The aim of this paper is to construct the new fundamental theorem of UP-algebras in the meaning of the congruence determined by a UP-homomorphism. We also give an application of the theorem to the first, second, and third UP-isomorphism theorems in UP-algebras.
In this paper, we introduce ten types of fuzzy soft sets over fully UP-semigroups, and investigate the algebraic properties of fuzzy soft sets under the operations of (extended) intersection and (restricted) union.Further, we discuss the relation between some conditions of fuzzy soft sets and fuzzy soft UP$\mathrm{_{s}}$-subalgebras (resp., fuzzy soft UP$\mathrm{_{i}}$-subalgebras, fuzzy soft near UP$\mathrm{_{s}}$-filters, fuzzy soft near UP$\mathrm{_{i}}$-filters, fuzzy soft UP$\mathrm{_{s}}$-filters, fuzzy soft UP$\mathrm{_{i}}$-filters, fuzzy soft UP$\mathrm{_{s}}$-ideals, fuzzy soft UP$\mathrm{_{i}}$-ideals, fuzzy soft strongly UP$\mathrm{_{s}}$-ideals, fuzzy soft strongly UP$\mathrm{_{i}}$-ideals) of fully UP-semigroups.
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