ON A NEW CLASS OF IMPLICATIONS: (g,min)-IMPLICATIONS AND SEVERAL CLASSICAL TAUTOLOGIES
2012 ◽
Vol 20
(01)
◽
pp. 1-20
◽
Keyword(s):
A new class of fuzzy implications, called (g, min )-implications, is introduced by means of the additive generators of continuous Archimedean t-conorms, called g-generators. Basic properties of these implications are discussed. It is shown that the (g, min )-implications are really a new class different from the known ( S , N )-, R -, QL - and Yager's f- and g-implications. Generalizations of three classical logic tautologies with implications, viz. law of importation, contraction law and distributivity over triangular norms ( t -norms) and triangular conorms ( t -conorms) are investigated. A series of necessary and sufficient conditions are proposed, under which the corresponding functional equations are satisfied.
2020 ◽
Vol 491
(2)
◽
pp. 124399
2010 ◽
Vol 1
(3)
◽
pp. 17-30
1981 ◽
Vol 91
(1-2)
◽
pp. 135-145
2009 ◽
Vol 2009
◽
pp. 1-8
◽
2020 ◽
Vol 25
(5)
◽
2011 ◽
Vol 59
(4)
◽
pp. 575-579
◽
2002 ◽
Vol 29
(7)
◽
pp. 417-425
◽
2021 ◽
Vol 26
(1)
◽
pp. 31-39