Abstract:

BR₀-distributivity has an important position in the structure of BR0algebras which says a→b∨c=(a→b)∨(a→c). It is proved that  residuated lattices with BR0-distributivity also have good properties.  BR₀-distributivity is introduced in residuated lattices, and its equivalent form is given. Then the BR0-distributivity is generalized in complete residuated lattices, and  BR₀-first infinite distributivity and BR₀-second infinite distributivity are obtained. Finally, the properties and relationship between two kinds of BR₀-infinite distributivity are  discussed in regular complete residuated lattices and the unite interval ［0,1］, respectively.

Key words: fuzzy logic; residuated lattice; BR₀-algebras; BR₀-distributivity; infinite distributivit