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On the scope of some formulas defining additive connectives in fuzzy logics

AuthorsGarcía-Cerdaña, Àngel CSIC ORCID ; Noguera, Carles CSIC ORCID; Esteva, Francesc CSIC ORCID
KeywordsResiduated lattices
Residuated fuzzy many-valued logics
Negation functions
Non-classical logics
Nilpotent minimum t-norm
Additive connectives
Left-continuous t-norms
Involutive left-continuous t-norms, IMTL-algebras
Issue Date2005
CitationFuzzy Sets and Systems 154: 56- 75 (2005)
AbstractIn (Fuzzy Sets and Systems 149 (2005) 297) Wang et al. 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 in (Beyond Two: Theory and Applications of Multiple-Valued Logic, 2003, 251.), and we obtain some families of logics presented in a simpler language. Finally, we discuss the standard completeness of these new logics. © 2005 Elsevier B.V. All rights reserved.
Identifiersdoi: 10.1016/j.fss.2005.01.004
issn: 0165-0114
Appears in Collections:(IIIA) Artículos
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