Soft Intervals and Soft Ordered Topology

Abstract

In this paper, the concept of soft interval is given and an example for soft Scott topology is illustrated by using the soft intervals. A tabular form for all soft closed intervals is presented. Then soft order topology is introduced and some application of it are expressed. Also we show that, the Soft Scott Topology and Soft Order Topology do not have to be same even on the same soft set.

A Soft Interval Based Decision Making Method and Its Computer Application

“…Then restriction of soft set relation ≤ to a soft subset (G, [17] Let (F, A, ≺) be a simple order soft set and let for a, b ∈ A, F (a) and F (b) be elements of (F, A) with F (a) ≺ F (b). Then four soft subsets of (F, A) given below are called soft intervals (SI) (respectively; soft open interval, soft half open intervals, soft closed interval) determined by F (a) and F (b) and they can be defined as follows:…”

“…Note that, if the soft set relation is choosen as F (e i ) ≤ F (e j ) :⇔ F (e i ) ⊆ F (e j ), then the Zhang's ISS [21] is a special case of the SI [17]. Hence, the soft closed intervals are ISSs [21].…”

“…In a similar work, Yao found [16] interval set theory as another mathematical tool to deal with uncertainties, while Zhang introduced the interval soft set (ISS) and applied the theory of ISS to solve DM problems [21]. Additionally, the concept of the soft intervals (SI), whose special case is Zhang's ISS, was also defined by Yaylalı et al [17]. More studies on decision making problems by using soft sets, fuzzy soft sets, and rough soft sets can be found in [4], [9], [16], [19], [20], [21], [22], [23], [24].…”