A New Approach to Soft Continuity

Kaur, Sandeep; Al-shami, Tareq M.; Özkan, Alkan; Hosny, Mona

doi:10.3390/math11143164

Cited by 4 publications

(1 citation statement)

References 41 publications

(40 reference statements)

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“…Moreover, Al-shami et al [8] initiated the concept of weakly soft β-open sets and examined weakly soft β-continuity. Kaur et al [9] introduced a new approach to studying soft continuous mappings using an induced mapping based on soft sets. Al Ghour and Al-Mufarrij [10] defined two new concepts of mappings over soft topological spaces: soft somewhat-r-continuity and soft somewhat-r-openness.…”

Section: Introductionmentioning

confidence: 99%

Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies

Taha,

Alqurashi

2024

Preprint

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In this manuscript, we first introduce some properties of r-fuzzy soft α-open sets in fuzzy soft topological spaces based on the manuscript Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). In addition, we define the concepts of fuzzy soft α-closure (α-interior) operators, and investigate some properties of them. Furthermore, the concept of r-fuzzy soft α-connected sets is defined and characterized with help of fuzzy soft α-closure operators. Thereafter, we introduce and study the concepts of fuzzy soft almost (weakly) α-continuous mappings, which are weaker forms of fuzzy soft α-continuous mappings, and we discuss some properties of fuzzy soft α-continuity. Moreover, we establish that fuzzy soft α-continuity → fuzzy soft almost α-continuity → fuzzy soft weakly α-continuity, but the converse may not be true. It is also we show that the composition is fuzzy soft almost α-continuous mapping if, is fuzzy soft α-continuous mapping and is fuzzy soft almost continuous mapping. Finally, some new types of compactness via r-fuzzy soft α-open sets are defined, and the relationships between them are examined.

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Section: Introductionmentioning

confidence: 99%

Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies

Taha,

Alqurashi

2024

Preprint

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Soft Homogeneous Components and Soft Products

Al Ghour

2024

Fuzzy. Info. Tech.

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Three Weaker Forms of Soft Faint Continuity

Al-Ghour,

Abuzaid

2024

Symmetry

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The authors of this paper introduce and discuss three weaker forms of soft faint continuity: soft faint semi-continuity, soft faint pre-continuity, and soft faint β-continuity. They characterize each of them in several ways. They also demonstrate how they are preserved under some restrictions. Moreover, they prove that a soft function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous) if its soft graph function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous). Moreover, they show that a soft function is soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous) iff it is soft semi-continuous provided that it has a soft regular codomain. Finally, the symmetry between our new ideas and their analogous topological ones is investigated.

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A New Approach to Soft Continuity

Cited by 4 publications

References 41 publications

Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies

Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies

Soft Homogeneous Components and Soft Products

Three Weaker Forms of Soft Faint Continuity

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