In this paper, two classes of generalized (U, N)-implications derived from commutative semi-uninorms and pseudo-uninorms are investigated. Then some properties of UI,N operations derived from implications are explored. Last the necessary and sufficient conditions such that a (UCS, N)-operation (or (UP, N)-operation) is an implication are given out.
BalasubramaniamJRaoCJM2002R-Implication operators and rule reduction in Mamdani-type fuzzy ststemsProc 6th Joint Conf on Information Sciences, Fuzzy Theory and Technology8284Durham, USA
4.
DuboisDPradeH1991Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributionsFuzzy Sets and Systems40143202
5.
FodorJRoubensM1994Fuzzy Preference Modelling and Multicriteria Decision SupportKluwerDordrecht
6.
GottwaldS2001A Treatise on Many-Valued LogicsResearch Studies PressBaldock
7.
MasMMonserratMTorrensJ2010A characterization of (U,N), RU, QL and D-implications derived from uninorms satisfying the law of importationFuzzy Sets and Systems16113691387
8.
SmetsPMagrezP1987Implication in fuzzy logicInternational Journal of Approximate Reasoning1327347
9.
TrillasEValverdeL1985On implication and indistinguishability in the setting of fuzzy logicManagement Decision Support Systems using Fuzzy Sets and Possibility TheoryKacprzykJYagerRR198212TüV-RhinelandCologne
10.
BalasubramaniamJJagan Mohan RaoC2004On the distributivity of implication operators over T- and S-normsIEEE Trans on Fuzzy and Systems12194198
11.
BaczyńskiMJayaramB2007On the characterizations of (S,N)– implicationsFuzzy Sets and Systems15817131727
12.
BustinceHFernandezJPraderaABeliakovG2011On (TS,N)-fuzzy implications6th International Summer School on Aggregation Operators (AGOP 2011)De BaetsBMesiarRTroianoL9398Benevento, Italy
13.
AguilóICarbonellMSuñerJTorrensJ2010Dual Representable Aggregation Functions and Their Derived SImplications, In: IPMU 2010, LNCSHüllermeierEKruseRHoffmannF6178408417SpringerHeidelberg
14.
OuyangY2012On fuzzy implications determined by aggregation operatorsInformation Sciences193153162
15.
BaczyńskiMJayaramB2009(U,N)– implications and their chatacterizationsFuzzy Sets and Systems16020492062
16.
BaczyńskiMJayaramB2008(S,N)- and R-implications: A stateof-the-art surveyFuzzy Sets and Systems15918361859
17.
BaczyńskiMJayaramB2011Intersections between some families of (U,N)- and RU-implicationsFuzzy Sets and Systems1673044
18.
De BaetsB1997Coimplicators, the forgotten connectivesTatra Mountains Math. Publ.12229240
19.
DeschrijverGKerreEE2004Uninorms in L*-fuzzy set theoryFuzzy Sets and Systems148243262
20.
WangZhudengFangJin-xuan2009Residual operations of left and right uninorms on a complete latticeFuzzy Sets and Systems1602231
21.
SuYongWangZhudeng2013Pseudo-uninorms and coimplications on a complete latticeFuzzy Sets and Systems2245362
22.
SuYongLiuHua-wen2015Characterizations of residual coimplications of pseudo-uninorms onacomplete latticeFuzzy Sets and Systems2614459
23.
FodorJKeresztfalviT1995Nonstandard conjunctions and implications in fuzzy logicInternational Journal of Approximate Reasoning126984
24.
LiuHua-wen2012Semi-uninorms and implications on a complete latticeFuzzy Sets and Systems1917282
25.
Suárez GarciaFGil ÁlvarezP1986Two families of fuzzy integralsFuzzy Sets and Systems186781
26.
BassanBSpizzichinoF2005Relations among univariate aging bivariate aging and dependence for exchange able lifetimesJ. Multivar. Anal.93313339
27.
DuranteFKlementEMesiarR2007Conjunctors and the irresidual implicators: Characterizations and construct methodsMediterr. J. Math.4343356
28.
DuranteFSempiC2005SemicopulaeKybernetika41315328
29.
ShiYVan GasseaBRuanaDKerreaEE2010On dependencies and independencies of fuzzy implication axiomsFuzzy Sets and Systems16113881405
30.
FodorJ1993A new look at fuzzy connectivesFuzzy Sets and Systems57141148
31.
JeneiS1998Geometry of left-continuous-norms with strong induced negationsBelg. J. Oper. Res. Statist. Comput. Sci.38516
