On the scope of some formulas defining additive connectives in fuzzy logics. (English) Zbl 1074.03010
Summary: In Fuzzy Sets Syst. 149, 297–307 (2005; Zbl 1060.03043), S. Wang, B. Wang and D. Pei defined a new fuzzy logic called NMG. They also introduced new formulas to define the additive connectives from multiplicative conjunction, residuated implication and bottom in NMG. However, they did not study the scope of these formulas in the general framework of fuzzy logics. This is the aim of this paper. Therefore, we add the definability formulas to known fuzzy logics as new axioms, following the method used by F. Esteva, L. Godo and À. García-Cerdaña [in: M. Fitting et al. (eds.), Beyond two: Theory and applications of multiple-valued logic. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 114, 251–272 (2003; Zbl 1038.03026)], and we obtain some families of logics presented in a simpler language. Finally, we discuss the standard completeness of these new logics.
MSC:
| 03B52 | Fuzzy logic; logic of vagueness |
Keywords:
Additive connectives; Involutive left-continuous t-norms; IMTL-algebras; MTL-algebras; Nilpotent minimum t-norm; NM-algebras; Negation functions; Residuated lattices; Residuated fuzzy many-valued logicsReferences:
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