{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T22:14:08Z","timestamp":1769552048393,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,5]],"date-time":"2018-01-05T00:00:00Z","timestamp":1515110400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71371156"],"award-info":[{"award-number":["71371156"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Express Academic Scholarship Funding Project of Southwest Jiaotong University","award":["A0920502051703-1"],"award-info":[{"award-number":["A0920502051703-1"]}]},{"name":"Doctoral Innovation Fund Program of Southwest Jiaotong University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Single-valued neutrosophic hesitant fuzzy set (SVNHFS) is a combination of single-valued neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the multiple criteria decision-making (MCDM) process. This paper investigates the MCDM problems in which the criteria under SVNHF environment are in different priority levels. First, the generalized single-valued neutrosophic hesitant fuzzy prioritized weighted average operator and generalized single-valued neutrosophic hesitant fuzzy prioritized weighted geometric operator are developed based on the prioritized average operator. Second, some desirable properties and special cases of the proposed operators are discussed in detail. Third, an approach combined with the proposed operators and the score function of single-valued neutrosophic hesitant fuzzy element is constructed to solve MCDM problems. Finally, an example of investment selection is provided to illustrate the validity and rationality of the proposed method.<\/jats:p>","DOI":"10.3390\/info9010010","type":"journal-article","created":{"date-parts":[[2018,1,8]],"date-time":"2018-01-08T04:21:21Z","timestamp":1515385281000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Generalized Single-Valued Neutrosophic Hesitant Fuzzy Prioritized Aggregation Operators and Their Applications to Multiple Criteria Decision-Making"],"prefix":"10.3390","volume":"9","author":[{"given":"Rui","family":"Wang","sequence":"first","affiliation":[{"name":"School of Traffic and Logistics, Southwest Jiaotong University, Chengdu 610031, China"},{"name":"Tangshan Graduate School, Southwest Jiaotong University, Tangshan 063000, China"}]},{"given":"Yanlai","family":"Li","sequence":"additional","affiliation":[{"name":"School of Traffic and Logistics, Southwest Jiaotong University, Chengdu 610031, China"},{"name":"National Lab of Railway Transportation, Southwest Jiaotong University, Chengdu 610031, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4126","DOI":"10.1016\/j.eswa.2015.01.003","article-title":"Fuzzy multiple criteria decision-making techniques and applications\u2014Two decades review from 1994 to 2014","volume":"42","author":"Mardani","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","article-title":"Interval valued intuitionistic fuzzy sets","volume":"31","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets Syst."},{"key":"ref_5","unstructured":"Wang, H., Smarandache, F., Zhang, Y., and Sunderraman, R. (2005, January 21\u201326). Single valued neutrosophic sets. Proceedings of the 10th International Conference on Fuzzy Theory and Technology, Salt Lake City, UT, USA."},{"key":"ref_6","unstructured":"Smarandache, F. (1999). A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s00521-014-1736-4","article-title":"The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making","volume":"26","author":"Liu","year":"2015","journal-title":"Neural Comput. Appl."},{"key":"ref_8","first-page":"410","article-title":"Single valued neutrosophic sets","volume":"4","author":"Wang","year":"2010","journal-title":"Multispace Multistruct."},{"key":"ref_9","unstructured":"Wang, H., Smarandache, F., Zhang, Y.Q., and Sunderraman, R. (2005). Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Torra, V., and Narukawa, Y. (2009, January 20\u201324). On hesitant fuzzy sets and decision. Proceedings of the IEEE International Conference on Fuzzy Systems, Jeju Island, Korea.","DOI":"10.1109\/FUZZY.2009.5276884"},{"key":"ref_11","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra","year":"2010","journal-title":"Int. J. Intell. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1016\/j.knosys.2012.09.009","article-title":"Interval-valued hesitant preference relations and their applications to group decision making","volume":"37","author":"Chen","year":"2013","journal-title":"Knowl.-Based Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhu, B., Xu, Z.S., and Xia, M.M. (2012). Dual hesitant fuzzy sets. J. Appl. Math., 2607\u20132645.","DOI":"10.1155\/2012\/879629"},{"key":"ref_14","first-page":"23","article-title":"Multiple-attribute decision-making method under a single-valued neutrosophic hesitant fuzzy environment","volume":"24","author":"Ye","year":"2014","journal-title":"J. Intell. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1007\/s00521-015-2163-x","article-title":"Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making","volume":"28","author":"Liu","year":"2017","journal-title":"Neural Comput. Appl."},{"key":"ref_16","unstructured":"Smarandache, F., and Pramanik, S. (2016). Some distance measures of single valued neutrosophic hesitant fuzzy sets and their applications to multiple attribute decision making. New Trends in Neutrosophic Theory and Applications, Ponsasbl. [2nd ed.]."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Liu, C.F., and Luo, Y.S. (2017). New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making. Pat. Anal. Appl., 1\u201311.","DOI":"10.12783\/dtetr\/iceta2016\/7001"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"303","DOI":"10.3233\/JIFS-151760","article-title":"Multiple criteria decision making method based on neutrosophic hesitant fuzzy heronian mean aggregation operators","volume":"32","author":"Liu","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"179","DOI":"10.15388\/Informatica.2016.81","article-title":"Correlation coefficients of interval neutrosophic hesitant fuzzy sets and its application in a multiple attribute decision making method","volume":"27","author":"Ye","year":"2014","journal-title":"Informatica"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3846\/20294913.2012.762951","article-title":"Intuitionistic fuzzy prioritized operators and their application in multi-criteria group decision making","volume":"19","author":"Yu","year":"2013","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.ijar.2007.08.009","article-title":"Prioritized aggregation operators","volume":"48","author":"Yager","year":"2008","journal-title":"Int. J. Approx. Reason."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.knosys.2011.11.004","article-title":"Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making","volume":"30","author":"Yu","year":"2012","journal-title":"Knowl.-Based Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1007\/s11424-015-4010-7","article-title":"Interval neutrosophic prioritized owa operator and its application to multiple attribute decision making","volume":"29","author":"Liu","year":"2016","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.knosys.2012.03.011","article-title":"Hesitant fuzzy prioritized operators and their application to multiple attribute decision making","volume":"31","author":"Wei","year":"2012","journal-title":"Knowl.-Based Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1863","DOI":"10.1007\/s00500-015-1887-y","article-title":"Interval-valued hesitant fuzzy einstein prioritized aggregation operators and their applications to multi-attribute group decision making","volume":"20","author":"Jin","year":"2016","journal-title":"Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0165-0114(84)90097-6","article-title":"Generalized means as model of compensative connectives","volume":"14","author":"Dyckhoff","year":"1984","journal-title":"Fuzzy Sets Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1016\/j.apm.2013.07.010","article-title":"Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making","volume":"38","author":"Ye","year":"2014","journal-title":"Appl. Math. Model."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1080\/03081079.2012.761609","article-title":"Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment","volume":"42","author":"Ye","year":"2013","journal-title":"Int. J. Gen. 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