{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:50Z","timestamp":1760242430517,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T00:00:00Z","timestamp":1502755200000},"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 develop a new linguistic aggregation operator based on the cloud model for solving linguistic group decision-making problem. First, an improved generating cloud method is proposed so as to transform linguistic variables into clouds, which modifies the limitation of the classical generating cloud method. We then address some new cloud algorithms, such as cloud possibility degree and cloud support degree which can be respectively used to compare clouds and determine the weights. Combining the cloud support degree with power aggregation operator, we develop a new cloud aggregation operator dubbed the cloud generalized power ordered weighted average (CGPOWA) operator. We study the properties of the CGPOWA operator and investigate its family including a wide range of aggregation operators such as the CGPA operator, CPOWA operator, CPOWGA operator, CPWQA operator, CWAA and CWGA operator. Furthermore, a new approach for linguistic group decision-making is presented on the basis of the improved generating cloud method and CGPOWA operator. Finally, an illustrative example is provided to examine the effectiveness and validity of the proposed approach.<\/jats:p>","DOI":"10.3390\/sym9080156","type":"journal-article","created":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T14:35:00Z","timestamp":1502807700000},"page":"156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Cloud Generalized Power Ordered Weighted Average Operator and Its Application to Linguistic Group Decision-Making"],"prefix":"10.3390","volume":"9","author":[{"given":"Jianwei","family":"Gao","sequence":"first","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ru","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.omega.2006.10.001","article-title":"Multiple criteria decision-making for engineering","volume":"36","author":"Wiecek","year":"2008","journal-title":"Omega"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1016\/j.cie.2008.09.041","article-title":"The induced continuous ordered weighted geometric operators and their application in group decision-making","volume":"58","author":"Wu","year":"2009","journal-title":"Comput. Ind. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1016\/j.cie.2011.06.005","article-title":"Methods for fuzzy complementary preference relations based on multiplicative consistency","volume":"61","author":"Xia","year":"2011","journal-title":"Comput. Ind. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.cie.2010.10.005","article-title":"Induced and uncertain heavy OWA operators","volume":"60","author":"Casanovas","year":"2011","journal-title":"Comput. Ind. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.cie.2014.12.030","article-title":"Multi-attribute group decision-making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers","volume":"81","author":"Gong","year":"2015","journal-title":"Comput. Ind. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.cie.2015.12.027","article-title":"Some new generalized aggregation operators for triangular intuitionistic fuzzy numbers and application to multi-attribute group decision-making","volume":"93","author":"Wan","year":"2016","journal-title":"Comput. Ind. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1016\/j.cie.2012.11.015","article-title":"A type-2 linguistic set theory and its application to multi-criteria decision-making","volume":"64","author":"Ngan","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1016\/j.cie.2013.05.011","article-title":"Some hybrid aggregating operators in linguistic decision-making with Dempster-Shafer belief structure","volume":"65","author":"Wei","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.cie.2015.11.012","article-title":"A group multi-granularity linguistic-based methodology for prioritizing engineering characteristics under uncertainties","volume":"91","author":"Wang","year":"2016","journal-title":"Comput. Ind. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0888-613X(97)10003-2","article-title":"Fusion of ordinal information using weighted median aggregation","volume":"18","author":"Yager","year":"1998","journal-title":"Int. J. Approx. Reason."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1002\/int.10127","article-title":"An overview of operators for aggregating information","volume":"18","author":"Xu","year":"2003","journal-title":"Int. J. Intell. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.omega.2004.04.008","article-title":"Deviation measures of linguistic preference relations in group decision-making","volume":"33","author":"Xu","year":"2005","journal-title":"Omega"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0888-613X(94)00035-2","article-title":"An approach to ordinal decision-making","volume":"12","author":"Yager","year":"1995","journal-title":"Int. J. Approx. Reason."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1080\/03081079708945181","article-title":"Understanding the median as a fusion operator","volume":"26","author":"Yager","year":"1997","journal-title":"Int. J. Gen. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0020-7373(92)90093-Z","article-title":"Applications and extensions of OWA aggregations","volume":"37","author":"Yager","year":"1992","journal-title":"Int. J. Man-Mach. Stud."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1109\/3468.618263","article-title":"Aggregation operators for linguistic weighted information","volume":"27","author":"Herrera","year":"1997","journal-title":"IEEE Trans. Syst. Man Cybern. Part A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/0165-0114(95)00163-8","article-title":"Applying fuzzy set theory to evaluate the rate of aggregative risk in software development","volume":"79","author":"Lee","year":"1996","journal-title":"Fuzzy Sets Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S0020-0255(03)00080-X","article-title":"A new algorithm for applying fuzzy set theory to evaluate the rate of aggregative risk in software development","volume":"153","author":"Lee","year":"2003","journal-title":"Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0020-0255(95)00025-K","article-title":"A sequential selection process in group decision-making with a linguistic assessment approach","volume":"85","author":"Herrera","year":"1995","journal-title":"Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1002\/(SICI)1098-111X(199702)12:2<153::AID-INT3>3.0.CO;2-P","article-title":"The weighted OWA operator","volume":"12","author":"Torra","year":"1997","journal-title":"Int. J. Intell. Syst."