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First, we establish the equivalence of (nondeterministic) lattice multiset finite automata (LMA) and deterministic lattice multiset finite automata (DLMA). Furthermore, we present some operations on lattice-valued regular multiset languages, and prove that the family of lattice-valued regular multiset languages is closed under this operations. We also introduce and study the minimal DLMAs and present an effective algorithm to obtain a minimal DLMA for a given LMA. Finally, we give a decomposition of lattice-valued regular multiset language by some simple lattice-valued regular multiset languages accepted by some special minimal DLMAs.<\/jats:p>","DOI":"10.3233\/jifs-161382","type":"journal-article","created":{"date-parts":[[2018,7,31]],"date-time":"2018-07-31T17:17:00Z","timestamp":1533057420000},"page":"627-637","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":15,"title":["Minimization of lattice multiset finite automata"],"prefix":"10.1177","volume":"35","author":[{"given":"Yongbing","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mathematics and Computation, Anqing Normal University, Anqing, China"},{"name":"College of Computer Science, Shaanxi Normal University, Xi\u2019an, China"}]},{"given":"Yongming","family":"Li","sequence":"additional","affiliation":[{"name":"College of Computer Science, Shaanxi Normal University, Xi\u2019an, China"}]}],"member":"179","published-online":{"date-parts":[[2018,7,27]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"36","article-title":"Multiset theory","volume":"30","author":"Blizard W.D.","year":"1989","unstructured":"BlizardW.D., Multiset theory, Notre Dame Journal of Formal Logic 30 (1989), 36\u201366.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45523-X_4"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054106003723"},{"key":"e_1_3_2_5_2","doi-asserted-by":"crossref","unstructured":"ChiswellI. 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