A new proof of the general representation for the entries of the inverse of any unreduced Hessenberg matrix of finite order is found. Also this formulation is extended to the inverses of reduced Hessenberg matrices. Those entries are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences for such computations and some elementary properties of ...

The concepts of (λ ,μ)−fuzzy subsemigroup and various (λ ,μ)−fuzzy ideals of a semigroup were introduced by generalizing (∈,∈∨q)−fuzzy subsemigroup and (∈,∈∨q)−fuzzy ideal. The regular semigroup was characterized by the properties of the middle parts of various (λ ,μ)−fuzzy ideals, and several equivalence conditions of regular semigroups were obtained.

In this paper, we introduce the concept of N -fuzzy quasi-ideals in ordered semigroups and investigate the basic theorem of quasi-ideals of ordered semigroups in terms of N -fuzzy quasi-ideals. We characterize left (resp. right) regular and completely regular ordered semigroups in terms of N -fuzzy quasi-ideals. We de ne semiprime N fuzzy quasi-ideals and characterize completely regular ordered...

Fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. The purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. To provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships ...

To deal with system uncertainty, finite automata have been generalized into fuzzy automata. Stamenkovic and Ciric proposed an approach using the position automata for the construction of fuzzy automata from fuzzy regular expressions. There exist multifarious methodologies for the construction of finite automata from regular expressions known as Thompson construction, Antimirov partial derivativ...

In formal language theory, we are mainly interested in the natural language computational aspects of ω-languages. Therefore in this respect it is convenient to consider fuzzy ω-languages. In this paper, we introduce two subclasses of fuzzy regular ω-languages called fuzzy n-local ω-languages and Buchi fuzzy n-local ω-languages, and give some closure properties for those subclasses. We define a ...