On Strongly -Continuous Mappings in Fuzzifying Topology
| Autor: | Ahmed Khalil, Ting Yang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Closed set
General Mathematics 010102 general mathematics MathematicsofComputing_GENERAL General Engineering Boundary (topology) 02 engineering and technology Topological space Type (model theory) Engineering (General). Civil engineering (General) Topology 01 natural sciences Fuzzy logic Set (abstract data type) TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Closure (mathematics) QA1-939 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing TA1-2040 0101 mathematics Derived set Mathematics |
| Zdroj: | Mathematical Problems in Engineering, Vol 2021 (2021) |
| ISSN: | 1563-5147 1024-123X |
| DOI: | 10.1155/2021/3244618 |
| Popis: | In this article, we will define the new notions (e.g., b − θ -neighborhood system of point, b − θ -closure (interior) of a set, and b − θ -closed (open) set) based on fuzzy logic (i.e., fuzzifying topology). Then, we will explain the interesting properties of the above five notions in detail. Several basic results (for instance, Definition 7, Theorem 3 (iii), (v), and (vi), Theorem 5, Theorem 9, and Theorem 4.6) in classical topology are generalized in fuzzy logic. In addition to, we will show that every fuzzifying b − θ -closed set is fuzzifying γ -closed set (by Theorem 3 (vi)). Further, we will study the notion of fuzzifying b − θ -derived set and fuzzifying b − θ -boundary set and discuss several of their fundamental basic relations and properties. Also, we will present a new type of fuzzifying strongly b − θ -continuous mapping between two fuzzifying topological spaces. Finally, several characterizations of fuzzifying strongly b − θ -continuous mapping, fuzzifying strongly b − θ -irresolute mapping, and fuzzifying weakly b − θ -irresolute mapping along with different conditions for their existence are obtained. |
| Databáze: | OpenAIRE |
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