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Syst."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>With the development of social and economic research, the judgements that people deal with are full of fuzziness and vagueness. It is convenient to use the linguistic q-rung orthopair fuzzy numbers to offer the qualitative uncertain information. Consequently, in this paper, we mainly study linguistic q-rung orthopair fuzzy preference relations (Lq-ROFPRs) and apply them to a multi-criteria decision-making (MCDM) problem. The multiplicative consistency of Lq-ROFPRs is first introduced, then a consistency-based model is established to derive the normalized linguistic q-rung orthopair fuzzy priority weight vector. The concept of acceptably multiplicative consistency is further defined, and an optimization model is formulated to repair the unacceptably multiplicative consistent Lq-ROFPR. To cope with the incomplete Lq-ROFPR, another programming model is built to ascertain the missing values. The weights of criteria are determined by constructing a possibility degree matrix. Subsequently, an MCDM problem with incomplete Lq-ROFPRs is considered and a step-by-step algorithm is put forward. Finally, the proposed method is applied to three examples, and the advantages of this new approach are also demonstrated.<\/jats:p>","DOI":"10.1007\/s40747-022-00961-w","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T05:02:45Z","timestamp":1673931765000},"page":"4483-4501","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Incomplete linguistic q-rung orthopair fuzzy preference relations and their application to multi-criteria decision making"],"prefix":"10.1007","volume":"9","author":[{"given":"Tao","family":"Li","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5458-8928","authenticated-orcid":false,"given":"Liyuan","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Zhenglong","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,1,17]]},"reference":[{"key":"961_CR1","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1007\/s13042-017-0637-0","volume":"9","author":"YJ Xu","year":"2018","unstructured":"Xu YJ, Liu X, Wang HM (2018) The additive consistency measure of fuzzy reciprocal preference relations. 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