Lower subsets of an ordered semigroup form in a natural way an ordered semigroup. This lower set operator gives an analogue of the power operator already studied in semigroup theory. We present a complete description of the lower set operator applied to varieties of ordered semigroups. We also obtain large families of fixed points for this operator applied to pseudovarieties of ordered semigrou...

In this paper, we introduced the concepts of roughness and fuzziness in ordered ternary semigroups. We proved that the lower and upper approximation of an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal) in an ordered ternary semigroup is an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal)....

We generalize recent results by G.A. Freiman, M. Herzog and coauthors on the structure theory of product-sets from the context of linearly (i.e., strictly and totally) ordered groups to linearly ordered semigroups. In particular, we find that if S is a finite subset of a linearly ordered semigroup generating a nonabelian subsemigroup, then |S2| ≥ 3 |S| − 2. On the road to this goal, we also pro...

In this paper, we apply the concept of fuzzy soft sets to ordered semigroup theory. The concepts of (∈γ ,∈γ ∨qδ)-fuzzy left (right) ideals, (∈γ ,∈γ ∨qδ)-fuzzy biideals and (∈γ ,∈γ ∨qδ)-fuzzy quasi-ideals are introduced and some related properties are obtained. Three kinds of lattice structures of the set of all (∈γ ,∈γ ∨qδ)-fuzzy soft left (right) ideals of an ordered semigroup are derived. The...

In this paper, we present the concepts of a fuzzy soft left (right) ideal and fuzzy soft interior ideal over an ordered semigroup S . Some basic results of fuzzy soft left (right) ideals and fuzzy soft interior ideals are investigated and the supported examples are provided. Different classes, regular, intra-regular, and simple ordered semigroups are characterized by means of fuzzy soft left (r...

There are described some algebraic structures on a space of belief functions on a two element frame namely so called Dempster s semigroup with Dempster s operation dempsteroids and their basic properties The present paper is devoted to the investi gation of automorphisms of Dempster s semigroup Full characterization of general and ordered automorphisms is obtained their parametric description i...