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An algebraic foundation for linguistic reasoning. (English) Zbl 1118.03062

Summary: It is well known that algebraization has been successfully applied to classical and nonclassical logics (Rasiowa and Sikorski, 1968). Following this direction, an order-based approach to the problem of finding 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 [C. H. Nguyen and V. N. Huynh, Fuzzy Sets Syst. 129, No. 2, 229–254 (2002; Zbl 1001.03023)] 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 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 is given.

MSC:

03G25 Other algebras related to logic
03B52 Fuzzy logic; logic of vagueness
68T37 Reasoning under uncertainty in the context of artificial intelligence

Citations:

Zbl 1001.03023
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