Version 1
: Received: 19 January 2024 / Approved: 21 January 2024 / Online: 22 January 2024 (09:55:40 CET)
Version 2
: Received: 13 March 2024 / Approved: 13 March 2024 / Online: 13 March 2024 (12:39:28 CET)
Ibtesam Alshammari, Islam M. Taha. On fuzzy soft β \beta -continuity and β \beta -irresoluteness: some new results[J]. AIMS Mathematics, 2024, 9(5): 11304-11319. doi: 10.3934/math.2024554
Ibtesam Alshammari, Islam M. Taha. On fuzzy soft β \beta -continuity and β \beta -irresoluteness: some new results[J]. AIMS Mathematics, 2024, 9(5): 11304-11319. doi: 10.3934/math.2024554
Ibtesam Alshammari, Islam M. Taha. On fuzzy soft β \beta -continuity and β \beta -irresoluteness: some new results[J]. AIMS Mathematics, 2024, 9(5): 11304-11319. doi: 10.3934/math.2024554
Ibtesam Alshammari, Islam M. Taha. On fuzzy soft β \beta -continuity and β \beta -irresoluteness: some new results[J]. AIMS Mathematics, 2024, 9(5): 11304-11319. doi: 10.3934/math.2024554
Abstract
In the present study. At first, some properties of r-fuzzy soft β-closed sets are introduced on fuzzy soft topological spaces based on the paper Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). Also, we define the closure and interior operators with respect to the classes of r-fuzzy soft β-closed and r-fuzzy soft β-open sets, and investigate some of their properties. In addition, the concept of r-fuzzy soft β-connected sets is introduced and characterized with help of fuzzy soft β-closure operators. Thereafter, some properties of a fuzzy soft β-continuity are studied. Furthermore, we introduce and study the concepts of fuzzy soft almost (weakly) β-continuous functions, which are weaker forms of a fuzzy soft β-continuity. Also, the relationships between these classes of functions are specified with the help of some illustrative examples. Finally, we explore new types of fuzzy soft functions called, fuzzy soft β-irresolute (strongly β-irresolute, β-irresolute open, β-irresolute closed and β-irresolute homeomorphism) functions, and discuss some properties of them. Also, we show that fuzzy soft strongly β-irresolute → fuzzy soft β-irresolute → fuzzy soft β-continuity, but the converse may not be true.
Computer Science and Mathematics, Geometry and Topology
Copyright:
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