{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T02:13:26Z","timestamp":1780539206991,"version":"3.54.1"},"reference-count":51,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,14]],"date-time":"2023-04-14T00:00:00Z","timestamp":1681430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Outstanding Member of Youth Innovation Promotion Association of Chinese Academy of Sciences","award":["Y2022052"],"award-info":[{"award-number":["Y2022052"]}]},{"name":"Outstanding Member of Youth Innovation Promotion Association of Chinese Academy of Sciences","award":["62131019"],"award-info":[{"award-number":["62131019"]}]},{"name":"Key projects of National Natural Science Foundation of China","award":["Y2022052"],"award-info":[{"award-number":["Y2022052"]}]},{"name":"Key projects of National Natural Science Foundation of China","award":["62131019"],"award-info":[{"award-number":["62131019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov\u2013Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS.<\/jats:p>","DOI":"10.3390\/axioms12040376","type":"journal-article","created":{"date-parts":[[2023,4,14]],"date-time":"2023-04-14T10:29:16Z","timestamp":1681468156000},"page":"376","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Distance Measures Based on Metric Information Matrix for Atanassov\u2019s Intuitionistic Fuzzy Sets"],"prefix":"10.3390","volume":"12","author":[{"given":"Wenjuan","family":"Ren","sequence":"first","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhanpeng","family":"Yang","sequence":"additional","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xipeng","family":"Li","sequence":"additional","affiliation":[{"name":"Systems Engineering Institute, Academy of Military Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. 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