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On topological structures of fuzzy parametrized soft sets
Serkan Atmaca1, Idris Zorlutuna1
1Department of Mathematics, Cumhuriyet University, 58140 Sivas, Turkey.
Thescientificworldjournal
|June 24, 2014
Summary
This study introduces topological structures for fuzzy parametrized soft sets and mappings. It defines quasi-coincidence and examines topological properties like continuity and compactness in these novel spaces.
Area of Science:
- Topology
- Fuzzy Set Theory
- Soft Set Theory
Background:
- Fuzzy parametrized soft sets offer a powerful framework for modeling uncertainty and vagueness.
- Existing topological structures do not fully capture the nuances of fuzzy parametrized soft sets.
- There is a need to extend topological concepts to these advanced mathematical structures.
Purpose of the Study:
- To introduce and define the topological structure of fuzzy parametrized soft sets.
- To define and investigate the basic properties of quasi-coincidence for fuzzy parametrized soft sets.
- To study topological concepts such as closure, interior, base, continuity, and compactness within fuzzy parametrized soft topological spaces.
Main Methods:
- Development of foundational definitions for fuzzy parametrized soft topological spaces.
- Formal definition of quasi-coincidence for fuzzy parametrized soft sets.
- Investigation of topological properties including closure, interior, base, continuity, and compactness.
Main Results:
- The topological structure of fuzzy parametrized soft sets and mappings is formally established.
- The concept of quasi-coincidence is defined and its fundamental properties are analyzed.
- Key topological properties are investigated and characterized within the new framework.
Conclusions:
- This research provides a novel topological framework for fuzzy parametrized soft sets.
- The study extends fundamental topological concepts to a more generalized setting.
- The findings lay the groundwork for future research in applied fuzzy topology and decision-making.
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