{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T09:52:35Z","timestamp":1770025955593,"version":"3.49.0"},"reference-count":12,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,12,16]]},"abstract":"<jats:p>This paper investigates minimal solutions of fuzzy relation inequalities with addition-min composition. It first shows the conditions that an element is a minimal solution of the inequalities, and presents the conditions that the inequalities have a unique minimal solution. It then proves that every solution of the inequalities has a minimal one and proposes an algorithm to searching for a minimal solution with computational complexity O\u00a0(n2) where n is the number of unknown variables of the inequalities. This paper finally describes all minimal solutions of the inequalities.<\/jats:p>","DOI":"10.3233\/jifs-202590","type":"journal-article","created":{"date-parts":[[2021,10,15]],"date-time":"2021-10-15T18:29:51Z","timestamp":1634322591000},"page":"6089-6095","source":"Crossref","is-referenced-by-count":3,"title":["Minimal solutions of fuzzy relation inequalities with addition-min composition1"],"prefix":"10.1177","volume":"41","author":[{"given":"Xiao","family":"Mi","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, People\u2019s Republic of China"}]},{"given":"Xue-ping","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, People\u2019s Republic of China"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-202590_ref1","first-page":"177","article-title":"Properties of fuzzy relation inequalities with addition-min composition","volume":"646","author":"Cao","year":"2018","journal-title":"Fuzzy Information and Engineering and Decision (B. 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