},{"key":"ref_21","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_22","first-page":"190","article-title":"Decision-making with distance measures and linguistic aggregation operators","volume":"12","author":"Casanovas","year":"2010","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.cie.2013.07.021","article-title":"The induced linguistic continuous ordered weighted geometric operator and its application to group decision-making","volume":"66","author":"Zhou","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.asoc.2014.09.027","article-title":"Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision-making","volume":"25","author":"Zhou","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1016\/j.ejor.2015.06.063","article-title":"Subjective and objective information in linguistic multi-criteria group decision-making","volume":"248","author":"Zeng","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1109\/3477.915345","article-title":"A model based on linguistic 2-tuples for dealing with multi granular hierarchical linguistic contexts in multi-expert decision-making","volume":"31","author":"Herrera","year":"2001","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"key":"ref_27","first-page":"746","article-title":"A 2-tuple fuzzy linguistic representation model for computing with words","volume":"8","author":"Herrera","year":"2015","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5881","DOI":"10.1016\/j.eswa.2011.11.120","article-title":"Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision-making","volume":"39","author":"Wei","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.knosys.2013.02.002","article-title":"2-Tuple linguistic hybrid arithmetic aggregation operators and application to multi-attribute group decision-making","volume":"45","author":"Wan","year":"2013","journal-title":"Knowl.-Based Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1080\/03081070500422836","article-title":"On generalized induced linguistic aggregation operators","volume":"35","author":"Xu","year":"2006","journal-title":"Int. J. Gen. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1142\/S0218488504003211","article-title":"EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations","volume":"12","author":"Xu","year":"2004","journal-title":"Int. J. Uncertain. Fuzziness Knowl.-Based Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5905","DOI":"10.1016\/j.eswa.2010.02.015","article-title":"Standard and mean deviation methods for linguistic group decision-making and their applications","volume":"37","author":"Xu","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_33","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_34","first-page":"597","article-title":"Interactive approach for multiple attribute decision-making with incomplete weight information under uncertain linguistic environment","volume":"31","author":"Xu","year":"2009","journal-title":"Syst. Eng. Electron."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.inffus.2004.06.005","article-title":"Induced uncertain linguistic OWA operators applied to group decision-making","volume":"7","author":"Xu","year":"2006","journal-title":"Inf. Fusion"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.dss.2004.08.011","article-title":"An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision-making with uncertain multiplicative linguistic preference relations","volume":"41","author":"Xu","year":"2006","journal-title":"Decis. Support Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1109\/3468.983429","article-title":"The power average operator","volume":"31","author":"Yager","year":"2001","journal-title":"IEEE Trans. Syst. Man Cybern. Part A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5427","DOI":"10.1016\/j.apm.2011.12.002","article-title":"Linguistic power aggregation operators and their application to multiple attribute group decision-making","volume":"36","author":"Xu","year":"2012","journal-title":"Appl. Math. Model."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.knosys.2011.08.004","article-title":"A generalization of the power aggregation operators for linguistic environment and its application in group decision-making","volume":"26","author":"Zhou","year":"2012","journal-title":"Knowl.-Based Syst."},{"key":"ref_40","first-page":"16","article-title":"Membership clouds and membership cloud generators","volume":"32","author":"Li","year":"1995","journal-title":"J. Comput. Res. Dev."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.ins.2014.02.130","article-title":"Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information","volume":"274","author":"Wang","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1109\/TFUZZ.2014.2317500","article-title":"Atanassov\u2019s interval-valued intuitionistic linguistic multi-criteria group decision-making method based on trapezium cloud model","volume":"23","author":"Wang","year":"2015","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Li, D.Y., and Du, Y. (2007). Artificial Intelligence with Uncertainty, Chapman & Hall\/CRC, Press.","DOI":"10.1201\/9781584889991"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1002\/int.20340","article-title":"A new cognitive model: Cloud model","volume":"24","author":"Li","year":"2009","journal-title":"Int. J. Intell. Syst."},{"key":"ref_45","first-page":"679","article-title":"On multiple attribute group decision-making with linguistic assessment information based on cloud model","volume":"20","author":"Wang","year":"2005","journal-title":"Control Decis."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.jcss.2013.07.007","article-title":"A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision-making","volume":"80","author":"Wan","year":"2014","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/j.amc.2008.05.047","article-title":"Designing a model of fuzzy TOPSIS in multiple criteria decision-making","volume":"206","author":"Iraj","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.ins.2008.10.012","article-title":"Using the fuzzy multi-criteria decision-making approach for measuring the possibility of successful knowledge management","volume":"179","author":"Chang","year":"2009","journal-title":"Inf. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/8\/156\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:42:23Z","timestamp":1760208143000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/8\/156"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,15]]},"references-count":48,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2017,8]]}},"alternative-id":["sym9080156"],"URL":"https:\/\/doi.org\/10.3390\/sym9080156","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2017,8,15]]}}}