In many applied disciplines like computer science, coding theory and formal languages, the use of fuzzified algebraic structures play a remarkable role. In this paper, we introduced some new types of generalization of an intuitionistic fuzzy interior ideal, called (α, β)-intuitionistic interior ideals of an ordered semigroup S. The important milestone of this paper is to link the ordinary inter...

in this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $m$-hyponormal operator‎. ‎we show that every analytic extension of a $n$th roots of $m$-hyponormal operator is subscalar of order $2k+2n$‎. ‎as a consequence‎, ‎we get that if the spectrum of such operator $t$ has a nonempty interior in $mathbb{c}$‎, ‎then $t$ has a nontrivial invariant subspace‎. ‎finally‎, ‎w...

Abstract. In this paper, we introduce generalized fuzzy weakly interior ideals of an ordered semigroup. We generalize fuzzy interior ideals of an ordered semigroup. We establish necessary and sufficient condition for a fuzzy set to be a generalized fuzzy weakly interior ideal. We establish three equivalent conditions for an ordered semigroup to be regular. We characterize semisimple ordered sem...

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 introduce a new notion of fuzzy r -interior which is an extension of Chang’s fuzzy interior. Using fuzzy r -interior, we define fuzzy r -semiopen sets and fuzzy r semicontinuous maps which are generalizations of fuzzy semiopen sets and fuzzy semicontinuous maps in Chang’s fuzzy topology, respectively. Some basic properties of fuzzy r -semiopen sets and fuzzy r -semicontinuous maps are invest...

The quotient operator plays an important role for query evaluation in relational databases. Its extension to fuzzy databases raises the question of the intended interpretation of the intermediary degrees attached to the items in the fuzzy relations. This note points out that the fuzzy quotient operator should be defined in slightly different ways depending on the possible interpretations of the...

in this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in ag -groupoids. generalizing the concepts of (,q) -fuzzy bi-ideals (interior ideal), we define ( , ) k q -fuzzy bi-ideals, ( , ) k q -fuzzy left (right)-ideals and ( , ) k q -fuzzy interior ideals in ag -groupoids and discuss some fundamental aspects of these i...

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎w...

Stability of a fuzzy control system is closely related to the analytical structure of the fuzzy controller, which is determined by its components such as input and output fuzzy sets and fuzzy rules. We first characterize the mathematical input–output structure of fuzzy controllers and then utilize the structure characteristics to advance stability analysis. We study how the components of a gene...