A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method
Hospital performance evaluation is vital for effective hospital management as it provides valuable information about a hospital’s condition and enables adaptable implementation based on various attributes. In this research, a multi-attribute group decision-making (MAGDM) method using a 2-tuple lingu...
- Autores:
-
Naz, Sumera
Muneeb ul Hassan, Muhammad
Fatima, Areej
Diaz Martínez, Jorge
Ospino Mendoza, Elisa
Aziz Butt, Shariq
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2023
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/13088
- Acceso en línea:
- https://hdl.handle.net/11323/13088
https://repositorio.cuc.edu.co/
- Palabra clave:
- 2-Tuple linguistic T-spherical fuzzy set
Maximizing deviation
TOPSIS
Key performance indicator
Hospital performance evaluation
- Rights
- embargoedAccess
- License
- Atribución 4.0 Internacional (CC BY 4.0)
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| dc.title.eng.fl_str_mv |
A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method |
| title |
A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method |
| spellingShingle |
A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method 2-Tuple linguistic T-spherical fuzzy set Maximizing deviation TOPSIS Key performance indicator Hospital performance evaluation |
| title_short |
A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method |
| title_full |
A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method |
| title_fullStr |
A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method |
| title_full_unstemmed |
A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method |
| title_sort |
A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method |
| dc.creator.fl_str_mv |
Naz, Sumera Muneeb ul Hassan, Muhammad Fatima, Areej Diaz Martínez, Jorge Ospino Mendoza, Elisa Aziz Butt, Shariq |
| dc.contributor.author.none.fl_str_mv |
Naz, Sumera Muneeb ul Hassan, Muhammad Fatima, Areej Diaz Martínez, Jorge Ospino Mendoza, Elisa Aziz Butt, Shariq |
| dc.subject.proposal.eng.fl_str_mv |
2-Tuple linguistic T-spherical fuzzy set Maximizing deviation TOPSIS Key performance indicator Hospital performance evaluation |
| topic |
2-Tuple linguistic T-spherical fuzzy set Maximizing deviation TOPSIS Key performance indicator Hospital performance evaluation |
| description |
Hospital performance evaluation is vital for effective hospital management as it provides valuable information about a hospital’s condition and enables adaptable implementation based on various attributes. In this research, a multi-attribute group decision-making (MAGDM) method using a 2-tuple linguistic T-spherical fuzzy set (2TLT-SFS) is proposed in the context of the cognitive information presented in the hospital evaluation process. The T-spherical fuzzy set is the most advanced generalization of the q-rung orthopair fuzzy set (q-ROFS) which is capable of handling the uncertainty, fuzziness and ambiguity in terms of four parameters: positivity (yes), negativity (no), impartiality (abstain), and denial (non-acceptance). The 2-tuple linguistic terminology is used to measure the validity of ambiguous data. We propose the 2TLT-SF Hamy mean (2TLT-SFHM) operator, 2TLT-SF weighted Hamy mean (2TLT-SFWHM) operator, 2TLT-SF dual Hamy mean (2TLT-SFDHM) operator and 2TLT-SF weighted dual Hamy mean (2TLT-SFWDHM) operator by combining the 2TLT-SFS and HM operator. Then, based on the proposed maximizing deviation method, a new optimization model is built that is able to exploit expert preference to find the best objective weights among attributes. Next, we extend the TOPSIS (technique for establishing order preference by similarity to the ideal solution) method to the 2TLT-SF-TOPSIS version which not only accounts for human cognition’s inherent uncertainty but also allows experts a wider context to express their decision. Finally, we give a case study about the selection of key performance indicators for hospital performance evaluation to support our proposed method. The findings from parameter analysis and comparative analysis demonstrate the method’s efficacy and reliability. The outcomes demonstrate that our approach successfully handles the assessment and choice of key performance indicators for hospital performance evaluation and captures the relationship between any number of attributes. |
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2023 |
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2023-06-17 |
