In this study, by generalizing the notion of fuzzy bi-ideals ordered semirings, (∈,∈∨(κ*,qκ))-fuzzy is established. We prove that are but converse not true, and an example provided to support proof. A condition given under which semirings coincide with bi-ideals. An equivalent certain correspondences between presented. Moreover, (κ*,κ)-lower part described depicted in terms several classes semi...

We consider weighted finite transition systems (wts) with weights from commutative naturally ordered semirings. Such semirings comprise distributive lattices as well as the natural numbers with ordinary addition and multiplication, and the max-plus-semiring. For these systems we explore the concepts of covering and cascade product. We show a cascade decomposition result for such wts using speci...

We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with addition and invertible multiplication). The are to minimize objective functions given by analogues of multivariate Puiseux polynomials, subject box constraints variables. A technique for variable elimination is pre...

Cost functions for tree automata are mappings from transitions to (tuples o0 polynomials over some semiring. We consider four semirings, namely N the semiring of nonnegative integers, A the "arctical semiring", T the tropical semiring and F the semiring of finite subsets of nonnegative integers. We show: for semirings N and A it is decidable in polynomial time whether or not the costs of accept...

While the existence of inverses is a natural condition in Algebra it is seldom satissed in Computer Science applications. Since the group-theoretical orientation has to be abandoned we consider an advantage when the non-conventional structures needed are linked to an already existing knowledge. We propose semirings as a candidate and we aim at the Computer Science applications such as processes...

When the first operation’s inverse axiom is deleted from ring, an algebraic structure, semiring, generated. Subsemiring one of subjects covered in semiring. The concepts fuzzy subsemiring, anti subsemiring and complement are introduced this paper. In addition, anti-subsemiring a wedge, or combination two more associated with non-empty subset semiring whose membership criteria defined by value z...

The framework of document spanners abstracts the task information extraction from text as a function that maps every (a string) into relation over document's spans (intervals identified by their start and end indices). For instance, regular are closure under Relational Algebra (RA) expressions with capture variables, expressive power is precisely captured class VSet-automata -- restricted trans...

We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets. We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use...

The aim of the paper is to show an example of interaction between the AI and OR elds of research using the Constraint Programming (CP) framework to glue them together. We solve a shortest path problem using the c-semiring-based framework for programming over soft constraints (SCLP), which is an extension of classical constraint solving and programming. The SCLP approac handle uniformly several ...