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To this end, the concept of order of the states of a complete residuated lattice-valued tree automaton (simply\u00a0<jats:italic>L<\/jats:italic>-valued tree automaton) is introduced along with several equivalence relations in the set of the states of an <jats:italic>L<\/jats:italic>-valued tree automaton. We obtain two main results from this study: one of the relations can lead to the creation of Kleene\u2019s theorem for <jats:italic>L<\/jats:italic>-valued tree automata, and the other one leads to the creation of a minimal v-valued tree automaton that accepts the same language as the given one.<\/jats:p>","DOI":"10.1051\/ita\/2018004","type":"journal-article","created":{"date-parts":[[2018,7,11]],"date-time":"2018-07-11T11:50:22Z","timestamp":1531309822000},"page":"23-42","source":"Crossref","is-referenced-by-count":7,"title":["State hyperstructures of tree automata based on lattice-valued logic"],"prefix":"10.1051","volume":"52","author":[{"given":"Maryam","family":"Ghorani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2018,7,11]]},"reference":[{"key":"R1","first-page":"155","volume":"8","author":"Ameri","year":"1997","journal-title":"Pure Math. 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