Homomorphisms on the monoid of fuzzy implications (II, *) - A complete characterization

Abstract

In [4], we had proposed a novel generating methods of fuzzy implications and investigated algebraic structures on the set of all fuzzy implications, which is denoted by II. Again in [5], we had defined a particular function gK on the monoid (II, *) (See Def. 16) and characterised the function K for which gK is a semigroup homomorphism (s.g.h) in two special cases, i.e., K is with trivial range and K (1, y ) = y for all y ∈ [0, 1](neutrality property). In this work we characterise the nontrivial range non neutral implications K such that gK is an s.g.h. and also present their representations. © Springer-Verlag 2013.