Weighted languages and weighted automata over multi-hemirings are capable of expressing quantitative properties of systems such as its average or discounted costs. We study the applicability of well-known semiring theory and algorithms in the field of multi-hemirings. To this end, we embed multi-hemirings into semirings and extend this embedding for weighted languages and weighted automata. We ...

In this paper, we consider the characterization of h -semisimple hemirings. First, the notions of ( , ) q ∈∈∨ -fuzzy h -ideals and ( , ) q ∈∈∨ -fuzzy h -interior ideals of a hemiring are introduced, and some of their properties are investigated. Then the concept of h -semisimple hemirings is introduced and its characterizations are established.

Hemirings [3] which provide a common generalization of rings and distributive lattices arise naturally in such diverse areas of mathematics as combinatorics, functional analysis, graph theory, automata theory, mathematical modelling and parallel computation systems etc.(for example, see [3], [4]). Hemirings have also been proved to be an important algebraic tool in theoretical computer science,...

In this paper we define a correspondence between the set of all fuzzy hideals of a Γ-hemiring S and the set of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. We deduce that the lattice of all fuzzy hideals of a Γ-hemiring is isomorphic to the lattice of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. Finally, the cartesian product of corresponding fuzzy h-idea...

The concept of (∈,∈∨ q)-fuzzy h-ideals of hemirings is introduced and some characterizations are described. We show that a hemiring S is hhemiregular if and only if for any (∈,∈∨ q)-fuzzy right h-ideal F and (∈,∈∨ q)fuzzy left h-ideal G, F ◦0.5 G = F ∩0.5 G. Finally, the concept of implicationbased fuzzy h-ideals of hemirings is considered. 2010 Mathematics Subject Classification: 16Y60, 13E05,...

The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the quasi-coincidence of a fuzzy point in a fuzzy set. By using this new concept, the authors define the notion of interval valued (∈,∈ ∨q)fuzzy h-ideals of hemirings and study their related properties. In addition, the authors also extend t...

A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset f of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if f is two-valued, f(0) = 1, and the set of all x in S such that f(x) = 1 is a prime (left) right h-ideal of S. Fina...

Characteristic, normal and completely normal intuitionistic fuzzy left h-ideals of hemirings are described. Key–Words: Hemiring, intuitionistic fuzzy left h-ideal, normal fuzzy set, fuzzy characteristic.