کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
390742 661298 2009 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
EQ-algebras
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
EQ-algebras
چکیده انگلیسی

We introduce a new class of algebras called EQ-algebras. An EQ-algebra has three basic binary operations (meet, multiplication and a fuzzy equality) and a top element. These algebras are intended to become algebras of truth values for a higher-order fuzzy logic (a fuzzy type theory, FTT). The motivation stems from the fact that until now, the truth values in FTT were assumed to form either an IMTL-, BL-, or MV-algebra, all of them being special kinds of residuated lattices in which the basic operations are the monoidal operation (multiplication) and its residuum. The latter is a natural interpretation of implication in fuzzy logic; the equivalence is then interpreted by the biresiduum, a derived operation. The basic connective in FTT, however, is a fuzzy equality and, therefore, it is not natural to interpret it by a derived operation. This defect is expected to be removed by the class of EQ-algebras introduced and studied in this paper. From the algebraic point of view, the class of EQ-algebras generalizes, in a certain sense, the class of residuated lattices and so, they may become an interesting class of algebraic structures as such.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Fuzzy Sets and Systems - Volume 160, Issue 20, 16 October 2009, Pages 2956-2978