{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:47:39Z","timestamp":1761709659308,"version":"build-2065373602"},"reference-count":65,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T00:00:00Z","timestamp":1579132800000},"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":["Grant No.61372187"],"award-info":[{"award-number":["Grant No.61372187"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific and technological project of Sichuan Province","award":["No.2019YFG0100"],"award-info":[{"award-number":["No.2019YFG0100"]}]},{"DOI":"10.13039\/501100010250","name":"Sichuan Province Youth Science and Technology Innovation Team","doi-asserted-by":"publisher","award":["No.2019JDTD0015"],"award-info":[{"award-number":["No.2019JDTD0015"]}],"id":[{"id":"10.13039\/501100010250","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Application Basic Research Plan Project of Sichuan Province","award":["No.2017JY0199"],"award-info":[{"award-number":["No.2017JY0199"]}]},{"name":"Scientific Research Project of Department of Education of Sichuan Province","award":["No.18ZA0273,15TD0027"],"award-info":[{"award-number":["No.18ZA0273,15TD0027"]}]},{"name":"Innovative Research Team of Nei jiang Normal University","award":["No.18TD08"],"award-info":[{"award-number":["No.18TD08"]}]},{"name":"Xi Hua Cup University Students Innovation and Entrepreneurship Project","award":["No.2019134"],"award-info":[{"award-number":["No.2019134"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Linguistic Pythagorean fuzzy (LPF) set is an efficacious technique to comprehensively represent uncertain assessment information by combining the Pythagorean fuzzy numbers and linguistic variables. In this paper, we define several novel essential operations of LPF numbers based upon Einstein operations and discuss several relations between these operations. For solving the LPF numbers fusion problem, several LPF aggregation operators, including LPF Einstein weighted averaging (LPFEWA) operator, LPF Einstein weighted geometric (LPFEWG) operator and LPF Einstein hybrid operator, are propounded; the prominent characteristics of these operators are investigated as well. Furthermore, a multi-attribute group decision making (MAGDM) approach is presented on the basis of the developed operators under an LPF environment. Ultimately, two application cases are utilized to demonstrate the practicality and feasibility of the developed decision approach and the comparison analysis is provided to manifest the merits of it.<\/jats:p>","DOI":"10.3390\/info11010046","type":"journal-article","created":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:14:41Z","timestamp":1579234481000},"page":"46","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Linguistic Pythagorean Einstein Operators and Their Application to Decision Making"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7576-5276","authenticated-orcid":false,"given":"Yuan","family":"Rong","sequence":"first","affiliation":[{"name":"School of Science, Xi Hua University, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Pei","sequence":"additional","affiliation":[{"name":"School of Science, Xi Hua University, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5304-235X","authenticated-orcid":false,"given":"Yi","family":"Liu","sequence":"additional","affiliation":[{"name":"Data Recovery Key Laboratory of Sichuan Province, School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641000, China"},{"name":"Numerical Simulation Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang 641000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.inffus.2018.01.013","article-title":"FLM-TOPSIS: The fuzzy linguistic multiset TOPSIS method and its application in linguistic decision making","volume":"45","author":"Pei","year":"2019","journal-title":"Inf. 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