This paper provides a new generalization of fuzzy finite state machines, fuzzy transformation semigroups and their relationship. Consider a cubic structure, we introduce cubic finite state machines, cubic transformation semigroups, cubic successor, cubic exchange properties cubic subsystems, cubic submachines, cubic q-twins, cubic retrievable and study fundamental properties of them. We provide...

This paper is devoted to characterizing so-called order isomorphisms intertwining the $$L^2$$ -semigroups of two quasi-regular Dirichlet forms. We first show that every unitary isomorphism semigroups composition h-transformation and quasi-homeomorphism. In addition, under assumption underlying spaces admit irreducible decompositions for forms, (not necessarily unitary) can be expressed as h-tra...

Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E}It is known that TE(X) is a subsemigroup of TX. In this paper, we discussthe Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE(X).

We describe products of arbitrary L, R, and H-classes with the set of idempotents of full transformation semigroups.

We give a thorough structural analysis of the principal one-sided ideals arbitrary semigroups, and then apply this to full transformation semigroups symmetric inverse monoids. One-sided these naturally occur as transformations with restricted range or kernel.

We continue our investigation on the relationship between regular languages and syntactic monoid size. In this paper we confirm the conjecture on two generator transformation semigroups. We show that for every prime n ≥ 7 there exist natural numbers k and ` with n = k + ` such that the semigroup Uk,` is maximal w.r.t. its size among all (transformation) semigroups which can be generated with tw...