let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

in this note we consider the notion of intuitionistic fuzzy (weak) dual hyper k-ideals and obtain related results. then we classify this notion according to level sets. after that we determine the relationships between intuitionistic fuzzy (weak) dual hyper k-ideals and intuitionistic fuzzy (weak) hyper k-ideals. finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

Day to day practice at a dental office is a challenging one where a dentist has to ideally confront a situation with his command and expertise. One such frequent situation arising is that concerned with isolation techniques associated with a restorative procedure. Various isolation techniques are put forth in practice which includes use of a saliva ejector, a rubber dam and gingival retraction ...

Medical international guidelines recommend regular psychiatric consultations for patients with epilepsy, in order to detect comorbidities. However, there is a lack of guidance about PNES that constitute both differential diagnosis and comorbidity epilepsy. While waiting the ideal collaboration between neurologists psychiatrists, we develop pragmatic approach. Wrong epilepsy Psychogenic nonepile...

in iri vision 2025 document, achieving economic outlook is pressed, but it requires establishing necessary infrastructures regarding to particular economic condition of the world in present age. one of these important infrastructures in order to achieve economic growth and development is doing business. in this paper, by using annual data of doing business -of an institute affiliated to the wor...

A hybrid approach integrating OWA (Ordered Weighted Averaging) aggregation into TOPSIS (technique for order performance by similarity to ideal solution) is proposed to tackle multiple criteria decision analysis (MCDA) problems. First, the setting of extreme points (ideal and anti-ideal points) in TOPSIS is redefined and extended for handling the multiple extreme points situation where a decisio...

The paper investigates a technique for order preference by similarity to ideal solution (TOPSIS) method to solve multi-attribute decision making problems with bipolar neutrosophic information. We define Hamming distance function and Euclidean distance function to determine the distance between bipolar neutrosophic numbers. In the decision making situation, the rating of performance values of th...

Introduction. The assessment of learning needs is one of the basic stages in education which leads to a change in medical education curriculum. Such assessment can be conducted based on different reasons. Therefore it should be defined, and the methods of application of the findings must be analyzed. One of the known methods of need assessment is the analysis of the differences between the p...

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.