{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T17:15:21Z","timestamp":1769188521081,"version":"3.49.0"},"reference-count":47,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,9,22]],"date-time":"2018-09-22T00:00:00Z","timestamp":1537574400000},"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, we combined entropy with linguisti neutrosophic cubic numbers and used it in daily life problems related to a corporation that is going to choose an area supervisor, which is the main target of our proposed model. For this, we first develop the theory of linguistic neutrosophic cubic numbers, which explains the indeterminate and incomplete information by truth, indeterminacy and falsity linguistic variables (LVs) for the past, present, as well as for the future time very effectively. After giving the definitions, we initiate some basic operations and properties of linguistic neutrosophic cubic numbers. We also define the linguistic neutrosophic cubic Hamy mean operator and weighted linguistic neutrosophic cubic Hamy mean (WLNCHM) operator with some properties, which can handle multi-input agents with respect to the different time frame. Finally, as an application, we give a numerical example in order to test the applicability of our proposed model.<\/jats:p>","DOI":"10.3390\/sym10100428","type":"journal-article","created":{"date-parts":[[2018,9,24]],"date-time":"2018-09-24T10:38:49Z","timestamp":1537785529000},"page":"428","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6438-1047","authenticated-orcid":false,"given":"Muhammad","family":"Gulistan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hazara University, Mansehra 21120, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hafiz Abdul","family":"Wahab","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University, Mansehra 21120, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of New Mexico, Albuquerque, NM 87301, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salma","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University, Mansehra 21120, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sayed Inayat Ali","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Islamia College University, Peshawar 25120, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,22]]},"reference":[{"key":"ref_1","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":"Inform. Control"},{"key":"ref_2","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_3","first-page":"83","article-title":"Cubic sets","volume":"4","author":"Jun","year":"2012","journal-title":"Ann. Fuzzy Math. Inform."},{"key":"ref_4","first-page":"659","article-title":"Cubic KU-subalgebras","volume":"89","author":"Akram","year":"2013","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yaqoob, N., Mostafa, S.M., and Ansari, M.A. (2013). On cubic KU-ideals of KU-algebras. ISRN Algebra.","DOI":"10.1155\/2013\/935905"},{"key":"ref_6","first-page":"733","article-title":"Cubic graphs with application","volume":"16","author":"Rashid","year":"2018","journal-title":"Int. J. Anal. Appl."},{"key":"ref_7","first-page":"169","article-title":"On cubic \u0393-hyperideals in left almost \u0393-semihypergroups","volume":"5","author":"Aslam","year":"2013","journal-title":"Ann. Fuzzy Math. Inform."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4161","DOI":"10.3233\/JIFS-171744","article-title":"Extensions of cubic ideals in weak left almost semihypergroups","volume":"34","author":"Gulistan","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.fiae.2017.03.005","article-title":"Structural properties of cubic sets in regular LA-semihypergroups","volume":"9","author":"Gulistan","year":"2017","journal-title":"Fuzzy Inf. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1007\/s13370-015-0367-y","article-title":"General cubic hyperideals of LA-semihypergroups","volume":"27","author":"Khan","year":"2016","journal-title":"Afr. Mat."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2707","DOI":"10.3233\/JIFS-17850","article-title":"Cubic hyperideals in LA-semihypergroups","volume":"34","author":"Yaqoob","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"947","DOI":"10.3233\/IFS-141377","article-title":"The generalized version of Jun\u2019s cubic sets in semigroups","volume":"28","author":"Khan","year":"2015","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2469","DOI":"10.3233\/JIFS-18112","article-title":"Neutrosophic cubic (\u03b1,\u03b2)-ideals in semigroups with application","volume":"35","author":"Khan","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_14","first-page":"607","article-title":"Generalized cubic relations in Hv-LA-semigroups","volume":"21","author":"Ma","year":"2018","journal-title":"J. Discret. Math. Sci. Cryptgr."},{"key":"ref_15","first-page":"767","article-title":"Direct product of generalized cubic sets in Hv-LA-semigroups","volume":"28","author":"Gulistan","year":"2016","journal-title":"Sci. Int."},{"key":"ref_16","unstructured":"Smarandache, F. (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press."},{"key":"ref_17","first-page":"287","article-title":"Neutrosophic set, a generalization of the intuitionistic fuzzy set","volume":"24","author":"Smarandache","year":"2005","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_18","unstructured":"Wang, H., Smarandache, F., Zhang, Q.Y., and Sunderraman, R. (2010). Single Valued Neutrosophic Sets, Infinite Study."},{"key":"ref_19","first-page":"25","article-title":"Triangular dense fuzzy neutrosophic sets","volume":"13","author":"De","year":"2016","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_20","first-page":"97","article-title":"Complex neutrosophic subsemigroups and ideals","volume":"16","author":"Gulistan","year":"2018","journal-title":"Int. J. Anal. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1142\/S1793005717500041","article-title":"Neutrosophic cubic sets","volume":"13","author":"Jun","year":"2017","journal-title":"New Math. Nat. Comput."