Assessment of enterprise performance based on picture fuzzy Hamacher aggregation operators. Symmetry, 11, 75. https://doi.org/10.3390/sym11010075

Wang, P., Wei, G., Wang, J., Lin, R., & Wei, Y. (2019). Dual hesitant q-rung orthopair fuzzy hamacher aggregation operators and their applications in scheme selection of construction project. Symmetry, 11, 771. https://doi.org/10.3390/sym11060771

Waseem, N., Akram, M., & Alcantud, J. C. R. (2019). Multi-attribute decision-making based on m-polar fuzzy Hamacher aggregation operators. Symmetry, 11, 1498. https://doi.org/10.3390/sym11121498

Darko, A. P., & Liang, D. (2020). Some q-rung orthopair fuzzy Hamacher aggregation operators and their application to multiple attribute group decision making with modified EDAS method. Engineering Applications of Artificial Intelligence, 87, 103259.

Akram, M., Bashir, A., & Garg, H. (2020). Decision-making model under complex picture fuzzy Hamacher aggregation operators. Computational and Applied Mathematics, 39, 1-38.

Ullah, K., Mahmood, T., & Garg, H. (2020). Evaluation of the performance of search and rescue robots using T-spherical fuzzy hamacher aggregation operators. International Journal of Fuzzy Systems, 22, 570-582.

Wang, L., Garg, H., & Li, N. (2021). Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight. Soft Computing, 25, 973-993.

Wei, G., Zhao, X., Wang, H., & Lin, R. (2013). Fuzzy power aggregation operators and their application to multiple attribute group decision making. Technological and Economic Development of Economy, 19, 377-396.

Smarandache, F. (2018). Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited. Neutrosophic Sets and Systems, 21, 153-166. http://fs.unm.edu/NSS2/index.php/111/article/view/316

Operadores de agregación de energía en problemas MADM bajo números neutrosóficos pitagóricos basados en operaciones t-norm y t-conorm de Hamacher