Let G $G$ be a finitely generated group. We show that for any finite symmetric generating set A $A$ , the language consisting of all geodesics in Cay ( ) $(G,A)$ with contracting property is regular language. An immediate consequence existence an infinite geodesic Cayley graph group implies element. In particular, torsion groups cannot contain geodesic. As application, this containing must eith...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

Algebraic structures especially an ordered semigroups play a prominent role in mathematics with wide ranging applications in many disciplines such as control engineering, computer arithmetics, coding theory, sequential machines and formal languages. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we generalize the concept of (α, β)-fuzzy le...

A fuzzy context-free K-grammar is a fuzzy context-free grammar with a countable rather than a finite number of rules satisfying the following condition: for each symbol α, the set containing all right-hand sides of rules with left-hand side equal to α forms a fuzzy language that belongs to a given family K of fuzzy languages. In this paper we study the effect of the non-self-embedding restricti...