EQ-algebras: primary concepts and properties
نویسنده
چکیده
In this paper, we introduce a special algebra called EQ-algebra which has three binary operations (meet, product, fuzzy equality) and a top element. The fuzzy equality is reflexive, symmetric and transitive with respect to the product. EQ-algebra is a natural algebra proposed as an algebra of truth values on the basis of which the fuzzy type theory (a higher-order fuzzy logic) should be developed. Till now, truth values in fuzzy type theory are supposed to form a special residuated lattice. However, since fuzzy equality is a derived operation in residuated lattice, it is not so natural for fuzzy type theory as the EQ-algebra.
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