2024-03-28T19:07:50Zhttp://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/1611572020-12-10T16:17:19Zcom_10261_60com_10261_4col_10261_313
2018-02-21T17:38:15Z
urn:hdl:10261/161157
On the scope of some formulas defining additive connectives in fuzzy logics
García-Cerdaña, Àngel
Noguera, Carles
Esteva, Francesc
Comisión Interministerial de Ciencia y Tecnología, CICYT (España)
Generalitat de Catalunya
Residuated lattices
Residuated fuzzy many-valued logics
Negation functions
Non-classical logics
NM-algebras
Nilpotent minimum t-norm
MTL-algebras
Additive connectives
Left-continuous t-norms
Involutive left-continuous t-norms, IMTL-algebras
In (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.
2018-02-21T17:38:15Z
2018-02-21T17:38:15Z
2005
2018-02-21T17:38:15Z
artículo
Fuzzy Sets and Systems 154: 56- 75 (2005)
http://hdl.handle.net/10261/161157
10.1016/j.fss.2005.01.004
http://dx.doi.org/10.13039/501100007273
http://dx.doi.org/10.13039/501100002809
eng
Sí
closedAccess
Elsevier