Soft somewhat open sets: soft separation axioms and medical application to nutrition

Abstract

This paper contributes to the growing literature on soft topology and decision-making problems. First, we establish new properties of soft somewhat open sets (briefly, sw-open sets) and study their behaviours via specific topologies such as extended soft topology, and product and sum of soft topologies. Then, we applied them to introduce novel families of soft topological spaces, namely pp-soft $swT_i$, tp-soft $swT_i$, pt-soft $swT_i$ and tt-soft $swT_i$-spaces, where $i=0, 1, 2$. These spaces are formulated using partial belonging, total belonging, partial non-belonging and total non-belonging relations between soft sw-open sets and ordinary points. We demonstrate that pt-soft $swT_i$ and tt-soft $swT_i$-spaces are identical for $i=0, 1, 2$, and pp-soft $swT_i$ and tp-soft $swT_i$-spaces are identical for $i=0, 1$. Also, we prove that the equivalence between tp-soft $swT_2$ and tt-soft $swT_2$-spaces. With the help of interesting examples, we elucidate the relationships between the given spaces as well as their relationships with their counterparts introduced in literature. Furthermore, we discuss the transmission of these spaces between soft topology and its parametric topologies. Some results related to hereditary and topological properties, and product and sum of soft spaces are investigated as well. Finally, we employ the concept of soft sw-open sets to evaluate the health of individuals’ diets and show how the places of flaws are determined. An illustrative example and algorithm are given to clarify the followed technique in this application.