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• W2934337119 abstract "In this paper, we mainly study multilattices on the set of finite nonempty subsets of [0,1] under different orders. Firstly, the relationships among orders ≤ 1, ≤ 2 and ≤ * are discussed. It is shown that the order ≤ * is contained in the orders ≤ 1 and ≤ 2, but the converse is not true, and that there is no inclusion between the orders ≤ 1 and ≤ 2. The lattice and multilattice structures of the set of finite nonempty subsets of [0,1] under ≤ 1 and ≤ * are studied, respectively. It is proved that the set of finite nonempty subsets of [0,1] is neither a lattice nor a multilattice with respect to the order ≤ *, and is not a multilattice with respect to the order ≤ 1. Finally, we extend order ≤ * to the set V([0, 1]) of finite vectors of [0,1] and develop a new order ⪯. It is verified that the quotient set V([0, 1])/ ≡ under the order ⪯ is not a lattice, but is a multilattice. Moreover, we give a method to construct maximal elements and minimal elements for finite vectors of [0,1] with respect to the order ⪯. The results will provide an application of hesitant fuzzy sets in rough sets, information fusion, fuzzy automata, fuzzy transitive systems, etc." @default.
• W2934337119 created "2019-04-11" @default.
• W2934337119 creator A5017773158 @default.
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• W2934337119 date "2019-07-01" @default.
• W2934337119 modified "2023-10-18" @default.
• W2934337119 title "Multilattices on typical hesitant fuzzy sets" @default.
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• W2934337119 doi "https://doi.org/10.1016/j.ins.2019.03.078" @default.
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