{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T03:41:26Z","timestamp":1782963686669,"version":"3.54.5"},"reference-count":44,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,8]],"date-time":"2022-11-08T00:00:00Z","timestamp":1667865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Project of Science and Technology in Guangzhou in China","award":["202102020948"],"award-info":[{"award-number":["202102020948"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In recent years, Dempster\u2013Shafer (D\u2013S) theory has been widely used in multi-criteria decision-making (MCDM) problems due to its excellent performance in dealing with discrete ambiguous decision alternative (DA) evaluations. In the general framework of D\u2013S-theory-based MCDM problems, the preference of the DAs for each criterion is regarded as a mass function over the set of DAs based on subjective evaluations. Moreover, the multi-criteria preference aggregation is based on Dempster\u2019s combination rule. Unfortunately, this an idea faces two difficulties in real-world applications: (i) D\u2013S theory can only deal with discrete uncertain evaluations, but is powerless in the face of continuous uncertain evaluations. (ii) The generation of the mass function for each criterion relies on the empirical judgments of experts, making it time-consuming and laborious in terms of the MCDM problem for large-scale DAs. To the best of our knowledge, these two difficulties cannot be addressed with existing D\u2013S-theory-based MCDM methods. To this end, this paper proposes a clustering MCDM method combining D\u2013S theory with the analytic hierarchy process (AHP) and the Silhouette coefficient. By employing the probability distribution and the D\u2013S theory to represent discrete and continuous ambiguous evaluations, respectively, determining the focal element set for the mass function of each criterion through the clustering method, assigning the mass values of each criterion through the AHP method, and aggregating preferences according to Dempster\u2019s combination rule, we show that our method can indeed address these two difficulties in MCDM problems. Finally, an example is given and comparative analyses with related methods are conducted to illustrate our method\u2019s rationality, effectiveness, and efficiency.<\/jats:p>","DOI":"10.3390\/e24111621","type":"journal-article","created":{"date-parts":[[2022,11,8]],"date-time":"2022-11-08T07:00:42Z","timestamp":1667890842000},"page":"1621","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Clustering Multi-Criteria Decision-Making Method for Large-Scale Discrete and Continuous Uncertain Evaluation"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9829-5948","authenticated-orcid":false,"given":"Siyuan","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science, South China Normal University, Guangzhou 510631, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjun","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Computer Science, South China Normal University, Guangzhou 510631, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jieyu","family":"Zhan","sequence":"additional","affiliation":[{"name":"School of Computer Science, South China Normal University, Guangzhou 510631, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,8]]},"reference":[{"key":"ref_1","first-page":"e140555","article-title":"Comparative analysis of multi-criteria decision making methods for the assessment of optimal SVC location","volume":"70","author":"Aydin","year":"2022","journal-title":"Bull. 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