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2024-06-27T12:38:36Z |
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2024-06-17 2024-06-27T12:38:36Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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Naz, S., Hassan, M.M.u., Fatima, A. et al. A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method. Granul. Comput. 8, 1659–1687 (2023). https://doi.org/10.1007/s41066-023-00388-9 |
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2364-4966 |
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https://hdl.handle.net/11323/13088 |
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10.1007/s41066-023-00388-9 |
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2364-4974 |
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Corporación Universidad de la Costa |
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REDICUC - Repositorio CUC |
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https://repositorio.cuc.edu.co/ |
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Naz, S., Hassan, M.M.u., Fatima, A. et al. A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method. Granul. Comput. 8, 1659–1687 (2023). https://doi.org/10.1007/s41066-023-00388-9 2364-4966 10.1007/s41066-023-00388-9 2364-4974 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
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eng |
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eng |
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Granular Computing |
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Akram M, Naz S, Edalatpanah SA, Mehreen R (2021) Group decision-making framework under linguistic q-rung orthopair fuzzy Einstein models. Soft Comput 25(15):10309–10334 Akram M, Naz S, Santos-Garcia G, Saeed MR (2022) Extended CODAS method for MAGDM with 2-tuple linguistic T-spherical fuzzy sets. AIMS Math 8(2):3428–3468 Akram M, Khan A, Ahmad U (2023) Extended MULTIMOORA method based on 2-tuple linguistic Pythagorean fuzzy sets for multi-attribute group decision-making. Granul Comput 8(2):311–332 Alahmadi RA, Ganie AH, Al-Qudah Y, Khalaf MM, Ganie AH (2023) Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure. Granul Computi. https://doi.org/10.1007/s41066-023-00378-x Atanassov KT (1999) Intuitionistic fuzzy sets. Physica (Heidelberg) 35:1–137 Chang KH, Chang YC, Lee YT (2014) Integrating TOPSIS and DEMATEL methods to rank the risk of failure of FMEA. Int J Inf Technol Decis Mak 13(06):1229–1257 Chen SM, Cheng SH, Lin TE (2015) Group decision making systems using group recommendations based on interval fuzzy preference relations and consistency matrices. Inf Sci 298:555–567 Deng X, Wang J, Wei G (2019) Some 2-tuple linguistic Pythagorean Heronian mean operators and their application to multiple attribute decision-making. J Exp Theoret Artif Intell 31(4):555–574 Garg H, Naz S, Ziaa F, Shoukat Z (2021) A ranking method based on Muirhead mean operator for group decision-making with complex interval-valued q-rung orthopair fuzzy numbers. Soft Comput 25(22):14001–14027 Gou X, Liao H, Xu Z, Herrera F (2017) Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: a case of study to evaluate the implementation status of haze controlling measures. Inf Fusion 38:22–34 Guleria A, Bajaj RK (2020) T-spherical fuzzy graphs: operations and applications in various selection processes. Arab J Sci Eng 45(3):2177–2193 Hadi-Vencheh A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 277:263–272 Hara T, Uchiyama M, Takahasi SE (1998) A refinement of various mean inequalities. J Inequal Appl 4:932025 Herrera F, Martinez L (2000a) An approach for combining linguistic and numerical information based on the 2-tuple fuzzy linguistic representation model in decision-making. Internat J Uncertain Fuzziness Knowl Based Syst 8(05):539–562 Herrera F, Martinez L (2000b) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752 Hwang CL, Yoon K (1981a) Methods for multiple attribute decision making, vol 186. Springer, Berlin, pp 58–191 Hwang CL, Yoon K (1981b) Multiple attributes decision making methods and applications, vol 444. Springer, Berlin, pp 445–446 Ju Y, Wang A, Ma J, Gao H, Santibanez Gonzalez ED (2020) Some q-rung orthopair fuzzy 2-tuple linguistic Muirhead mean aggregation operators and their applications to multiple-attribute group decision making. Int J Intell Syst 35(1):184–213 Krylovas A, Zavadskas EK, Kosareva N, Dadelo S (2014) New KEMIRA method for determining criteria priority and weights