An Algebraic Foundation for Linguistic Reasoning

It is well known that algebraization has been successfully applied to classical and non-classical 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.