International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Storage Operators and Multiplicative Quantifiers in Many-valued Logics
Journal of Logic and Computation
A comprehensive theory of trichotomous evaluative linguistic expressions
Fuzzy Sets and Systems
On expansions of WNM t-norm based logics with truth-constants
Fuzzy Sets and Systems
Derivation digraphs for dependencies in ordinal and similarity-based data
Information Sciences: an International Journal
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The starting point of this paper are the works of Hajek and Vychodil on the axiomatization of truth-stressing and-depressing hedges as expansions of Hajek's BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the expansions over Godel logic. We propose weaker axiomatizations over an arbitrary core fuzzy logic which have two main advantages: (i) they preserve the standard completeness properties of the original logic and (ii) any subdiagonal (resp. superdiagonal) non-decreasing function on [0,1] preserving 0 and 1 is a sound interpretation of the truth-stresser (resp. depresser) connectives. Hence, these logics accommodate most of the truth hedge functions used in the literature about of fuzzy logic in a broader sense.