We extend arc consistency algorithms proposed in the literature in order to deal with not necessarily invertible semirings. As a result, consistency algorithms can now be used as a preprocessing procedure in soft CSPs defined over a larger class of semirings: either partially ordered, or with non idempotent ×, or not closed ÷ operator, or constructed as cartesian product or Hoare power sets of ...

We propose a new class of mathematical structures called (m, n)-semirings (which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for (m, n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail a...

this paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

We consider (subclasses of) polynomial bottom-up and top-down tree series transducers over a partially ordered semiring A = (A,⊕, ,0,1, ), and we compare the classes of tree-to-tree-series and o-tree-to-tree-series transformations computed by such transducers. Our main result states the following. If, for some a ∈ A with 1 a, the semiring A is a weak a-growth semiring and either (i) the semirin...

We introduce two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction , and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. We then compare the two approaches and we discuss the relationship between them.

This paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

In bottleneck combinatorial problems, admissible solutions are compared with respect to their maximal elements. In such problems, one may work with an ordinal evaluation scale instead of a numerical scale. We consider here a generalization of this problem in which one only has a partially ordered scale (instead of a completely ordered scale). After the introduction of a mappimax comparison oper...

A tree series over a semiring with partially ordered carrier set can be considered as a fuzzy set. We investigate conditions under which it can also be understood as a fuzzi ed recognizable tree language. In this sense, su cient conditions are presented which, when imposed, ensure that every cut set, i.e., the pre-image of a prime lter of the carrier set, is a recognizable tree language. Moreov...

In this paper, we first consider n × n upper-triangular matrices with entries in a given semiring k. Matrices of this form with invertible diagonal entries form a monoid Bn(k). We show that Bn(k) splits as a semidirect product of the monoid of unitriangular matrices Un(k) by the group of diagonal matrices. When the semiring is a field, Bn(k) is actually a group and we recover a well-known resul...