in solving MCDM problem. Int J Inf Technol Decis Mak 13(06):1119–1133 Kumar K, Chen SM (2022a) Group decision making based on advanced intuitionistic fuzzy weighted Heronian mean aggregation operator of intuitionistic fuzzy values. Inf Sci 601:306–322 Kumar K, Chen SM (2022b) Group decision making based on weighted distance measure of linguistic intuitionistic fuzzy sets and the TOPSIS method. Inf Sci 611:660–676 Li Z, Gao H, Wei G (2018a) Methods for multiple attribute group decision making based on intuitionistic fuzzy dombi hamy mean operators. Symmetry 10(11):574 Li Z, Wei G, Lu M (2018b) Pythagorean fuzzy hamy mean operators in multiple attribute group decision making and their application to supplier selection. Symmetry 10(10):505 Liang Z (2020) Models for multiple attribute decision making with fuzzy number intuitionistic fuzzy Hamy mean operators and their application. IEEE Access 8:115634–115645 Liang D, Xu Z (2017) The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Appl Soft Comput 60:167–179 Liu P, Chen SM, Wang Y (2020a) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Inf Sci 512:830–854 Liu P, Zhu B, Wang P, Shen M (2020b) An approach based on linguistic spherical fuzzy sets for public evaluation of shared bicycles in China. Eng Appl Artif Intell 87:103295 Liu P, Naz S, Akram M, Muzammal M (2022) Group decisionmaking analysis based on linguistic q-rung orthopair fuzzy generalized point weighted aggregation operators. Int J Mach Learn Cybern 13(4):883–906 Mahmood T, Ullah K, Khan Q, Jan N (2019) An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput Appl 31(11):7041–7053 Mohammadkarim B, Jamil S, Pejman H, Seyyed MH, Mostafa N (2011) Combining multiple indicators to assess hospital performance in Iran using the Pabon Lasso Model. Australas Med J 4(4):175–179 Naz S, Akram M, Al-Shamiri MA, Khalaf MM, Yousaf G (2022a) A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators. Math Biosci Eng 19(4):3843–3878 Naz S, Akram M, Muhiuddin G, Shafiq A (2022b) Modified EDAS method for MAGDM based on MSM operators with 2-tuple linguistic-spherical fuzzy sets. Math Probl Eng. https://doi.org/10.1155/2022/5075998 Naz S, Akram M, Muzammal M (2022c) Group decision-making based on 2-tuple linguistic T-spherical fuzzy COPRAS method. Soft Comput. https://doi.org/10.1007/s00500-022-07644-1 Naz S, Akram M, Saeid AB, Saadat A (2022d) Models for MAGDM with dual hesitant q-rung orthopair fuzzy 2-tuple linguistic MSM operators and their application to COVID-19 pandemic. Expert Syst 39(8):e13005 Naz S, Akram M, Sattar A, Al-Shamiri MMA (2022e) 2-tuple linguistic q-rung orthopair fuzzy CODAS approach and its application in arc welding robot selection. AIMS Math 7(9):17529–17569 Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156(2):445–455 Quek SG, Selvachandran G, Munir M, Mahmood T, Ullah K, Son LH, Priyadarshini I (2019) Multi-attribute multi-perception decisionmaking based on generalized T-spherical fuzzy weighted aggregation operators on neutrosophic sets. Mathematics 7(9):780 Rong Y, Liu Y, Pei Z (2020) Complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean operators and its application to emergency program selection. Int J Intell Syst 35(11):1749–1790 Sadeghifar J, Ashrafrezaee N, Hamouzadeh P, Taghavi Shahri M, Shams L (2011) Relationship between performance indicators and hospital evaluation score at hospitals affiliated to Urmia University of Medical Sciences. Nurs Midwifery J 9(4):10 Salsabeela V, Athira TM, John SJ, Baiju T (2023) Multiple criteria group decision making based on q-rung orthopair fuzzy soft sets. Granul Computi. https://doi.org/10.1007/s41066-023-00369-y Taslimi MS, Zayandeh M (2013) Challenges of hospital performance assessment system development: Literature review. Hakim Res J 16(1):35–41 Ullah K, Mahmood T, Jan N (2018) Similarity measures for Tspherical fuzzy sets with applications in pattern recognition. Symmetry 10(6):193 Ullah K, Mahmood T, Garg H (2020) Evaluation of the performance of search and rescue robots using T-spherical fuzzy Hamacher aggregation operators. Int J Fuzzy Syst 22(2):570–582 Verma R, Aggarwal A (2021) On matrix games with 2-tuple intuitionistic fuzzy linguistic payoffs. Iran J Fuzzy Syst 18(4):149–167 Wang WP (2009) Evaluating new product development performance by fuzzy linguistic computing. Expert Syst Appl 36(6):9759–9766 Wang J, Wei G, Lu J, Alsaadi FE, Hayat T, Wei C, Zhang Y (2019) Some q-rung orthopair fuzzy Hamy mean operators in multiple attribute decision-making