{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T10:23:54Z","timestamp":1774952634838,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,18]],"date-time":"2018-05-18T00:00:00Z","timestamp":1526601600000},"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":["71532002"],"award-info":[{"award-number":["71532002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61702023"],"award-info":[{"award-number":["61702023"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Fund for Humanities and Social Sciences of Beijing Jiaotong University","award":["2016JBZD01"],"award-info":[{"award-number":["2016JBZD01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The proposed q-rung orthopair fuzzy set (q-ROFS) and picture fuzzy set (PIFS) are two powerful tools for depicting fuzziness and uncertainty. This paper proposes a new tool, called q-rung picture linguistic set (q-RPLS) to deal with vagueness and impreciseness in multi-attribute group decision-making (MAGDM). The proposed q-RPLS takes full advantages of q-ROFS and PIFS and reflects decision-makers\u2019 quantitative and qualitative assessments. To effectively aggregate q-rung picture linguistic information, we extend the classic Heronian mean (HM) to q-RPLSs and propose a family of q-rung picture linguistic Heronian mean operators, such as the q-rung picture linguistic Heronian mean (q-RPLHM) operator, the q-rung picture linguistic weighted Heronian mean (q-RPLWHM) operator, the q-rung picture linguistic geometric Heronian mean (q-RPLGHM) operator, and the q-rung picture linguistic weighted geometric Heronian mean (q-RPLWGHM) operator. The prominent advantage of the proposed operators is that the interrelationship between q-rung picture linguistic numbers (q-RPLNs) can be considered. Further, we put forward a novel approach to MAGDM based on the proposed operators. We also provide a numerical example to demonstrate the validity and superiorities of the proposed method.<\/jats:p>","DOI":"10.3390\/sym10050172","type":"journal-article","created":{"date-parts":[[2018,5,21]],"date-time":"2018-05-21T04:07:30Z","timestamp":1526875650000},"page":"172","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":117,"title":["A Novel Approach to Multi-Attribute Group Decision-Making with q-Rung Picture Linguistic Information"],"prefix":"10.3390","volume":"10","author":[{"given":"Li","family":"Li","sequence":"first","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0246-5058","authenticated-orcid":false,"given":"Runtong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7522-8593","authenticated-orcid":false,"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7872-5744","authenticated-orcid":false,"given":"Xiaopu","family":"Shang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Kaiyuan","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1142\/S021962201830001X","article-title":"Decision making methods based on fuzzy aggregation operators: Three decades review from 1986 to 2017","volume":"17","author":"Mardani","year":"2018","journal-title":"Int. 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