The notions of $${{\mathcal {N}}}$$ -ideal types $$(\in , \in )$$ and \! \vee \, {q})$$ soft $${\mathcal N}_{\in }$$ -set, {N}}}_{q}$$ {N}}}_{\in {q}}$$ -subalgebra in BCK/BCI-algebra are introduced, several properties investigated. Characterizations N}$$ discussed.

We propose in this paper a new point of view which uni es two well known lter families for approximating ideal fractional delay lters: Lagrange Interpolator Filters (LIF) and Thiran Allpass Filters. We achieve this uni cation by approximating the ideal Fourier transform of the fractional delay according to two di erent Pad e approximations: series expansions and continued fraction expansions, a...

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of int-soft positive implicative ideals is introduced, and related properties are investigated. Relations between an int-soft ideal and an int-soft positive implicative ideal are established. Cha...

In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double-framed soft sets is introduced, and applications in BCK/BCI-algebras are discussed. The notions of double-framed soft algebras in BCK/BCIalgebras are introduced, and related properties are investigated. Characterizations of doubleframed soft algebras are...

Dictyostelium discoideum belongs to a group of multicellular life forms that can also exist for long periods as single cells. This ability to shift between uni- and multicellularity makes the group ideal for studying the genetic changes that occurred at the crossroads between uni- and multicellular life. In this Primer, I discuss the mechanisms that control multicellular development in Dictyost...

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union soft q-ideals are introduced, and related properties are investigated. Conditions for a union soft ideal to be a union soft q-ideal are established. Characterizations of a union soft q...