and their application to enterprise resource planning systems selection. Int J Intell Syst 34(10):2429–2458 Wang W, Tian G, Zhang T, Jabarullah NH, Li F, Fathollahi-Fard AM, Li Z (2021) Scheme selection of design for disassembly (DFD) based on sustainability: a novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory. J Clean Prod 281:124724 Wei C, Ren Z, Rodrı´guez RM (2015) A hesitant fuzzy linguistic TODIM method based on a score function. Int J Comput Intell Syst 8(4):701–712 Wu S, Wang J, Wei G, Wei Y (2018) Research on construction engineering project risk assessment with some 2-tuple linguistic neutrosophic Hamy mean operators. Sustainability 10(5):1536 Wu L, Wang J, Gao H (2019) Models for competiveness evaluation of tourist destination with some interval-valued intuitionistic fuzzy Hamy mean operators. J Intell Fuzzy Syst 36(6):5693–5709 Xu Z, Zhang X (2013) Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl Based Syst 52:53–64 Yager RR (2013) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965 Yager RR (2016) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230 Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353 Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning UI. Inf Sci 8(3):199–249 Zeb A, Khan MSA, Ibrar M (2019) Approaches to multi-attribute decision making with risk preference under extended Pythagorean fuzzy environment. J Intelli Fuzzy Syst 36(1):325–335 Zhao H, Xu Z, Wang H, Liu S (2017) Hesitant fuzzy multi-attribute decision-making based on the minimum deviation method. Soft Comput 21(12):3439–3459 |
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Atribución 4.0 Internacional (CC BY 4.0)© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/embargoedAccesshttp://purl.org/coar/access_right/c_f1cfNaz, SumeraMuneeb ul Hassan, MuhammadFatima, AreejDiaz Martínez, JorgeOspino Mendoza, ElisaAziz Butt, Shariq2024-06-27T12:38:36Z2024-06-172024-06-27T12:38:36Z2023-06-17Naz, S., Hassan, M.M.u., Fatima, A. et al. A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method. Granul. Comput. 8, 1659–1687 (2023). https://doi.org/10.1007/s41066-023-00388-92364-4966https://hdl.handle.net/11323/1308810.1007/s41066-023-00388-92364-4974Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Hospital performance evaluation is vital for effective hospital management as it provides valuable information about a hospital’s condition and enables adaptable implementation based on various attributes. In this research, a multi-attribute group decision-making (MAGDM) method using a 2-tuple linguistic T-spherical fuzzy set (2TLT-SFS) is proposed in the context of the cognitive information presented in the hospital evaluation process. The T-spherical fuzzy set is the most advanced generalization of the q-rung orthopair fuzzy set (q-ROFS) which is capable of handling the uncertainty, fuzziness and ambiguity in terms of four parameters: positivity (yes), negativity (no), impartiality (abstain), and denial (non-acceptance). The 2-tuple linguistic terminology is used to measure the validity of ambiguous data. We propose the 2TLT-SF Hamy mean (2TLT-SFHM) operator, 2TLT-SF weighted Hamy mean (2TLT-SFWHM) operator, 2TLT-SF dual Hamy mean (2TLT-SFDHM) operator and 2TLT-SF weighted dual Hamy mean (2TLT-SFWDHM) operator by combining the 2TLT-SFS and HM operator. Then, based on the proposed maximizing deviation method, a new optimization model is built that is able to exploit expert preference to find the best objective weights among attributes. Next, we extend the TOPSIS (technique for establishing order preference by similarity to the ideal solution) method to the 2TLT-SF-TOPSIS version which not only accounts for human cognition’s inherent uncertainty but also allows experts a wider context to express their decision. Finally, we give a case study about the selection of key performance indicators for hospital performance evaluation to support our proposed method. The findings from parameter analysis and comparative analysis demonstrate the method’s efficacy and reliability. The outcomes demonstrate that our approach successfully handles the assessment and choice of key performance indicators for hospital performance evaluation and captures the relationship between any number of attributes.29 páginasapplication/pdfengSpringer International PublishingSwitzerlandhttps://link.springer.com/article/10.1007/s41066-023-00388-9A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation methodArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Granular