Abstract
In accordance with Tarski point of view, in this chapter the theory of closure operators is proposed as a unifying tool for fuzzy logics. Indeed, let F be the set of formulas of a given language. Then an abstract fuzzy logic is defined by a fuzzy semantics (i.e. a class of valuations of the formulas in F) and by a closure operator in the lattice of the fuzzy subsets of F (we call deduction operator). One proves that Pavelka’s logic, similarity logic and graded consequence theory can be represented in this way.
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Biacino, L., Gerla, G. (1999). Closure Operators in Fuzzy Set Theory. In: Bezdek, J.C., Dubois, D., Prade, H. (eds) Fuzzy Sets in Approximate Reasoning and Information Systems. The Handbooks of Fuzzy Sets Series, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5243-7_4
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DOI: https://doi.org/10.1007/978-1-4615-5243-7_4
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