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Erschienen in:
01.11.2014 | Methodologies and Application
A unified algorithm for finding \(k\)-IESFs in linguistic truth-valued lattice-valued propositional logic
Erschienen in: Soft Computing | Ausgabe 11/2014
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Abstract
As a symbolic approach for computing with words, linguistic truth-valued lattice-valued propositional logic \(\fancyscript{L}_{V(n\times 2)}P(X)\) can represent and handle both imprecise and incomparable linguistic value-based information. Indecomposable extremely simple form (IESF) is a basic concept of \(\alpha \)-resolution automated reasoning in lattice-valued logic based in lattice implication algebra (LIA). In this paper we establish a unified method for finding the structure of \(k\)-IESF in \(\fancyscript{L}_{V(n\times 2)}P(X)\). Firstly, some operational properties of logical formulae in \(L_6P(X)\) are studied, and some rules are obtained for judging whether a given logical formula is a \(k\)-IESF, which are used to contrive an algorithm for finding \(k\)-IESF in \(L_6P(X)\). Then, all the results are extended into \(\fancyscript{L}_{V(n\times 2)}P(X)\). Finally, a unified algorithm for finding all \(k\)-IESFs in \(\fancyscript{L}_{V(n\times 2)}P(X)\) is proposed. This work provides theoretical foundations and algorithms for \(\alpha \)-resolution automated reasoning in linguistic truth-valued lattice-valued logic based in linguistic truth-valued LIAs and formal tools for symbolic natural language processing.