Fuzzy \(\mathcal I\)-ideals in \(I\)-algebras (Q2706525)

BCI-semigroups or IS-algebras are ``ringlike'' in that a semigroup multiplication \(\bullet\) is distributive over a BCI-algebra operation \(*\) acting in lieu of the usual addition operation \(+\) for abelian groups. Not only can one investigate such IS-algebras along the lines of ring-theory, including a theory of ideals and homomorphisms as the authors have already done, but one may also pursue this approach into the realm of fuzzy algebra where ideals (or I-ideals) become fuzzy I-ideals while the behavior of these under the standard mappings such as homomorphisms is then automatically of interest. In this ever widening realm one may find a variety of wanderers, immigrants and inhabitants of long standing bringing a plentitude of expertise to the subject. In this case too the authors represent these types and over the time the development of this branch of the (fuzzy) algebra tree will also be useful to other algebraists looking for interesting examples of structures not yet well-known to everyone.