More On Anti-Inverse Semigroups
Nous donnons une caractérisation complète de tous les morphismes binaires qui préservent les mots sturmiens et montrons que les mots infinis engendrés par ces morphismes sont rigides.
∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.The basic concepts are M -hyperidentities, where M is a monoid of hypersubstitutions. The set of all M -solid varieties of semigroups forms a complete sublattice of the lattice of all varieties of semigroups. We fix some specific varieties V of commutative semigroups and study the set of all M -solid subvarieties of V , in particular, if V is nilpotent.
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.
Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are...
Based on the results of generalized additions, multiplications and differences proven in Part I and II of this paper a framework for a general integral is presented. Moreover it is shown that many results of the literature are contained as special cases in our results.