EQ-algebras from the point of view of generalized algebras with fuzzy equalities

Authors:
Zhen Ming Ma;Bao Qing Hu
Affiliations:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China and School of Science, Linyi University, Linyi 276005, PR China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China
Venue:
Fuzzy Sets and Systems
Year:
2014

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Abstract

EQ-algebras introduced by Novak are algebras of truth values for a higher-order fuzzy logic (fuzzy type theory). In this paper, the compatibility of multiplication w.r.t. the fuzzy equality in an arbitrary EQ-algebra is examined. Particularly, an example indicates that the compatibility axiom does not always hold, and then a class of EQ-algebras satisfying the compatibility axiom is characterized by introducing a residuated integral-meet-semilattice-ordered-monoid-valued fuzzy algebra called a generalized algebra with a fuzzy equality.