Affiliations: School of Knowledge Science, Japan Advanced Institute
of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan.
E-mail: huynh@jaist.ac.jp; nakamori@jaist.ac.jp | Graduate School of Information Science and Technology,
Hokkaido University Kita 14, Nishi 9, Kita-ku, Sapporo 060-0814, Japan.
E-mail: murahiko@main.eng.hokudai.ac.jp
Abstract: It is well known that algebraization has been successfully applied
to classical and nonclassical logics (Rasiowa and Sikorski, 1968). Following
this direction, an ordered-based approach to the problem of finding out a tool
to describe algebraic semantics of Zadeh's fuzzy logic has been
introduced and developed by Nguyen Cat-Ho and colleagues during the last
decades. In this line of research, RH algebra has been introduced in [20] as a
unified algebraic approach to the natural structure of linguistic domains of
linguistic variables. It was shown that every RH algebra of a linguistic
variable with a chain of the primary terms is a distributive lattice. In this
paper we will examine algebraic structures of RH algebras corresponding to
linguistic domains having exactly two distinct primary terms, one being an
antonym of the other, called symmetrical RH algebras. Computational results for
the relatively pseudo-complement operation in these algebras will be given.
Keywords: Linguistic reasoning, fuzzy logic, linguistic variable, hedge algebra, RH-algebra, distributive lattice