ComputingAkram M, Naz S, Edalatpanah SA, Mehreen R (2021) Group decision-making framework under linguistic q-rung orthopair fuzzy Einstein models. Soft Comput 25(15):10309–10334Akram M, Naz S, Santos-Garcia G, Saeed MR (2022) Extended CODAS method for MAGDM with 2-tuple linguistic T-spherical fuzzy sets. AIMS Math 8(2):3428–3468Akram M, Khan A, Ahmad U (2023) Extended MULTIMOORA method based on 2-tuple linguistic Pythagorean fuzzy sets for multi-attribute group decision-making. Granul Comput 8(2):311–332Alahmadi RA, Ganie AH, Al-Qudah Y, Khalaf MM, Ganie AH (2023) Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure. Granul Computi. https://doi.org/10.1007/s41066-023-00378-xAtanassov KT (1999) Intuitionistic fuzzy sets. Physica (Heidelberg) 35:1–137Chang KH, Chang YC, Lee YT (2014) Integrating TOPSIS and DEMATEL methods to rank the risk of failure of FMEA. Int J Inf Technol Decis Mak 13(06):1229–1257Chen SM, Cheng SH, Lin TE (2015) Group decision making systems using group recommendations based on interval fuzzy preference relations and consistency matrices. Inf Sci 298:555–567Deng X, Wang J, Wei G (2019) Some 2-tuple linguistic Pythagorean Heronian mean operators and their application to multiple attribute decision-making. J Exp Theoret Artif Intell 31(4):555–574Garg H, Naz S, Ziaa F, Shoukat Z (2021) A ranking method based on Muirhead mean operator for group decision-making with complex interval-valued q-rung orthopair fuzzy numbers. Soft Comput 25(22):14001–14027Gou X, Liao H, Xu Z, Herrera F (2017) Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: a case of study to evaluate the implementation status of haze controlling measures. Inf Fusion 38:22–34Guleria A, Bajaj RK (2020) T-spherical fuzzy graphs: operations and applications in various selection processes. Arab J Sci Eng 45(3):2177–2193Hadi-Vencheh A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 277:263–272Hara T, Uchiyama M, Takahasi SE (1998) A refinement of various mean inequalities. J Inequal Appl 4:932025Herrera F, Martinez L (2000a) An approach for combining linguistic and numerical information based on the 2-tuple fuzzy linguistic representation model in decision-making. Internat J Uncertain Fuzziness Knowl Based Syst 8(05):539–562Herrera F, Martinez L (2000b) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752Hwang CL, Yoon K (1981a) Methods for multiple attribute decision making, vol 186. Springer, Berlin, pp 58–191Hwang CL, Yoon K (1981b) Multiple attributes decision making methods and applications, vol 444. Springer, Berlin, pp 445–446Ju Y, Wang A, Ma J, Gao H, Santibanez Gonzalez ED (2020) Some q-rung orthopair fuzzy 2-tuple linguistic Muirhead mean aggregation operators and their applications to multiple-attribute group decision making. Int J Intell Syst 35(1):184–213Krylovas A, Zavadskas EK, Kosareva N, Dadelo S (2014) New KEMIRA method for determining criteria priority and weights in solving MCDM problem. Int J Inf Technol Decis Mak 13(06):1119–1133Kumar K, Chen SM (2022a) Group decision making based on advanced intuitionistic fuzzy weighted Heronian mean aggregation operator of intuitionistic fuzzy values. Inf Sci 601:306–322Kumar K, Chen SM (2022b) Group decision making based on weighted distance measure of linguistic intuitionistic fuzzy sets and the TOPSIS method. Inf Sci 611:660–676Li Z, Gao H, Wei G (2018a) Methods for multiple attribute group decision making based on intuitionistic fuzzy dombi hamy mean operators. Symmetry 10(11):574Li Z, Wei G, Lu M (2018b) Pythagorean fuzzy hamy mean operators in multiple attribute group decision making and their application to supplier selection. 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texttext/plain111912https://repositorio.cuc.edu.co/bitstreams/5f703b1a-3de5-4c3b-a608-25dc2d186746/download2b2fb459f7d7f38f4bf0cd2c6060f0a2MD53THUMBNAILA decision-making mechanism for multi-attribute group decision-making using 2.pdf.jpgA decision-making mechanism for multi-attribute group decision-making using 2.pdf.jpgGenerated Thumbnailimage/jpeg15691https://repositorio.cuc.edu.co/bitstreams/955a8a91-0554-4c8c-a236-2c476eea5c6a/download710b2af6c70ee28edf05498da6bc52feMD5411323/13088oai:repositorio.cuc.edu.co:11323/130882024-09-17 12:45:50.659https://creativecommons.org/licenses/by/4.0/© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa 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ada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
 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