},{"key":"ref_22","first-page":"99","article-title":"P-union and P-intersection of neutrosophic cubic sets","volume":"25","author":"Jun","year":"2017","journal-title":"Anal. Univ. Ovidius Constanta"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Gulistan, M., Yaqoob, N., Rashid, Z., Smarandache, F., and Wahab, H. (2018). A study on neutrosophic cubic graphs with real life applications in industries. Symmetry, 10.","DOI":"10.3390\/sym10060203"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1615\/Int.J.UncertaintyQuantification.2017020446","article-title":"Applications of neutrosophic cubic sets in multi-criteria decision-making","volume":"7","author":"Zhan","year":"2017","journal-title":"Int. J. Uncertain. Quantif."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Hashim, R.M., Gulistan, M., and Smrandache, F. (2018). Applications of neutrosophic bipolar fuzzy sets in HOPE foundation for planning to build a children hospital with different types of similarity measures. Symmetry, 10.","DOI":"10.3390\/sym10080331"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","article-title":"The concept of a linguistic variable and its application to approximate reasoning Part I","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0165-0114(95)00107-7","article-title":"A model of consensus in group decision making under linguistic assessments","volume":"79","author":"Herrera","year":"1996","journal-title":"Fuzzy Sets Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/S0165-0114(99)00024-X","article-title":"linguistic decision analysis: Steps for solving decision problems under linguistic information","volume":"115","author":"Herrera","year":"2000","journal-title":"Fuzzy Sets Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.ins.2003.10.006","article-title":"A method based on linguistic aggregation operators for group decision making with linguistic preference relations","volume":"166","author":"Xu","year":"2004","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1080\/18756891.2015.1061394","article-title":"An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers","volume":"8","author":"Chen","year":"2015","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Zhang, H. (2014). Linguistic intuitionistic fuzzy sets and application in MAGDM. J. Appl. Math.","DOI":"10.1155\/2014\/432092"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Fang, Z.B., and Ye, J. (2017). Multiple attribute group decision-making method based on linguistic neutrosophic numbers. Symmetry, 9.","DOI":"10.3390\/sym9070111"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1007\/s13042-016-0630-z","article-title":"A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety","volume":"9","author":"Peng","year":"2017","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1186\/s40064-016-3247-5","article-title":"Aggregation operators of neutrosophic linguistic numbers for multiple attribute group decision making","volume":"5","author":"Ye","year":"2016","journal-title":"SpringerPlus"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Li, Y.Y., Zhang, H., and Wang, J.Q. (2017). Linguistic neutrosophic sets and their application in multicriteria decision-making problems. Int. J. Uncertain. Quantif., 7.","DOI":"10.1615\/Int.J.UncertaintyQuantification.2017019627"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"932025","DOI":"10.1155\/S1025583498000253","article-title":"A refinement of various mean inequalities","volume":"4","author":"Hara","year":"1998","journal-title":"J. Inequal. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1080\/03081079008935104","article-title":"Fuzzy sets and systems","volume":"17","author":"Zadeh","year":"1990","journal-title":"Int. J. Gen. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/S0019-9958(72)90199-4","article-title":"A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory","volume":"20","author":"Termini","year":"1972","journal-title":"Inf. Control"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1109\/TSMC.1977.4309751","article-title":"Introduction to the theory of fuzzy subsets-vol. 1: Fundamental theoretical elements","volume":"7","author":"Kaufmann","year":"1977","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0020-0255(86)90006-X","article-title":"Fuzzy entropy and conditioning","volume":"40","author":"Kosoko","year":"1986","journal-title":"Inf. Sci."},{"key":"ref_41","first-page":"59","article-title":"Softness of a soft set: Soft set entropy","volume":"6","author":"Majumdar","year":"2013","journal-title":"Ann. Fuzzy Math. Inf."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/S0165-0114(98)00402-3","article-title":"Entropy for intuitionistic fuzzy sets","volume":"118","author":"Szmidt","year":"2001","journal-title":"Fuzzy Sets Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1080\/03081077908547452","article-title":"On the measure of fuzziness and negation, Part I: Membership in the unit interval","volume":"5","author":"Yager","year":"1979","journal-title":"Int. J. Gen. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"247","DOI":"10.3233\/IFS-141295","article-title":"An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers","volume":"28","author":"Ye","year":"2015","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_45","first-page":"40","article-title":"The neutrosophic entropy and its five components","volume":"7","author":"Patrascu","year":"2015","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Liu, P., and You, X. (2018). Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0193027"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Ye, J. (2017). Linguistic neutrosophic cubic numbers and their multiple attribute decision-making method. Information, 8.","DOI":"10.3390\/info8030110"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/10\/428\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:22:04Z","timestamp":1760196124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/10\/428"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,22]]},"references-count":47,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["sym10100428"],"URL":"https:\/\/doi.org\/10.3390\/sym10100428","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,22]]}}}