The variety of biresiduated algebras including the structures of D-algebra and MV-algebra was introduced together with a corresponding logical system. A many-valued space over a biresiduated algebra is a set equipped with an equivalence function and a distance function such that these functions are complementary. A cartesian closed category of many-valued spaces is presented.
Fuzzy set, MY-algebra, Heyting algebra, Brouwer algebra, D-algebra, residuated lattice, biresiduated algebra, equivalence function, distance function, category.
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