{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T20:39:28Z","timestamp":1770064768663,"version":"3.49.0"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,2]],"date-time":"2019-02-02T00:00:00Z","timestamp":1549065600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a new concept of the triangular neutrosophic cubic fuzzy numbers (TNCFNs), their score and accuracy functions are introduced. Based on TNCFNs, some new Einstein aggregation operators, such as the triangular neutrosophic cubic fuzzy Einstein weighted averaging (TNCFEWA), triangular neutrosophic cubic fuzzy Einstein ordered weighted averaging (TNCFEOWA) and triangular neutrosophic cubic fuzzy Einstein hybrid weighted averaging (TNCFEHWA) operators are developed. Furthermore, their application to multiple-attribute decision-making with triangular neutrosophic cubic fuzzy (TNCF) information is discussed. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.<\/jats:p>","DOI":"10.3390\/sym11020180","type":"journal-article","created":{"date-parts":[[2019,2,5]],"date-time":"2019-02-05T11:31:07Z","timestamp":1549366267000},"page":"180","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Group Decision Making Based on Triangular Neutrosophic Cubic Fuzzy Einstein Hybrid Weighted Averaging Operators"],"prefix":"10.3390","volume":"11","author":[{"given":"Aliya","family":"Fahmi","sequence":"first","affiliation":[{"name":"Department of mathematics, Hazara University Mansehra, Dhodial 21130, Pakistan"}]},{"given":"Fazli","family":"Amin","sequence":"additional","affiliation":[{"name":"Department of mathematics, Hazara University Mansehra, Dhodial 21130, Pakistan"}]},{"given":"Madad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,2]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/0165-0114(94)90229-1","article-title":"New Operations Defined Over the Intuitionistic Fuzzy Sets","volume":"61","author":"Atanassov","year":"1994","journal-title":"Fuzzy Sets Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0165-0114(96)84610-0","article-title":"Structures on intuitionistic fuzzy relations","volume":"78","author":"Bustince","year":"1996","journal-title":"Fuzzy Sets Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0165-0114(02)00127-6","article-title":"On the relationship between some extensions of fuzzy set theory","volume":"133","author":"Deschrijver","year":"2003","journal-title":"Fuzzy Sets Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.1016\/j.ins.2006.11.005","article-title":"On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision","volume":"177","author":"Deschrijver","year":"2007","journal-title":"Inf. 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